Go Math! Practice Fluency Workbook Grade 6 Chapter 6 Representing Ratios and Rates Exercise 6.2 Answer Key

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6: Representing Ratios and Rates

Question. David drove 135 miles in 3 hours. Find the unit rate.

Given: David drove 135 miles in 3 hours.

To find:  We have to find the unit rate.

Divide the distance by the time to get the unit rate.

David drove 135 miles in 3 hours.

Unit rate = ​135/3

Unit rate = 45 miles/hour.

The unit rate of David is 45 miles per hour.

Question. Three medium apples have about 285 calories. Find the unit rate.

Given: Three medium apples have about 285 calories.

To find:  We have to find the unit rate.

Divide the calories by the number of apples to get the unit rate.

Three medium apples have about 285 calories,

Unit rate = 285/3

Unit rate = 95 calories/apple.

The unit rate is 95 calories/apple.

Go Math! Practice Fluency Workbook Grade 6 Chapter 6 Representing Ratios and Rates Exercise 6.2 Answer Key

Question. A 13-ounce package of pistachios costs $5.99. Find the unit rate.

Given: A 13-ounce package of pistachios costs $5.99.

To find:  We have to find the unit rate.

Divide the number of ounces of packages by the total cost of pistachios to get the unit rate.

A 13-ounce package of pistachios costs $5.99.

Unit rate = 5.99/13

Unit rate = 0.4608 $/ ounce of package.

The unit rate is $0.4608 per ounce of a package of pistachios.

Question. Morgan’s favorite spaghetti sauce is available in two sizes pint and quart. Each size and its price are shown in the table. Find the unit rate to the nearest cent per ounce for pint size.

Given: Morgan’s favorite spaghetti sauce is available in two sizes: pint and quart. Each size and its price are shown in the table.

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6 Representing Ratios and Rates 59

To find: We have to find the unit rate to the nearest cent per ounce for pint size.

Divide the price of the spaghetti sauce by its quantity to get the unit rate.

The “pint” size has 16 quantities and its cost is $3.98

The unit rate of pint-size =3.98/16

The unit rate of pint-size =0.25 dollars/ounce.

The unit rate to the nearest cent per ounce for pint-size is $ 0.25 /ounce.

Question. Morgan’s favorite spaghetti sauce is available in two sizes pint and quart. Each size and its price are shown in the table. If a coupon offers $1.00 off the 16 ounce size. Which size is the better buy then?

Given: Morgan’s favorite spaghetti sauce is available in two sizes: pint and quart. Each size and its price are shown in the table.

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6 Representing Ratios and Rates 59

To find: If a coupon offers $1.00 off the 16-ounce size. Which size is the better buy then?

Just subtract the coupon amount from the pint-size and then recalculate the unit rate.

After that compare both unit rates and decide on the better one.

Now the initial price for the pint size is $3.98, then if a coupon is applied to it, then its cost will be reduced by $1.00.

The new price will be =​3.98−1.00 = 2.98

So the unit rate of pint size will be ​= 2.98/16 = 0.18 and the unit rate of quart size was $0.18/ounce.

As we can see here, after applying the coupon their unit rate became equal so we can say that both are the better choices as there is no difference between the unit price of both sizes.

After applying the coupon their unit rate became equal so we can say that both are the better choices as there is no difference between the unit price of both sizes.

Question. A 24-ounce box of cornflakes costs 4.59. Find the unit rate to the nearest cent per ounce.

Given: A 24-ounce box of cornflakes costs 4.59.

To find: We have to find the unit rate to the nearest cent per ounce

Divide the cost of the box of cornflakes by the ounces to get the unit rate per ounce.

An A24-ounce box of cornflakes costs $4.59

Dividing to find the unit rate, we get

Unit rate = 4.59/24

Unit rate = $0.191/ounce.

For part (a), the unit rate to the nearest cent per ounce is $0.191/ounce.

Question. Karyn proof reads 15 pages in 2 hours for $40. Find her proofreading rate in pages per hour.

Given: Karyn proofreads 15 pages in 2 hours for $40

To find: We have to find her proofreading rate in pages per hour.

Just divide the number of pages by the number of hours given.

Karyn proofreads 15 pages in 2 hours for $40.

Her proofreading rate will be = ​15/2 =7.5

Her proofreading rate is 7.5 pages per hour.

Karyn proofreads 7.5 pages per hour.

Question. Jack shells 315 peanuts in 15 minutes. Find the unit rate.

Given: Jack shells 315 peanuts in 15 minutes.

To find: We have to find the unit rate.

Just divide the number of peanuts shelled by Jack in a given number of minutes.

Jack shells 315 peanuts in 15 minutes.

Now, let’s divide the number of peanuts by the number of minutes, we get

Unit rate = 315/15

Jack shells 315 peanuts in 15 minutes.

Now, let’s divide the number of peanuts by the number of minutes, we get

= \(\frac{315}{15} \times \frac{15}{15}[latex]

= [latex]\frac{21}{1}\)

 

Unit rate   = 21/1

This means the unit rate = is 21 peanuts per minute.

Jack shells 21 peanuts per minute.

Question. Sharmila received 81 texts in 9 minutes. Find the unit rate.

Given: Sharmila received 81 texts in 9 minutes.

To Find: We have to find the unit rate.

Just divide the number of texts received by the number of minutes.

Sharmila received 81 texts in 9 minutes.

Now, let’s divide the number of texts by the number of minutes in order to find out the unit rate.

Unit rate = 81/9

Make the denominator “1”, by multiplying and dividing the above expression by 9, we get

Unit rate ​=81/9 =9/1

This means the unit rate = 9 texts per minute.

Sharmila receives 9 texts per minute.

Question. Karim reads 56 pages in 2 hours. Find the unit rate.

Given: Karim reads56 pages in 2 hours

To find: Unit rate

We want to know the pages Karim reads per hour so we set up a ratio with hours in the denominator.

The total pages go in the numerator.

So the fraction is 56/2

To make denominator 1 divide both the numerator and denominator with 2.

To find pages read by Karim in 1 hour we will divide the total pages read by him by the hour.

So fraction is

→56pages/2hours =56/2

Divide numerator and denominator by 2 ,

\(\frac{56}{2} \div \frac{2}{2}=\frac{28}{1}\)

 

Which means 28pages/hour =28 pages per hour

Karim read 28 pages per hour.

Question. The weight of whole wheat bread is 16 oz for $2.24. The weight of Pita bread is 20 oz for $3.60 and the weight of 7-grain bread is 16 oz for $2.56. Find the best buy.

Given: The weight of whole wheat bread is 16oz for $2.24. The weight of Pita bread is 20oz for $3.60 and the weight of 7-grain bread is 16oz for $2.56.

To find: best buy

To find the best buy find a unit rate for each type of bread per oz that is divided the cost by weight. The unit rate which has the lowest price is the best buy of bread.

For whole wheat, the bread weight is 16oz and the cost is $2.24.

The unit rate of whole wheat bread is 2.24/16 =0.14

The unit rate of whole wheat bread is 0.14 $ per oz.

For Pita, the bread weight is 20oz and the cost is $3.60.

The unit rate of Pita bread is 3.60/20 =0.18

The unit rate of Pita bread is 0.18 $ per oz.

For 7-grain bread, the weight is 16oz and the cost is $2.56.

The unit rate of 7-grain bread is 2.56/16 =0.16

The unit rate of 7-grain bread is 0.16 $ per oz.

By comparing unit rates we can say that 0.14 $ per oz is the lowest unit rate which is whole wheat bread.

The best buy is whole wheat bread which weighs 16oz and cost $2.24.

Go Math Answer Key

Go Math! Practice Fluency Workbook Grade 6 Chapter 5 Operations with Decimals Exercise 5.4 Answer Key

Go Math! Practice Fluency Workbook Grade 6 California 1st Edition Chapter 5 Operations with Decimals

Page 31 Problem 1 Answer

Given: 3.6 divided by 1.2.

Hence, We have to find a quotient by using a decimal grid.

Firstly, We will use10×10 a grid where one column represents 0.1 unit.

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 1 1

Then, we divide the grid according to the given expression.

From the given expression that is 3.6/1.2, Therefore, the decimal g

Where red lines represent 3.6 value. As one column is of 0.1 unit.

Then we divide1.2 according to the red line. As yellow, light green, and dark green represent 1.2 unit.

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 1 2

 

So, we get 3 equal parts of 3.6 according to 1.2. The value of 3.6/1.2 is 3.

Page 31 Problem 2 Answer

Go Math! Practice Fluency Workbook Grade 6 Chapter 5 Operations with Decimals Exercise 5.4 Answer Key

Given: 3.27divided by 3.0.

Hence, We have to find a quotient by using a decimal grid.

Firstly, We will use10×10 a grid where one column represents 0.1 unit.

Then, we divide the grid according to the given expression.

From the given expression that is 3.27/3.0,

Therefore, the decimal grid is,

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 2 1

Here red lines represent 3.27 value. As one column is of 0.1 unit.
Then we divide3.0 according to the red line. As yellow represent 3.0 unit which gives only one part.

And, rest parts that are dark green and the light green represents 0.3 unit which gives 9 and its value is 0.9.

So, We get 1.09 equal parts of 3.27 according to 3.0 The value of 3.27/3.0 is 1.09.

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 2 1

Page 31 Problem 3 Answer

Given: 142.5/9.5. Hence, We have to find a quotient.

Firstly, We will simply the given expression then, by using the long division method we solve the given expression.

From the expression that is 142.5/9.5, Change the divisor to a whole number by moving the decimal point one place to the right.

Then move the decimal point in the dividend the same, one place to the right.

We then have, 1452/95 =15.000

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 3 1

By using the long division method we get,

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 3 2

The quotient of 142.5/9.5 is 15.0.

Page 31 Problem 4 Answer

Given:39.6/3. Hence, We have to find a quotient.

We will use the long division method we solve the given expression.

From the expression that is, 39.6/3 = 13.2

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 4 1

By using the long division method we get,

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 4 2

The quotient of 39.6/3 is 13.2

Page 31 Problem 5 Answer

Given:10.88/2. Hence, We have to find a quotient.

We will use the long division method we solve the given expression.

From the expression that is, 10.88/2 = 5.44

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 5 1

By using the long division method we get,

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 5 2

The quotient of 10.88/2 is 5.44.

Page 31 Problem 6 Answer

Given:10.5/1.5. Hence, We have to find a quotient.

Firstly, We will simply the given expression then,

By using the long division method we solve the given expression.

From the expression that is 10.5/1.5, Change the divisor to a whole number by moving the decimal point one place to the right.

Then move the decimal point in the dividend the same, one place to the right.

We then have,105/15 = 7.0

By using the long division method we get,

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 6

The quotient of10.5/1.5 is 7.0.

Page 31 Problem 7 Answer

Given:9.75/1.3. Hence, We have to find a quotient.

Firstly, We will simply the given expression then, by using the long division method we solve the given expression.

From the expression that is 9.75/1.3, Change the divisor to a whole number by moving the decimal point one place to the right.

Then move the decimal point in the dividend the same, one place to the right.

We then have, 97.5/13 = 7.50

By using the long division method we get,

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 7

The quotient of 9.75/1.3 is 7.50.

Page 31 Problem 8 Answer

Given: 37.5/2.5. Hence, We have to find a quotient.

Firstly, We will simply the given expression then, By using the long division method we solve the given expression.

From the expression that is 37.5/2.5, Change the divisor to a whole number by moving the decimal point one place to the right.

Then move the decimal point in the dividend the same, one place to the right.

We then have, 37.5/2.5 = 15.0

By using the long division method we get,

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 8

The quotient of 37.5/2.5 is 15.0.

Page 31 Problem 9 Answer

Given: 3.78/0.9.

Hence, We have to find a quotient.

Firstly, We will simply the given expression then, by using the long division method we solve the given expression.

From the expression that is 3.78/0.9.

Change the divisor to a whole number by moving the decimal point one place to the right.

Then move the decimal point in the dividend the same, one place to the right.

We then have, 37.8/9 = 4.20

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 9 1

By using the long division method we get,

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 9 2

The quotient of 3.78/0.9 is 4.20.

Page 31 Problem 10 Answer

Given: We have a division question.To find: We have to first estimate the result and then find the accurate result.We will divide to get the result.

We will round off the divisor and dividend to the nearest whole number if necessary.

The divisor will divide the dividend evenly and we will get the estimated result. 2.5 round off to 3. We get, 36/3 = 12

Firstly, we will remove the decimal point from the denominator of the division expression and we get the result as 36/2.5 = 360/25

The long division is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 10

The estimated result is12

The accurate result is14.4

Page 31 Problem 11 Answer

Given: We have a division question.To find: We have to first estimate the result and then find the accurate result.We will divide to get the result.

We will first multiply both of them by ten. We get,7/0.25=70/2.5

We will round off the divisor and dividend to the nearest whole number if necessary.

The divisor will divide the dividend evenly and we will get the estimated result. After rounding them off, we get 72/3 = 24

Firstly, we will remove the decimal point from the denominator of the division expression by multiplying both the denominator and numerator by 100.

We get, 7/0.25= 700/25

The long division is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 11

The estimated result is 24

The accurate result is28

Page 31 Problem 12 Answer

Given: We have a division question.To find: We have to first estimate the result and then find the accurate result.We will divide to get the result.

We will round off the divisor and dividend to the nearest whole number if necessary. The divisor will divide the dividend evenly and we will get the estimated result.

After rounding them off, we get ​142.5/9.5≈140/10 =14

Firstly, we will remove the decimal point from the denominator of the division expression by multiplying both the denominator and numerator by 10.

We get, 142.5/9.5=1425/95

The long division is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 12

The estimated result is14

The accurate result is15

Page 31 Problem 13 Answer

Given: We have that a telescope photographs a star’s image once every 0.045s

To find: We have to find the complete images can the camera capture in 3s We will divide and get the required answer.

Firstly, we will remove the decimal point from the denominator of the division expression by multiplying both the denominator and numerator by 1000.

We get, 3/0.045 = 3000/45

The number of complete images that the camera can capture in 3s is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 13

As we want the number of complete images that the camera can capture, we get 66

The number of complete images that the camera can capture is 66

Page 31 Problem 14 Answer

Given: We have that land along a fault line moved 24.8cm over the past 175 years.

To find: We have to find how much did the land move each year. We will divide the total movement of the land and get the result by the total number of years.

Firstly, we will remove the decimal point from the denominator of the division expression by multiplying both the denominator and numerator by 10.

We get, 24.8/175 = 248/1750

Each year the land along the fault line moves,

We will take the first three digits after decimals. The result is 0.141cm

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 14

The land moves each year by 0.141cm

Page 32 Exercise 1 Answer

Given: We have a division question.To find: We have to find the quotient.We will divide to get the result.

Firstly, we will remove the decimal point from the denominator of the division expression by multiplying both the denominator and numerator by 10.

We get, 0.6/5=6/50 After division, we get

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals e 1

The quotient of the given division is 0.12

Page 32 Exercise 2 Answer

Given: We have a division question.

To find: We have to find the quotient.We will divide to get the result.

Firstly, we will remove the decimal point from the denominator of the division expression by multiplying both the denominator and numerator by 100.

We get, 0.78/6 = 78/600

After division, we get

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals e2

The quotient of the given division is0.13

Page 32 Exercise 3 Answer

Given: We have a division question.To find: We have to find the quotient.We will divide to get the result.

Firstly, we will remove the decimal point from the denominator of the division expression by multiplying both the denominator and numerator by 100.

We get, 0.32/4=32/400 After division, we get

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals e3

The quotient of the given division is0.08

Page 32 Exercise 4 Answer

Given: We have a division question.To find: We have to find the quotient.We will divide to get the result.

Firstly, we will remove the decimal point from the denominator of the division expression by multiplying both the denominator and numerator by 1000.

We get, 0.99/0.0033 = 9900/33 After division, we get

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals e4

The quotient of the given division is300

Page 32 Exercise 5 Answer

Given: We have a division question.To find: We have to find the quotient.We will divide to get the result.

Firstly, we will remove the decimal point from the denominator of the division expression by multiplying both the denominator and numerator by 100.

We get, 0.08/0.4 = 8/40 After division, we get

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals e5

The quotient of the given division is 0.2

Page 32 Exercise 6 Answer

Given: We have a division question.To find: We have to find the quotient.We will divide to get the result.

Firstly, we will remove the decimal point from the denominator of the division expression by multiplying both the denominator and numerator by 100.

We get, 0.63/0.9 = 63/90 After division, we get

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals e6

The quotient of the given division is 0.7

Page 32 Exercise 7 Answer

Given: We have a division question.To find: We have to find the quotient.We will divide to get the result.

Firstly, we will remove the decimal point from the denominator of the division expression by multiplying both the denominator and numerator by 1000.

We get, 0.4/0.008 = 400/8 After division, we get

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals e7

The quotient of the given division is50

Page 32 Exercise 8 Answer

Given: We have a division question.To find: We have to find the quotient.We will divide to get the result.

Firstly, we will remove the decimal point from the denominator of the division expression by multiplying both the denominator and numerator by 1000.

We get, 0.032/0.04 = 32/40 After division, we get

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals e8

The quotient of the given division is 0.8

Go Math Answer Key

 

 

Go Math! Practice Fluency Workbook Grade 6 Chapter 5 Operations with Decimals Exercise 5.3 Answer Key

Go Math! Practice Fluency Workbook Grade 6 California 1st Edition Chapter 5 Operations with Decimals

Page 29 Problem 1 Answer

Given expression; 0.2×0.6

To find; Product and decimal multiplication on the grids.

In order to find the solution, count the common shaded region.

For multiplication on the grids, shade2 rows and 6
column and count the common shaded region.

So, there are 12 square which are common shaded. As one square is equal to 0.1. Hence, 0.2×0.6=0.12

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 1

Product of given expression is 0.12 and decimal multiplication on the grids is :

Page 29 Problem 2 Answer

Given expression: 0.3×0.7

To find; Product and decimal multiplication on the grids. In order to find the solution, count the common shaded region.

For multiplication on the grids, shade3 row and 7 column and count the common shaded region.

So, there are 21 square which are common shaded. As one square is equal to 0.1 Hence, 0.3×0.7=0.21

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 2

Product of given expression is 0.21 and decimal multiplication on the grids is ;

Page 29 Problem 3 Answer

Given expression: 1.2×3.3= To find Product and an area model to represent the multiplication problem.

In order to find the solution, count large square, rectangle and small square.

Go Math! Practice Fluency Workbook Grade 6 Chapter 5 Operations with Decimals Exercise 5.3 Answer Key

For area model to represent the multiplication problem, draw 1

square and its right of it draw 2 rectangles to represent 1.2 And then draw 2 square and 3 rectangle below the first square to represent 3.3

Now, count large square, rectangle and small square .

So, there are 3 large square, 9 rectangle and 6 small square. Therefore,1.2×3.3=3.96

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 3

The product of given expression is 3.96 and area model to represent the multiplication problem is,

Page 29 Problem 4 Answer

Given expression : 4.1×2.1= To find : Product and an area model to represent the multiplication problem.

In order to find the solution, count large square, rectangle and small square.

For area model to represent the multiplication problem , draw 4 square and 1 rectangle to the right of it to represent 4.1

And then draw 1 square and 1 rectangle below the first square to represent 2.1

Now , count large square, rectangle and small square.

So, there are8 large square, 6 rectangle and 1 small square. Therefore,4.1×2.1=8.61

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 4

The product of given expression is 8.61 and area model to represent the multiplication problem is ;

Page 29 Problem 5 Answer

Given ; ​0.1 ×0.2

​Hence, We have to find the product of the given expression.

Firstly, Starting in the right-hand column(units) multiply then, Next, we multiply the same number by the next number across.

To multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor.

From the given expression that is,​0.1×0.2

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 5

Now, calculate the expression ; The product of 0.1×0.2 is 0.02

Page 29 Problem 6 Answer

Given ; ​0.9×6
​Hence, We have to find the product of the given expression.

Firstly, Starting in the right-hand column(units) multiply then, Next, we multiply the same number by the next number across.

To multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor.

From the given expression that is, ​0.9×6

Now, calculate the expression;​​0.9×6=5.4

The product of 0.9×6is5.4

Page 29 Problem 7 Answer

Given expression is0.3×0.8

To find its product using the method of multiplication.

The given expression is0.3×0.8

To multiply two decimals, we will first ignore the decimal points and multiply the factors as if they were whole numbers.

We then count how many decimal places each factor has and add them to get the number of decimal places for the product:

Now to find its product, =0.3×0.8 =0.24

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 7

The solution for the given expression0.3×0.8 is 0.24.

Page 29 Problem 8 Answer

Given expression, is1.6×2.9 To find its product. Using the method of multiplication.

The given expression is1.6×2.9

To multiply two decimals, we will first ignore the decimal points and multiply the factors as if they were whole numbers.

We then count how many decimal places each factor has and add them to get the number of decimal places for the product:

Now to find its product,=1.6×2.9 =4.62

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 8

The solution for the given expression1.6×2.9 is 4.64.

Page 29 Problem 9 Answer

Given expression, is1.5×0.41 To find its product. Using the method of multiplication.

The given expression is1.5×0.41

To multiply two decimals, we will first ignore the decimal points and multiply the factors as if they were whole numbers.

We then count how many decimal places each factor has and add them to get the number of decimal places for the product:

Now to find its product, =1.5×0.41 =0.615

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 9

The solution for the given expression1.5×0.41 is 0.615.

Page 29 Problem 10 Answer

Given expression, is0.24×2.68 To find its product. Using the method of multiplication.

The given expression is0.24×2.68

To multiply two decimals, we will first ignore the decimal points and multiply the factors as if they were whole numbers.

We then count how many decimal places each factor has and add them to get the number of decimal places for the product:

Now to find its product, =0.24×2.68 =0.6432

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 10

The solution for the given expression0.24×2.68 is 0.6432.

Page 29 Problem 11 Answer

Given expression, is3.13×4.69 To find its product. Using the method of multiplication.

The given expression is3.13×4.69

To multiply two decimals, we will first ignore the decimal points and multiply the factors as if they were whole numbers.

We then count how many decimal places each factor has and add them to get the number of decimal places for the product:

Now to find its product, =3.13×4.69 = 14.6797

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 11

The product of the given expression3.13×4.69 is 14.6797.

Page 29 Problem 12 Answer

Given expression is5.48×15.12 To find its product. Using the method of mulitplication.

The given expression is5.48×15.12

To multiply two decimals, we will first ignore the decimal points and multiply the factors as if they were whole numbers.

We then count how many decimal places each factor has and add them to get the number of decimal places for the product:

Now to find its product, =5.48×15.12 = 82.5876

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 12

The solution for the given expression5.48×15.12 is 82.5876

Page 29 Problem 13 Answer

Given: Each bucket can hold 2.5 pounds of apples. To find how many pounds 7 buckets can hold. Using the method of multiplication.

It is given that the bucket can hold 2.5 pounds of apple, now to find how many many 7 bucket can hold,

To multiply two decimals, we will first ignore the decimal points and multiply the factors as if they were whole numbers.

We then count how many decimal places each factor has and add them to get the number of decimal places for the product:

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 13

Now to find its product, =2.5×7 =17.5 Therefore,7 buckets can hold 17.5 pounds of apple.

Page 29 Problem 14 Answer

Given: Canvas costs $7.50 per square meter. To find the cost of 3.5 square meters. Using the method of multiplication.

It is given that the cost of the canvas is $7.50 per square meter and to find the cost of3.5 square meter,

To multiply two decimals, we will first ignore the decimal points and multiply the factors as if they were whole numbers.

We then count how many decimal places each factor has and add them to get the number of decimal places for the product:

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals 14

Now to find its product, =7.50×3.5 = 26.25 Therefore, the cost of 3.5 square meter canvas is $26.25.

Page 30 Exercise 1 Answer

Given expression, is0.23×3 To find its product. Using the method of multiplication.

The given expression is0.23×3

To multiply two decimals, we will first ignore the decimal points and multiply the factors as if they were whole numbers.

We then count how many decimal places each factor has and add them to get the number of decimal places for the product:

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals e1

Now to find its product, =0.23×3 =0.69

The product of the given expression0.23×3 is 0.69.

Page 30 Exercise 2 Answer

The given expression is0.41×2 To find its product. Using the method of multiplication.

The given expression is0.41×2

To multiply two decimals, we will first ignore the decimal points and multiply the factors as if they were whole numbers.

We then count how many decimal places each factor has and add them to get the number of decimal places for the product:

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals e2

Now to find its product, =0.41×2 = 0.82

The solution for the given expression 0.41×2 is 0.82

Page 30 Exercise 3 Answer

The given expression is0.01×5 To find its product. Using the method of multiplication.

The given expression is0.01×5

To multiply two decimals, we will first ignore the decimal points and multiply the factors as if they were whole numbers.

We then count how many decimal places each factor has and add them to get the number of decimal places for the product:

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 5 Operations with Decimals e3

Now to find its product, = 0.01×5 = 0.005

The solution for the given expression 0.01×5 is 0.005.

Page 30 Exercise 4 Answer

Given that Find each product. 0.32×2

To find the product, you must solve the multiplication problem. You can solve multiplication problems through repeated or fast addition.

0.32×2=0.64

The product of the given term is 0.32×2=0.64

Page 30 Exercise 5 Answer

Given that product of the following number 0.15×3

To find the product, you must solve the multiplication problem. You can solve multiplication problems through repeated or fast addition.

The product of following number is 0.15×3=0.45

The product. More generally, it is possible to take the product 0.45

Page 30 Exercise 6 Answer

Given:0.42×2.

Hence, We have to find the product of the given expression.

Firstly, Starting in the right-hand column(units) multiply then, Next, we multiply the same number by the next number across.

To multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor.

From the given expression that is, 0.42×2

Can be written as, ​0.42 ×2 = 0.84

​The product of0.42×2 is 0.84.

Page 30 Exercise 7 Answer

Given:0.04×8.

Hence, We have to find the product of the given expression.

Starting in the right-hand column(units) multiply then, Next, we multiply the same number by the next number across.

And, to multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor.

From the given expression that is, 0.04×8

Can be written as, ​0.04 ×8 = 0.24

​The product of 0.04×8 is 0.24.

Page 30 Exercise 8 Answer

Given:0.22×4.

Hence, We have to find the product of the given expression.

Starting in the right-hand column(units) multiply then, Next, we multiply the same number by the next number across.

As, to multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor.

From the given expression that is, 0.22×4

Can be written as, ​0.22 × 4 =0.88

​The product of 0.22×4 is 0.88.

Page 30 Exercise 9 Answer

Given:0.2×0.8.

Hence, We have to find the product of the given expression.

Firstly, Starting in the right-hand column(units) multiply then, Next, we multiply the same number by the next number across.

To multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor.

From the given expression that is, 0.2×0.8

Can be written as 0.2 ×0.8 = 0.16

The product of 0.2×0.8 is 0.16.

Page 30 Exercise 10 Answer

Given:0.7×0.9.

Hence, We have to find the product of the given expression.

Starting in the right-hand column(units) multiply then, Next, we multiply the same number by the next number across.

And, to multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor.

From the given expression that is, 0.7×0.9

Can be written as, 0.7 × 0.9 = 0.63

The product of 0.7×0.9 is 0.63.

Page 30 Exercise 11 Answer

Given:0.5×0.5.

Hence, We have to find the product of the given expression.

Starting in the right-hand column(units) multiply then, Next, we multiply the same number by the next number across.

As, to multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor.

From the given expression that is, 0.5×0.5

Can be written as, 0.5 × 0.5 = 0.25

The product of 0.5×0.5 is 0.25.

Page 30 Exercise 12 Answer

Given:0.3×0.6.

Hence, We have to find the product of the given expression.

Firstly, Starting in the right-hand column(units) multiply then, Next, we multiply the same number by the next number across.

To multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor.

From the given expression that is, 0.3×0.6

Can be written as, 0.3 × 0.6 = 0.18

The product of 0.3×0.6 is 0.18.

Page 30 Exercise 13 Answer

Given:0.5×0.2.

Hence, We have to find the product of the given expression.

Starting in the right-hand column(units) multiply then, Next, we multiply the same number by the next number across.

And, to multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor.

From the given expression that is, 0.5×0.2

Can be written as, 0.5 × 0.2 = 0.10

The product of0.5×0.2 is 0.10.

Page 30 Exercise 14 Answer

Given:0.4×0.4.

Hence, We have to find the product of the given expression.

Starting in the right-hand column(units) multiply then, Next, we multiply the same number by the next number across.

As, to multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor.

From the given expression that is, 0.4×0.4

Can be written as, 0.4 × 0.4 = 0.16

The product of 0.4×0.4 is 0.16.

Page 30 Exercise 15 Answer

Given:0.1×0.9.

Hence, We have to find the product of the given expression.

Firstly, Starting in the right-hand column(units) multiply then, Next, we multiply the same number by the next number across.

To multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor.

From the given expression that is, 0.1×0.9

Can be written as 0. 1 × 0.9= 0.09

The product of0.1×0.9 is 0.09.

Page 30 Exercise 16 Answer

Given:0.4×0.7.

Hence, We have to find the product of the given expression.

Starting in the right-hand column(units) multiply then, Next, we multiply the same number by the next number across.

And, to multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor.

From the given expression that is, 0.4 × 0.7 Can be written as, 0.4 × 0.7 = 0.21

The product of 0.4×0.7 is 0.28.

Go Math Answer Key

 

Go Math! Practice Fluency Workbook Grade 6 Chapter 6 Representing Ratios and Rates Exercise 6.1 Answer Key

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6: Representing Ratios and Rates

Question. Read the table and find the ratio for lion and elephant by using the method of ratio and proportion.

Given table is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6 Representing Ratios and Rates 1

To find the ratio for lion and elephant.

Using the method of ratio and proportion.                       

The number of lions in the zoo is 9 and the number of elephants in the zoo is 12

now to find the ratio of a lion to elephant,

ratio of lion to elephant = lion / elephant,

Now substitute all the values in the above formula, 

= \(\frac{9}{12}\)

Go Math! Practice Fluency Workbook Grade 6 Chapter 6 Representing Ratios and Rates Exercise 6.1 Answer Key

simplify,

= \(\frac{3}{4}\)

The ratio of a lion to elephant is 3:4

Question. Read the table and find the ratio of giraffes and otters by using the method of ratio and proportion.

Given table is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6 Representing Ratios and Rates 3

To find the ratio of giraffes and otters.

Using the method of ratio and proportion.

The number of giraffes in the zoo is 8 and the number of otters in the zoo is 16

now to find the ratio of giraffes to otters,

the ratio of giraffes to otters = giraffes/otters

Now substitute all the values in the above formula,

= \(\frac{8}{16}\)

simplify,

= \(\frac{1}{2}\)

The ratio of giraffes to otters is 1:2

Question. Read the table find the ratio of lions and seals by using the method of ratio and proportion.

Given table is

 Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6 Representing Ratios and Rates 5

To find the ratio of lions and seals.

Using the method of ratio and proportion.

The number of lions in the zoo is 9 and the number of seals in the zoo is 10

now to find the ratio,

the ratio of the lions to seals = lion/seals

Now substitute all the values in the above formula,

= \(\frac{9}{10}\)

The ratio of lions to seals is 9:10

Question. Read the table find the ratio of seals to elephants by using the method of ratio and proportion.

Given table is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6 Representing Ratios and Rates 8

To find the ratio of seals to elephants.

Using the method of ratio and proportion.

The number of seals in the zoo is 10 and the number of elephants in the zoo is 12

now to find the ratio,

the ratio of the seals to elephants = seals/elephants

Now substitute all the values in the above formula,

= \(\frac{10}{12}\)

simplify,

= \(\frac{5}{6}\)

The ratio of the seals to elephants is 5:6

Question. Read the table find the ratio of elephants to lions by using the method of ratio and proportion.

Given table is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6 Representing Ratios and Rates 11

To find the ratio of elephants to lions.

Using the method of ratio and proportion.

The number of elephants in the zoo is 12 and the number of lions in the zoo is 9 to find the ratio,
the ratio of the elephant to lion = elephant/lion

Now substitute all the values in the above formula,

= \(\frac{12}{9}\)

simplify,

= \(\frac{4}{3}\)

 

The ratio of elephants to lions is 4:3

Question. Find the three equivalent ratios for the 4/3 expression using the method of ratio.

Given table is

The given expression is  4/3

To find the three equivalent ratios for the given expression.

Using the method of ratio.

To find the three equivalent ratios for the given expression,  4/3

This ratio is in reduced form, the equivalent ratio can be found by multiplying both parts of the ratios by the same constants.

\(\frac{4 \times 2}{3 \times 2}=\frac{8}{6}\)

 

Likewise, do the same procedure for the next two ratios,

\(\begin{aligned}
& \frac{4 \times 3}{3 \times 3}=\frac{12}{9} \\
& \frac{4 \times 4}{3 \times 4}=\frac{16}{12}
\end{aligned}\)

 

The three equivalent ratios for the given ratio of 4/3

are 8:3 or 12:9 or 16:12

Question. Find the three equivalent ratios for the 12/14 expression. Using the method of ratio.

The given expression is 12/14

To find the three equivalent ratios for the given expression.

Using the method of ratio.

The given ratio is 12/14

to write the reduced form of this ratio,

\(\frac{6 \times 2}{7 \times 2}=\frac{12}{14}\)

 

so its reduced form is 6/7

multiply and divide the ratio by the same constant,

\(\frac{6 \times 3}{7 \times 3}=\frac{18}{21}\)

 

Now do the same procedure for the next two ratios,

\(\begin{aligned}
& \frac{6 \times 4}{7 \times 4}=\frac{24}{28} \\
& \frac{6 \times 5}{7 \times 5}=\frac{30}{35}
\end{aligned}\)

 

The three equivalent ratios for the given ratio12 by 14

is 18:21 or 24:28 or 30:35

Question. Find the three equivalent ratios for the 6/9 expression using the method of ratio.

The given expression is 6/9

To find the three equivalent ratios for the given expression.

Using the method of ratio.

The given ratio is 6/9

to find its reduced form,

\(\frac{6}{9}=\frac{2 \times 3}{3 \times 3}\)

 

so its reduced form is 2/3

now multiply and divide the ratio by the same constant,

\(\frac{2 \times 2}{3 \times 2}=\frac{4}{6}\)

 

Now do the procedure to find the next two ratios,

\(\begin{aligned}
& \frac{2 \times 4}{3 \times 4}=\frac{8}{12} \\
& \frac{2 \times 5}{3 \times 5}=\frac{10}{15}
\end{aligned}\)

 

The three equivalent ratios for the given ratio  6/9 are

\(\frac{4}{6}\) or 4:6

\(\frac{8}{12}[\latex] or 8:12

[latex]\frac{10}{15}\) or 10:15

Question. Find the three ratios equivalent to the ratio of cats to dogs in a park is 3 to 4 using the method of ratio.

Given the ratio of cats to dogs in a park is 3 to 4

To find the three ratios equivalent to the given ratio.

Using the method of ratio.

The given ratio of cats to dogs is 3:4

now multiply and divide the ratio by the same constant,

= \(\frac{3 \times 2}{4 \times 2}\)

= \(\frac{6}{8}\)

 

Now do the same procedure to find the next two ratios,

\(\begin{aligned}
& \frac{3 \times 3}{4 \times 3}=\frac{9}{12} \\
& \frac{3 \times 4}{4 \times 4}=\frac{12}{16}
\end{aligned}\)

 

The three ratios of cats to dogs in a park are

\(\frac{6}{8}\) or 6 : 8

\(\frac{9}{12}\) or 9 : 12

\(\frac{12{16}\) or 12 : 16

 

Question. Find the three ratios of rainy days to sunny days is 5/7 using the method of ratios.

Given the ratio of rainy days to sunny days is 5/7

To find the three ratios of rainy days to sunny days.

Using the method of ratios.

The ratio of rainy days to sunny days is 5/7

now multiply and divide the ratio by the same constant,

= \(\frac{5 \times 2}{7 \times 2}\)

simplify,

= \(\frac{10}{14}\)

 

Now repeat the same procedure to find the ratios of the next two,

\(\begin{aligned}
& \frac{5 \times 3}{7 \times 3}=\frac{15}{21} \\
& \frac{5 \times 4}{7 \times 4}=\frac{20}{28}
\end{aligned}\)

 

The three equivalent ratios of rainy days to sunny days are

\(\frac{10}{14}\) or 10 : 14

\(\frac{15}{21}\) or 15 : 21

\(\frac{20}{28}\) or 20 : 28

 

Question. Find the three equivalent ratios for the protein to fiber in a granola bar is 9/2 using the method of ratio.

Given the ratio of protein to fiber in a granola bar is 9/2

To find the three equivalent ratios for the protein to fiber in a granola bar.

Using the method of ratio.

The given ratio of the protein to fiber in a granola bar is 9/2

now to multiply and divide the ratio by the same constant,

= \(\frac{9 \times 2}{2 \times 2}\)

= \(\frac{18}{4}\)

 

Now repeat the same procedure to find the next two ratios,

\(\begin{aligned}
& \frac{9 \times 3}{2 \times 3}=\frac{27}{6} \\
& \frac{9 \times 4}{2 \times 4}=\frac{36}{8}
\end{aligned}\)

 

The three equivalent ratios of protein to fiber in a granola bar are

\(\frac{18}{4}\) or 18 : 4

\(\frac{27}{6}\) or 27 : 6

\(\frac{36}{8}\) or 36 : 8

 

Question. Find how many angelfishes are there in the pet shop. Using the method of ratio.

Given the ratio of the clownfish to angelfish is 5:4

and the angelfish to golden fish is 4:3

To find how many angelfishes are there in the pet shop. Using the method of ratio.

The given ratio of clownfish to angelfish is 5:4 and the ratio of angelfish to goldfish is 4:3 there are 60 fishes are there in the pet shop.

from this, it is clear that clownfish=5

angelfish=4

goldfish=3

Using the above values now find the total number of angelfish in the pet shop,

= \(\frac{60}{5}\)

= 12

multiply by 4

= 12 x 4

= 48

 

There are 48 angelfishes are there in the pet shop.

Question. Find the ratio between the days of May month to days in a particular year.

Given: Days in May to days in a year.

To find: We have to find the ratio between the days of May month to days in a particular year.

Just find out the number of days present in May month.

Then find the number of days in a year.

Then divide the days of May month by days in a year to get the ratio.

The May month consists of 31 days.

and in a year, there are usually 365 days.

Now if we divide these days, we get

Ratio = \(\frac{31}{365}\)

Ratio = 31 : 365

 

The ratio between the days of May month to days in a particular year is 31:365.

Question. Find the ratio between the numbers of sides of a triangle to the number of sides a square.

Given: Sides of a triangle to sides of a square.

To find: We have to find the ratio between the number of sides of a triangle to the number of sides a square has.

Just find out the number of sides of a triangle.

Then find the number of sides of a square.

Then divide them to find the ratio.

As we know, any triangle has “3” sides.

and any square always has “4” sides.

Now let’s take the division of the number of sides of a triangle and the number of sides of a square, we get the ratio as,

Ratio = \(\frac{3}{4}\)

Ratio = 3 : 4

 

The ratio of the sides of a triangle to the sides of a square is 3:4.

Question. Find the ratio between 8 triangles to 12 circles.

Given: There are 8 triangles and 12 circles are given.

To find: We have to find the ratio between 8 triangles to 12 circles.

Take division of them.

Then simplify them to obtain different ratios.

We have given 8 triangles and 12 circles.

The ratio for the above statement is   8/12  i.e. 8:12.

Dividing the ratio 8:12 i.e. 8 by 12 by 4 in both numerator and denominator, we get,

\(\frac{\frac{8}{4}}{\frac{12}{4}}=\frac{2}{3}\)

i.e. the ratio is 2:3.

Dividing the ratio 8:12 i.e. 8 by12 by 2 in both numerator and denominator, we get

\(\frac{\frac{8}{2}}{\frac{12}{2}}=\frac{4}{6}\)

i.e. the ratio is 4:6.

Multiplying the ratio 8:12 i.e. 8 by12 by 2 in both numerator and denominator, we get

\(\frac{8}{12} \times \frac{2}{2}\),

= \(\frac{16}{24}\)

i.e. the ratio is 16:24.

The three equivalent ratios of 8 triangles and 12 circles are,

​2 : 3

4 : 6

16 : 24

Question. Find the three equivalent ratios between 20 pencils and 25 erasers.

Given: There are 20 pencils and 25 erasers are given.

To find: We have to find the three equivalent ratios between 20 pencils and 25 erasers.

Take division of them.

Then simplify them to obtain different ratios.

We have been given 20 pencils and 25 erasers.

The ratio for the above statement is 20:25.

If we multiply and divide the numerator and denominator of the ratio 20/25 by “2”, we get

Ratio ​=20

= \(\frac{20}{25} \times \frac{2}{2}\)

= \(\frac{40}{50}\)

= 40 : 50

 

Dividing the ratio  40/50, by 10 in both the numerator and denominator, we get

\(\frac{\frac{40}{10}}{\frac{50}{10}}=\frac{4}{5}\)

i.e. the ratio is 4:5.

Dividing the ratio  40/50, by 5 in both the numerator and denominator, we get

\(\frac{\frac{40}{5}}{\frac{50}{5}}=\frac{8}{10}\)

i.e. the ratio is 8:10.

Three equivalent ratios of 20 pencils and 25 erasers are

​40 : 50

4 : 5

8 : 10

Question. Find the three equivalent ratios between 5 girls and 6 boys.

To find: There are 5 girls and 6 boys are given.

To find: We have to find the three equivalent ratios between 5 girls and 6 boys.

Take division of them.

Then simplify them to obtain different ratios.

We have given 5 girls and 6 boys.

Now divide them to get the different ratios.

Now let’s divide the number of girls and the number of boys, we get

= \(\frac{5}{6}\)

Ratio = 5 : 6

Now if we multiply and divide this ratio by “2”, we get

\(\frac{5}{6} \times \frac{2}{2}\)

= \(\frac{10}{12}\)

Ratio  = 10 : 12

Now if we multiply and divide this ratio by “3”, we get

\(\frac{15}{18}\)

Ratio = 15 : 18

Three equivalent ratios of 5 girls and 6 boys are,

​⇒ 5 : 6
⇒ 10 : 12
⇒ 15 : 18

Question. Find the three equivalent ratios between 10 pants and 14 shirts.

Given: There are 10 pairs of pants and 14 shirts given.

To find: We have to find the three equivalent ratios between 10 pants and 14 shirts.

Take division of them.

Then simplify them to obtain different ratios.

We have given 10 pairs of pants and 14 shirts.

The ratio is expressed as 10:14.

If we multiply the numerator and denominator by “2”, we get

= \(\frac{10}{14} \times \frac{2}{2}\)

= \(\frac{20}{28}\)

Ratio = 20 : 28 ​

The ratio obtained after the simplification of 20:28 is determined by dividing the numerator and denominator of 20/28 by 4, thus, we obtain

\(\frac{20}{28}\)

= \(\frac{5}{7}\)

i.e. the ratio is 5:7

The ratio 10:14, i.e. 10 by 14 is multiplied by 3 in both the numerator and denominator.

We obtain

\(\frac{10}{14} \times \frac{3}{3},\)

= \(\frac{30}{42}\)

i.e. the ratio is 30:42.

Three equivalent ratios of10 pants and14 shirts are,

​20 : 28

5 : 7

30 : 42

Go Math Answer Key

 

 

Go Math Practice Fluency Workbook Grade 6, California 1st Edition

Go Math Practice Fluency Workbook Grade 6, California 1st Edition

 

Go Math! Practice Fluency Workbook Grade 6 Chapter 7 Applying Ratios and Rates Exercise 7.2 Answer Key

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition Chapter 7 Representing Ratios and Rates

Question. Find the unknown value in the proportion 4/5 = ?/20 and to round to the nearest tenth value.

Given a proportion 4/5 =?/20

To find the unknown value in the proportion and to round to the nearest tenth if needed.

Since proportions are comparisons between two equal ratios their fractions in the lowest term must be equal and by finding the

relationship between the two given ratios we can calculate the unknown value.

The given proportion is 4/5 =?/20

The denominators of both ratios are given so compare them to find the relationship between the two numbers.

Then by calculating what number the numerator is to be multiplied we can find the unknown value.

From the given proportion we see that5.4=20

So, we need to multiply by 4

4/5 =4.4/5.4

Multiply, 4/5 =?/20

So, the unknown value is 16

The unknown value in the proportion 4/5 =?/20 is 16

Question. Find the unknown value in the proportion 3/7 = ?/35 and to round to the nearest tenth.

Given a proportion 3/7 =?/35

To find the unknown value in the proportion and to round to the nearest tenth if needed.

Since proportions are comparisons between two equal ratios their fractions in the lowest term must be equal and by finding the relationship between the two given ratios we can calculate the unknown value.

From the given proportion we see that7.5=35

So, we need to multiply by 5

Go Math! Practice Fluency Workbook Grade 6 Chapter 7 Applying Ratios and Rates Exercise 7.2 Answer Key

3/7 =3.5/7.5

Multiply, 3/7 =15/35

So, the unknown value is 15

The unknown value in the proportion 3/7 =?/35 is15

Question. Find the unknown value in the proportion 4/3 = 12/? and to round to the nearest tenth value.

Given a proportion 4/3 =12/?

To find the unknown value in the proportion and to round to the nearest tenth if needed.

Since proportions are comparisons between two equal ratios their fractions in the lowest term must be equal and by finding the

relationship between the two given ratios we can calculate the unknown value.

The given proportion is 4/3 =12/?

The numerators of both ratios are given so compare them to find the relationship between the two numbers.

Then by calculating what number the denominator is to be multiplied we can find the unknown value.

From the given proportion we see that 4.3=12

So, we need to multiply by 3

4/3 =4.3/3.3

Multiply, 4/3 =12/9

So, the unknown value is 9

The unknown value in the proportion 4/3 =12/? is 9

Question. Find the unknown value in the proportion 13/15 = 52/? and to round to the nearest tenth value.

Given a proportion 13/15 =52/?

To find the unknown value in the proportion and to round to the nearest tenth if needed.

Since proportions are comparisons between two equal ratios their fractions in the lowest term must be equal and by finding the between the two given ratios, we can calculate the unknown value.

The given proportion is 13/15 =52/?

The numerators of both ratios are given so compare them to find the relationship between the two numbers.

Then by calculating what number the denominator is to be multiplied we can find the unknown value.

From the given proportion we see that 13.4=52

So, we need to multiply by 4

13/15 =13.4/15.4

Multiply, 13/15 =52/60

So, the unknown value is 60

The unknown value in the proportion 13/15 =52/? is 60

Question. Wayne has a recipe on a three-inch-by-five-inch index card that he wants to enlarge to 15 inches long. Find out how wide the enlargement.

Given that Wayne has a recipe on a three-inch-by-five-inch index card that he wants to enlarge to 15 inches long.

To find out how wide the enlargement will be.

The given dimensions are written in the form of a ratio and we know that comparisons between two equal ratios will have the same fractions in the lowest term so by finding the relationship between the two given values we can calculate the width of the index card.

It is given that Wayne has a recipe on a 3-inch-by-5-inch index card.

So, the length of the card is 5 inches and the width of the card is 3 inches.

The ratio of the index card is width/length =3/5

Wayne wants to enlarge it to 15 inches long so to get a length of 15 we have to multiply the denominator by 3

Then multiply the numerator and denominator by 3 to get the new dimensions since they are equivalent ratios.

3/5 =3.3/5.3

Multiply, 3/5 =9/15

So, the width of the card will be 9 inches.

Wayne has a recipe on a 3-inch-by-5-inch index card that he wants to enlarge to 15 inches long then the enlargement will be 9 inches wide.

Question. Sharon is decreasing the size of a diagram of a leaf that is 30 centimeters long by 10 centimeters wide. Find out how long centimeters.

Given that Sharon is decreasing the size of a diagram of a leaf that is 30 centimeters long by 10 centimeters wide.

If the reduced diagram is 4 centimeters wide then, to find out how long will the diagram be.

The given dimensions are written in the form of a ratio and we know that comparisons between two equal ratios will have the

same fractions in the lowest term so by finding the relationship between the two given values we can calculate the length of the diagram of a leaf.

It is given that Sharon is decreasing the size of a diagram of a leaf that is 30 centimeters long by 10 centimeters wide.

So, the length of the diagram is 30cm and the width is10cm

The ratio of the diagram is length/width =30/10

Reduce the ratio to its simplest form,

​length/width =3⋅10/1⋅10

length/width =3/1

If the reduced diagram is four centimeters wide, then to get a width of4 to multiply the denominator by 4

Then multiply the numerator and denominator by 4 to get the new dimensions since they are equivalent ratios.

3/1 =3.4/1.4

Multiply, 3/1 =12/4

So, the length of the diagram will be 12cm

Sharon is decreasing the size of a diagram of a leaf that is 30 centimeters long by 10 centimeters wide to 4 centimeters wide, then the diagram will be 12 centimeters long.

Question. A wood stove burns four same-sized logs in two hours. Find out the number of logs the stove can burn in eight hours.

Given that a wood stove burns four same-sized logs in two hours.

To find out the number of logs the stove can burn in eight hours.

The given information is written in the form of a ratio and we know that comparisons between two equal ratios will have the

same fractions in the lowest term so by finding the unit rate we can calculate the number of logs the stove can burn in eight hours.

It is given that a wood stove burns 4 same-sized logs in 2 hours.

The number of logs is 4 and the number of hours it takes is 2

So, the ratio is logs/hours =4/2

To calculate the unit rate, reduce the ratio.

logs/hours =2.2/2.1

Cancel common factors, logs/hours =2/1

In one hour, the woodstove burns 2 logs.

So, the number of logs the stove burns is 2 times the number of hours it takes.

So, in8 hours, the stove will burn twice the number of hours it takes

⇒2⋅8=16

So, in 8 hours the stove burns 16 logs.

A wood stove burns 4 same-sized logs in 2 hours, then the stove can burn 16 logs in 8 hours.

Question. The number of stamps is in 2012 five U.S. postal stamps cost $2.20. Find out how much seven stamps cost.

Given that in 2012 five U.S. postal stamps cost $2.20.

To find out how much seven stamps cost.

The given information is written in the form of a ratio and we know that comparisons between two equal ratios will have the same fractions in the lowest term so by finding the unit rate we can calculate the cost of seven stamps.

It is given that in 2012, five U.S. postal stamps cost $2.20

The number of stamps is five and their cost is $2.20

So, the ratio is

cost/stamps =2.20/5

To calculate the unit rate, reduce the ratio.

cost/stamps =0.44×5/5.1

Cancel common factors,

cost/stamp =0.44/1

For one stamp, the cost is $0.44

So, the cost of the stamps is 0.44 times the number of stamps.

The cost of seven stamps is0.44 times7

That is,0.44×7=3.08

So, the cost of seven stamps is $3.08

In 2012, five U.S. postal stamps cost $2.20 then seven stamps cost $3.08

Question. The distance between Saugerties and Kingston in inches. Find the actual distance between Saugerties and Kingston.

Given the distance between Saugerties and Kingston in inches.

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 12

To find the actual distance between Saugerties and Kingston.

The distance between Saugerties and Kingston in inches is given and the scale of the map is given so using the scale calculates

the actual distance between Saugerties and Kingston in miles.

It is given that the distance between Saugerties and Kingston is 4 inches.

It is also given that scale in the map is 1in =2.5mi.

So, on the map, the number of miles is equal to 2.5 times the number of inches.

If the distance is 4 inches then the number of miles is 2.5 times 4

That is, the actual distance between Saugerties and Kingston is = 2.5×4

Multiply,

The actual distance between Saugerties and Kingston is 10 miles.

The actual distance between Saugerties and Kingston is10mi.

Question. The scale of a map is 1in = 250mi and City A is 378mi miles from City B. Find how far is its distance on the map and round to the nearest tenth if needed.

Given that the scale of a map is 1in=250mi and City A is 378mi miles from City B.

To find how far is its distance on the map and round to the nearest tenth if needed.

Using the scale of the map, calculate the relationship between inches and miles to find the distance between City A and City B in inches on the map.

It is given that the scale of a map is 1in =250mi

So, the number of miles is equal to 250 times the number of inches on the map.

That is, the number of inches on the map is equal to the number of miles divided by250

If the actual distance between City A and City B is 378mi then the distance on the map is 378 divided by 250 =378/250

Dividing,=1.512

Rounding to the nearest tenth,≈1.5in

The scale of a map is 1in=250 mi. and City A is378 miles from City B then its distance on the map is rounded to the nearest tenth is 1.5 in

Question. The Twelve eggs cost $2.04. Find the cost of eighteen eggs.

Given twelve eggs cost $2.04

To find the cost of eighteen eggs.

The given proportion is reduced to its simplest form so that the denominator is one then the cost of eighteen eggs is calculated.

It is given that the cost of twelve eggs is $2.04

Then the proportion is cost/eggs =2.04/12

To calculate the unit rate, reduce the ratio.

cost/eggs =0.17×12/12×1

Cancel common factors,

cost/eggs =0.17/1

The cost of one egg is $0.17

So, the cost of eggs is 0.17 times the number of eggs.

The cost of 18 eggs is 0.17 times 18

0.17×18=3.06

Then the cost of 18 eggs is $3.06

If twelve eggs cost $2.04 then eighteen eggs cost $3.06

Question. Seven pounds of grapes cost $10.43. Find how much three pounds cost.

Given seven pounds of grapes cost $10.43

To find how much three pounds would cost.

The given proportion is reduced to its simplest form so that the denominator is one then the cost of three pounds of grapes is calculated.

It is given that seven pounds of grapes cost $10.43

Then the proportion is

cost/pound =10.43/7

To calculate the unit rate, reduce the ratio.

cost/pound =1.49×7/7×1

Cancel common factors,

cost/pound =1.49/1

For one pound of grapes, the cost is $1.49

So, the cost of the grapes is 1.49 times the number of pounds.

The cost of three pounds is1.49 times3

1.49×3=4.47

Then the cost of three pounds of grapes is $4.47

If seven pounds of grapes cost $10.43 then three pounds of grapes cost $4.47

Question. Roberto wants to reduce a drawing that is 12 inches long by 9 inches wide. Find the width of the new drawing.

Given that Roberto wants to reduce a drawing that is 12 inches long by 9 inches wide.

If his new drawing is 8 inches long then, we have to find the width of the new drawing.

The given proportion is reduced to its simplest form so that the number needed to be multiplied is found and the width of the new drawing is calculated.

It is given that Roberto wants to reduce a drawing that is 12 inches long by 9 inches wide.

The length of the drawing is 12 inches and the width of the drawing is 9 inches.

Then the proportion is

length/width =12/9

Reducing to its simplest form.

length/width =4.3/3.3

length/width =4/3

If his new drawing is 8 inches long, then we can multiply the numerator by 2

So, multiply the numerator and denominator by 2 since they are equivalent ratios.

length/width =4.2/3.2

Multiply,

length/width =8/6

The width of the new drawing is 6 inches.

Roberto wants to reduce a drawing that is 12 inches long by 9 inches wide to 8 inches long, then the new drawing will be 6 inches wide.

Go Math! Practice Fluency Workbook Grade 6 Chapter 7 Applying Ratios and Rates Exercise 7.3 Answer Key

Go Math! Practice Fluency Workbook Grade 6 California 1st Edition, Chapter 7 Representing Ratios and Rates

Question. Use Proportions to convert 4ft feet to inches.

Given: 4ft

Find: we need to convert it to inches.

We will use proportions to convert feet to inches.

Let 4ft be equal to x inches

1ft=12in

ratio=1/12

Also,4ft=x in

ratio=4/x

Both ratios are equal, so

4/x =1/12

x=12×4

x=48in​

Both ratios are equal, so 4/x =  1/12

x=12×4

x=48in

4ft is equal to 48 inches.

Question. Use Proportions to convert 6 quarts to gallons.

Given: 6 quarts

Find: we need to convert it to gallons.

We will use proportions to convert quarts to gallons.

Let 6 quarts be equal to x gallons

1gal=4qt

ratio=1/4

Also, xgal=6qt

ratio =x/6

Both ratios are equal, so

x/6 =1/4

x =6/4

=1.5gal

6qt is equal to 1.5gal gallons.

Go Math! Practice Fluency Workbook Grade 6 Chapter 7 Applying Ratios and Rates Exercise 7.3 Answer Key

Question. Use proportions to convert 5km kilometers to meters.

Given: 5km

Find: we need to convert it to meters.

We will use proportions to convert kilometers to meters.

Let 5km be equal to x meters

1km=1000m

ratio=1/1000

Also, 5km=xm

ratio=5/x

Both ratios are equal, so

5/x =1/1000

x=1000×5

x=5000m

5km is equal to 5000m meters.​

Question. Use Proportions to convert 2000g grams to kilograms.

Given: 2000g

Find: we need to convert it to kilograms.

We will use proportions to convert grams to kilograms.

Let 2000 be equal to x kg

1kg=1000g

ratio=1/1000

Also, xkg=2000g

ratio=x/2000

Both ratios are equal, so

x/2000 =1/1000

x=2000/1000

=2kg

2000g is equal to 2 kg kilograms.

Question. Use the conversion factor to 5qt convert quarts to cups.

Given: 5qt

Find: we need to convert it to cups.

We will use the conversion factor to convert quarts to cups.

It is known that1qt=4cups

conversion factor= 4/1 =4

​5qt =cf×5

5qt =4×5 =20cups

5quarts is equal to 20 cups

Question. Use the conversion factor to 600cm convert centimeters to meters.

Given: 600cm

Find: we need to convert it to meters.

We will use the conversion factor to convert centimeters to meters.

It is known that100cm=1m

conversion factor, cf=1/100

​600cm=cf×600

600cm=600×1/100

600cm=6m

600cm is equal to 6m

Question. Use proportions to 1mile convert miles to feet.

Given: 1mile

Find: we need to convert it to feet.

We will use proportions to convert miles to feet.

Let 1mile be equal to x ft

1mile=5280ft

ratio=1/5280

Also,1mile=xft

ratio=1/x

Both ratios are equal, so

1/5280 =1/x

x=5280ft

The altitude is 1 mile which is 5280 ft.

Question. Use proportions to 0.7 km convert kilometers to meters.

Given: 0.7km

Find: we need to convert it to meters.

We will use proportions to convert kilometers to meters.

Let 0.7km be equal to x meters

1km=1000m

ratio=1/1000

Also,0.7km=xm

ratio=0.7/x

Both ratios are equal, so

0.7/x =1/1000

x=0.7×1000

x=700m

The distance is 0.7km which is equal to 700m.

Question. Read the table and find the conversion factor and multiply or divide it to get our values.

Given a table

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 13

We need to convert values from inches to feet to yard.

We will find the conversion factor and multiply or divide it to get our values.

1ft=12in

conversion factor,cf1=12

1yd=3ft

conversion factor,cf2=3

For moving right, we will multiply and for moving left, we will divide by the conversion factor.

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 14

The table will be

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 15

The filled table will be

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 16

Question. A sheet of paper is 81/2 x 11 inches. Find the length of the frame that is 4 papers long along the length.

Given: A sheet of paper is 81/2×11 inches

Find: we need to find the length of the frame that is 4 papers long along the length.

We will multiply the length by 4 times along the length of the paper.

Given Length=11in

We will multiply by 4

11×4=44 in

1ft=12in

Conversion factor,cf=12

We will divide the length in inches by the conversion factor

length in feet =​44/12

=3.67ft

The length of the frame is 44 in and 3.67ft

Question. A scale from feet to yards and find the conversion factor and use it to represent a larger bar with conversion factor times smaller bars.

Given: A scale from feet to yards

Find: we need to draw a bar model.

We will find the conversion factor and use it to represent a larger bar with conversion factor times smaller bars.

Given a scale from feet to yards 1yd=3ft

Conversion factor =3/1 =3

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 17

 

The bar model for feet to yards will be

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 18

Question. A scale from cups to fluid ounces and find the conversion factor and use it to represent a larger bar with conversion factor times smaller bars.

Given: A scale from cups to fluid ounces

Find: we need to draw a bar model.

We will find the conversion factor and use it to represent a larger bar with conversion factor times smaller bars.

Given a scale from cups to fluid ounces

1cup=8ounces

Conversion factor, cf=8

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 19

The bar model for converting cups to fluid ounces will be

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 19

Bar models are good to represent conversions with small conversion factors as it is easy to represent. But in the case of a large conversion factor, it becomes very difficult to draw so many bars and also very tough to represent them. For converting miles to feet, it has a conversion factor of 5280 which is very large. Hence, the bar model is not a good choice to represent the conversion of miles to feet.

The bar model is not a good choice to represent the conversion of miles to feet.

Go Math! Practice Fluency Workbook Grade 6 Chapter 7 Applying Ratios and Rates Exercise 7.1 Answer Key

Go Math! Practice Fluency Workbook Grade 6 California 1st Edition, Chapter 7 Representing Ratios and Rates

Question. The table shows information about the packets of flavoring added to an amount of water to make soup. Find the rate of ounces of water needed for each packet of flavoring.

Given: The table shows information about the packets of flavoring added to an amount of water to make soup.

To find: the rate of ounces of Water needed for each packet of flavoring.

The rate of ounces of Water needed for each packet of flavoring is 24/2

We will divide the ratio by 2

By using this rate we will find the remaining rate as

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 1

The rate of ounces of Water needed for each packet of flavoring is 12.

The table shows information about the packets of flavoring added to an amount of water to make soup. Find the use the unit rate to help you complete the table.

Given: The table shows information about the packets of flavoring added to an amount of water to make soup.

To find: Use the unit rate to help you complete the table.

The unit rate is 12

To find ounces of water multiply the packet of flavoring with 12

To find a packet of flavoring divide ounces of water by 12

Go Math! Practice Fluency Workbook Grade 6 Chapter 7 Applying Ratios and Rates Exercise 7.1 Answer Key

We have a unit rate of 12.

For the first column packets of flavoring is 5, Multiply it by the unit rate,

Ounces of water ​=12×5 =60

For the second column ounces of water are 84

Divide it by unit rate,

Packets of flavoring ​= 84/12 =7

For the third column packets of flavoring are 10.

Multiply it by the unit rate,

Ounces of water ​=12×10 =120

For the fourth column ounces of water are 144.

Multiply it by the unit rate,

Packets of flavoring​=144/12 =12

Completed table is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 2

We have to draw a graph using the table.

Table is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 3

We will take packets of flavoring as the x-axis and ounces of water as the y-axis.

We will get a straight line passing through points.

The table from which we have to plot is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 3

Taking packets of flavoring as the x-axis and ounces of water as the y-axis.

We will plot points on the graph and draw a line passing through all points.

the graph can be represented as

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6 Representing Ratios and Rates 68

The graph formed by using the information in the table is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6 Representing Ratios and Rates 68

Question. Table shows information about the packets of flavoring added to an amount of water to make soup. How much water should be added to 23 packets of flavoring?

Given: The table shows information about the packets of flavoring added to an amount of water to make soup.

To find: How much water should be added to 23 packets of flavoring?

The unit rate is 12.

To find ounces of water multiply packets of flavoring by unit rate.

The unit rate is 12.

The packets of flavoring are 23.

Multiplying packets of flavoring and unit rate,

Water needed ​=23×12 =276

276 ounces of water should be added to 23 packets of flavoring.

Question. Table shows information about the packets of flavoring added to an amount of water to make soup. Find the point (9.5, 114) makes sense in this context.

Given: The table shows information about the packets of flavoring added to an amount of water to make soup.

To find: If the point (9.5, 114) makes sense in this context.

Suppose 9.5 packets of flavoring and 114 ounces of water.

If we divide ounces of water by packet of flavoring we get,

114/9.5 =12

which is the unit rate in this problem.

So, 114/9.5 is the equivalent fraction of 24/2.

The point (9.5,114) is the equivalent fraction of point (2,24).

Question. Given a table that shows information about the packets of flavoring added to an amount of water to make soup. Find if the relationship shown uses addition or multiplication.

Given a table that shows information about the packets of flavoring added to an amount of water to make soup.

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 4

To find if the relationship shown uses addition or multiplication.

The rate of ounces of water needed for each packet of flavoring is calculated and from that, we can identify which operation is used to define the relationship between the packets of flavoring and ounces of water.

The rate of ounces needed for each packet of flavoring is found from exercise−1

So, the rate of ounces of water needed is 24/2 =12 ounces per packet.

Since 12 ounces of water is needed for each packet, the number of ounces of water is calculated by 12 times the number of packets.

Then, the relationship uses multiplication.

A table that shows the information about the packets of flavoring added to an amount of water to make soup is given then the relationship shown uses multiplication because the number of ounces of water is calculated by 12 times the number of packets.

Use equivalent ratios and complete the table. The ratios in the table are equivalent ratios so we reduce the first ratio to its lowest term and use that to find the other ratios.

Given a table

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 5

Use equivalent ratios and complete the table.

The ratios in the table are equivalent ratios so we reduce the first ratio to its lowest term and use that to find the other ratios.

The given table is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 6

The first ratio from the table is A/B =6/2

Cancel common factors, A/B =3.2/2.1

Simplify the ratio, A/B =3/1

The simplified ratio means that the value of A is three times the value of B

⇒ A=3B

Then, the value of B is calculated by dividing the value of A by three.

⇒ B=A/3

Now we can complete the table.

For A=9,B=9/3

Divide,

B=3

For B=4, A=3.4

Multiply, A=12

For B=5,

A=3.5

Multiply, A=15

For A=18,

B=18/3

Divide, B=6

For B=7,

A=3.7

Multiply, A=21

For B=8,

A=3.8

Multiply, A=24

Substituting all these values in the table.

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 8

The completed table formed using equivalent ratios is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 9

Question. Show if the ratios are equivalent by simplifying any four of them.

Given a table

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 10

To show if the ratios are equivalent by simplifying any four of them.

Any four of the ratios in the table are reduced to their simplest forms to see if their fractions are the same to show that they are equivalent ratios.

Consider the completed table from the exercise − 1

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 11

To simplify any four ratios show that they are equivalent.

Consider the first four ratios and reduce them to their lowest terms.

The first ratio is A/B =6/2

Dividing,=3/1

The second ratio is 9/3 =3.3/3.1

Cancel common factors, =3/1

The third ratio is 12/4 =4.3/4.1

Cancel common factors,=3/1

The fourth ratio is 15/5 =5.3/5.1

Cancel common factors,=3/1

The four ratios when simplified to their lowest term are 3/1

So, the four ratios are equivalent.

Simplifying any four of the ratios 6/2,9/3,12/4,15/5 we found that they all reduced to 3/1 so the ratios are equivalent.

Question. An equivalent ratio of 69/3. Find the rate of A/B and to complete the equivalent ratio.

Given an equivalent ratio of 69/3

To find the rate of A/B and to complete the equivalent ratio.

From the previous exercises, we know the ratio of A/B from which we can define the rate of that ratio and then calculate the equivalent ratio using that.

From exercise 1,2 we see that the ratios are equivalent and they are all reduced to 3/1

Since all the simplified ratios are equal to 3/1, the rate of A/B =3/1

The rate of A/B =3/1 shows the relationship between the numerator and denominator, which means that the numerator is 3 times the denominator.

That is, A=3B

So, the denominator is calculated by dividing the numerator by3

So the given ratio has its numerator69

So, the denominator is 69/3 =23

Then the equivalent ratio is 69/23

The rate of A/B =3/1 and the completed equivalent ratio is 69/23

Question. Find how many A’s are needed for 63 B’s, then to write the ratio.

Given B=63

To use the rate to find how many A’s are needed for 63 B′s, then to write the ratio.

From the previous exercise, we know the rate of A/B from which we know the relationship between the numerator and denominator

so the value of A for B=63 is calculated and the ratio is found.

From exercise−3, we know that the rate of A/B =3/1 which means that the numerator is 3 times the denominator.

If there are 63B′s then the value of A is calculated by multiplying the denominator by 3

A=63.3

Multiply, A=189

The ratio of A/B for63B′s is 189/63

Using the rate the number of A′s needed for 63B′s is 189, then the ratio is 189/63

Go Math Answer Key

Go Math! Practice Fluency Workbook Grade 6 Chapter 7 Applying Ratios and Rates Exercise 7.4 Answer Key

Go Math! Practice Fluency Workbook Grade 6 California 1st Edition, Chapter 7 Representing Ratios and Rates

Question. Use a conversion factor 40yd to convert yards to meters.

Given: 40yd

Find: we need to convert it to meters.

We will use a conversion factor to convert yards to meters

Given 40yd

1yd=0.91m

conversion factor=0.91

We will multiply it by a conversion factor

40yd=40×0.91

=36.4m

40 yards is equal to 36.4m

Question. Use a conversion factor 5 ounces convert ounces to millimeters.

Given: 5 ounces

Find: we need to convert it to milliliters.

We will use a conversion factor to convert ounces to milliliters

Given 5 ounces

1ounce=29.57ml

conversion factor=29.57

We will multiply it by a conversion factor

5ounces=5×29.57

=147.85ml

5 fluid ounces of water is equal to 147.85ml of water.

Go Math! Practice Fluency Workbook Grade 6 Chapter 7 Applying Ratios and Rates Exercise 7.4 Answer Key

Question. Use the conversion factor 52 pounds to convert pounds to kilograms.

Given: 52pounds

Find: we need to convert it to kilograms.

We will use the conversion factor to convert pounds to kilograms.

Given 52pounds

1pound=0.45kg

conversion factor=0.45

We will multiply it by a conversion factor

52pounds=52×0.45

=23.4kg

52 pounds of potatoes is equal to 23.4kg of potatoes.

Question. Use a conversion factor 7km to convert the kilometer to the mile.

Given: 7km

Find: we need to convert it to miles.

We will use a conversion factor to convert the kilometer to the mile.

Given 7km

1km=1.6mile

conversion factor=1.6

We will divide it by the conversion factor

7km=7/1.6

7km=4.375mile

7km distance is equal to 4.375 miles.

Question. Mia’s cat weighs 13 pounds, 7 ounces and find that weight in kilograms.

Given: Mia’s cat weighs 13 pounds, 7 ounces

To Find: What is that weight in kilograms

The weight of the cat is 13 pounds 7 ounces.

13 pound​=13×0.4535

= 5.895kg

7 ounce​=7×0.0283

= 0.1981kg

13 pounds 7 ounces is​ 5.895+0.1981

= 6.0931kg

Mia’s cat weighs 13 pounds, 7 ounces. and the same weight in kilograms is about 6.0931kg.

Question. The quilt is 2.44 meters long and 1.83 meters wide. Find the area of the quilt in square feet.

Given: The quilt is 2.44 meters long and 1.83 meters wide.

To Find: Area of the quilt in square feet.

Length2.44m in the foot will be,

=2.44×3.2804

=8.0052ft

Width 1.83m in the foot will be,

=1.83×3.2804

=6.0039ft

Area​=8.0052×6.0039

=48.0624sqft

D’Quan’s grandmother made a quilt for his bed. The quilt is 2.44 meters long and 1.83 meters wide. The area of the quilt in square feet is about480624sqft or 480624ft²

Question. Every day an adult should consume 64 fluid ounces. Josey had already consumed 700 milliliters of water. How may more liters should he drink today?

Given: Every day an adult should consume 64 fluid ounces.

Josey has already consumed 700 milliliters of water

To Find: How many more liters should he drink today?

We know that 1 fluid ounce is near to about29.6ml

Now converting 64 fluid ounces to milliliters,

64×29.6=1894.4ml

Josey consumes 700ml,

The difference is about 1894.4−700=1194.4ml

To Converting into liters divide ml by1000,

1194.4/1000

=1.1944l

An adult drinks 64 fluid ounces of water every day. Josey has already consumed 700 milliliters of water. 1.1944 liters he should drink today.

Question. Read the table and convert from feet to meters.

Given: Conversion factor chart

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 20

To Find: Convert from feet to meters.

In order to convert feet to meters we have to multiply feet by 0.305 meters.

To convert from feet to meters, multiply by 0.305m.

Question. Read the table to convert from quarts to liters.

Given: Conversion Chart

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 21

To Find: To convert from quarts to liters.

In order to convert quarts to liters we have to multiply quarts by 0.946liter.

To convert from quarts to liters, multiply by 0.946 liters.

Question. Read the table to convert from pounds to kilograms.

Given: Conversion Chart

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 22

To Find: To convert from pounds to kilograms.

In order to convert pounds to kilograms, we have to multiply pounds by 0.454 kilograms.

To convert from pounds to kilograms, multiply by 0.454 kilograms.

Question. Read the table and convert from gallons to liters.

Given: Conversion Chart

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 23

To Find: To convert from gallons to liters.

In order to convert gallons to liters, we have to multiply gallons by 3.79 liters.

To convert from pounds to kilograms, multiply by 3.79l.

Question. Read the table and find the 9 yards ≈ ________ meters.

Given: Conversion factor

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 24

To Find: 9 yards ≈ ——— meters.

From the chart, we can see that,

1 yard≈ 0.914 meter

9 yard≈ 9×0.914

9 yards≈ 8.226 meters.

Therefore, 9 yards ≈ 8.226 meters.

Question. Read the table and find the 4 ounces ≈ _______ grams.

Given: Conversion factor

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 25

To Find: 4 ounces ≈ _______grams

From the chart, we can see that,

1 ounce ≈ 28.4grams

4 ounces ≈ 4×28.4

4 ounces≈ 113.6 grams

We concluded that 4 ounces ≈ 113.6gm.

Question. Read the table and find the 12 fluid ounces ≈ _______ milliliters.

Given: Conversion factor table

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 26

To Find: 12 fluid ounces ≈ milliliters.

From the chart, we can see that,

1 fluid ounce ≈ 29.6 milliliters

12 fluid ounces ≈ 12×29.6

12 fluid ounces ≈ 355.6 milliliters

We concluded that 12 fluid ounces ≈ 355.6ml.

Question. Read the table and find the 3 miles ≈ _____kilometers

Given: Convertor factor table

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 27

To Find: 3 miles ≈ ____ kilometers.

From the chart, we can see that,

1 mile ≈ 1.61 km

3 miles ≈ 3×1.61

3 miles ≈ 4.83km

We concluded that 3 miles ≈ 4.83km.

Question. Read the table and find the 24 pounds ≈ _______ kilograms.

Given: Conversion factor table

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 28

To Find: 24 pounds ≈ _______kilograms.

From the chart, we can see that,

1 pound ≈ 0.454 kilogram

24 pound ≈ 24×0.454

24 pounds ≈ 10.89 kg

We concluded that 24 pounds ≈ 10.89kg.

Question. Read the table and find the 7 gallons ≈ _______ liters.

Given: Conversion factor table

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 7 Applying Ratios and.Rates 29

To Find: 7 gallons ≈ ____ liters.

From the conversion table,

1 gallon ≈ 3.79l

7 gallons ≈ 7×3.79

7 gallons ≈ 26.53l

We concluded that 7 gallons ≈ 26.531.

Go Math! Practice Fluency Workbook Grade 6 Chapter 6 Representing Ratios and Rates Exercise 6.3 Answer Key

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6: Representing Ratios and Rates

Question. Mark uses the ratio of 3 tablespoons of sugar to 2 tablespoons of milk in a recipe. Find the Complete table of the equivalent fractions.

Given: Mark uses the ratio of 3 tablespoons of sugar to 2 tablespoons of milk in a recipe.

To Find: To find the Complete table of the equivalent fractions.

Our fraction is 3/2.

To complete the table multiply fraction by 2/2, so we will get the values of the table.

For finding equivalent fractions write numbers such that division is equal to 3/2

The ratio of sugar and milk is 3/2.

To find the equivalent ratio multiply the given ratio by 2/2,

\(\frac{3 \times 2}{2 \times 2}=\frac{6}{4}\)

 

To find the next equivalent ratio multiply 6/4 by 2/2,

\(\frac{6 \times 2}{4 \times 2}=\frac{12}{8}\)

 

To get an equivalent fraction,

For numerator 18 write the denominator in such a way that after dividing we will get 3/2.

So, the number in the denominator will be 12, so, the equivalent fraction is 18/12.

For denominator 20 write the numerator in such a way that after dividing the ratio we will get 3/2.

So, the number in the numerator is 30, so the equivalent fraction is 30/20.

The complete table is

Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6 Representing Ratios and Rates 64

Question. Mark’s ratio is 3 tablespoons sugar to 2 tablespoons milk. Sharri is using 4 tablespoons of sugar to 3 tablespoons of milk. Eve is using 9 tablespoons of sugar to 6 tablespoons of milk. Find the Girl’s ratio equivalent to Mark’s.

Given: Mark’s ratio is 3 tablespoons sugar to 2 tablespoons milk. Sharri is using 4 tablespoons of sugar to 3 tablespoons of milk. Eve is using 9 tablespoons of sugar to 6 tablespoons of milk.

Go Math! Practice Fluency Workbook Grade 6 Chapter 6 Representing Ratios and Rates Exercise 6.3 Answer Key

To find: Girl’s ratio equivalent to Mark’s

Write ratios in fraction form.

Reduce the ratios of Sharri and Eve if it is possible.

If the reduced answer is similar to Mark’s it is the answer.

Mark’s ratio is 3 tablespoons sugar to 2 tablespoons milk. So, the ratio is 3/2.

Sharri is using 4 tablespoons of sugar to 3 tablespoons of milk. So, the ratio is 4/3

Eve is using 9 tablespoons of sugar to 6 tablespoons of milk. So, the ratio is 9/6

It can be reduced by dividing the numerator and denominator by 3.

So, the ratio is 3/2

Eve’s ratio is equivalent to Mark’s.

Question. The school cafeteria makes cheese sauce by using 15 cups of Swiss cheese and 17 cups of cheddar cheese. Perry uses 5 cups of Swiss cheese and 7 cups of cheddar cheese. Find that is perry using the correct ratio.

Given: The school cafeteria makes cheese sauce by using 15 cups of Swiss cheese and 17 cups of cheddar cheese. Perry uses 5 cups of Swiss cheese and 7 cups of cheddar cheese.

To find: Is Perry using the correct ratio

We have Perry’s ratio as 5/7 and the school cafeteria’s ratio as 15/17.

There is not any number multiplied by 5/7 that gives 15/17, so the ratio is not equivalent.

Hence, Perry is not using the correct ratio as 5/7 is not equivalent to 15/17.

Perry is not using the correct ratio because 15/17 is not equivalent to 5/7.

Question. The price of 6 tickets for the tournament is $15 which is bought by the Chess club. Find the total money paid for 9 members.

Given: The price of 6 tickets for the tournament is $15 which is bought by the Chess club.

To Find: The Total money paid for 9 members.

Find the unit rate of a ticket for 6 members for a price of $15

Multiply the unit rate by 9 to get the cost of tickets for 9 members.

The chess club bought tickets for 6 members for a price of $15.

The price of a ticket for 1 member is

→15/6 ( dividing price by the number of members)

Dividing the numerator and denominator by 6,

\(\frac{15}{6} \div \frac{6}{6}=\frac{2.5}{1}\)

 

The price of the ticket is $2.5 per member.

To find ticket prices for 9 members

Multiply the price of a ticket for 1 member by 9,

$2.5×9 = $22.5

They have paid $22.5 if all 9 members want to go.

Question. Car averages 22 miles per gallon of gas. How far a car can travel on 5 gallons of gas.

Given: car averages 22 miles per gallon of gas.

To find: how far a car can travel on 5 gallons of gas

We know the car’s average is 22 miles per gallon of gas, for 5 gallons of gas, we will multiply the average per gallon by 5,

→ 22×5=110 miles

They can travel 110 miles on 5 gallons of gas.

Question. Café A offers 2 free bottled glasses of water or juices for every 20 purchased. Café B offers 3 free bottled glasses of water or juices for every 25 purchased. Café A’s ratio of free drinks to purchased drinks.

Given: Café A offers 2 free bottled glasses of water or juices for every 20 purchased. Café B offers 3 free bottled glasses of water or juices for every 25 purchased.

To find: Café A’s ratio of free drinks to purchased drinks

Free bottled waters of Café A are 2.

The purchased juice of Café A is 20.

To write the ratio of free water bottles to purchased juice divide free bottled water by purchased juice.

The ratio of free drinks to purchased drinks of Café A is 2/20

Dividing the numerator and denominator by 2, we get a ratio of 1/10.

Café A’s ratio of free drinks to purchased drinks is 1/10

Question. Make a list of equivalent fractions of 2/3 and 3/4. Compare ratios by using the list.

Given : 2/3 and 3/4

To find: Compare ratios by using the list.

Make a list of equivalent fractions of 2/3 and 3/4.

Highlight fractions from lists in which we have the same denominator.

Compare highlighted fractions.

List of fractions equivalent to 2/3 : 2/3 ,4/6 ,6/9, (8/12) ,10/15,…

List of fractions equivalent to 3/4 : 3/4 ,6/8 ,(9/12) ,12/16 ,…

We have highlighted ratios with equal denominators.

Ratios with the same denominator from the list are 8/12 and 9/12.

Comparing the ratios we get,

8/12<9/12

So, 2/3<3/4.

Using the list of equivalent ratios of 2/3 and 3/4, and comparing the ratios with equal denominators, i.e. ​

2/3 = 8/12 and 3/4 = 9/12

​the relation is obtained 2/3<3/4.

Question. Make a list of equivalent fractions of 4/5 and 3/7. Compare ratios by using the list.

Given : 4/5 and 3/7

To find: Compare ratios by using the list.

Make a list of equivalent fractions of 4/5 and 3/7.

Highlight fractions from lists in which we have the same denominator.

Compare highlighted fractions.

List of fractions equivalent to 4/5 : 4/5 ,8/10 ,12/15 ,16/20 ,20/25 ,24/30 ,(28/35)…

List of fractions equivalent to 3/7 : 3/7 ,6/14 ,9/21 ,12/28 ,(15/35)…

We have highlighted ratios with equal denominators.

Ratios with the same denominator from the list are 28/35 and 15/35.

Comparing ratios we get, 28/35 > 15/35

So, 4/5 > 3/7

The comparison of the ratio is 4/5 > 3/7

Question. Jack’s recipe for oatmeal uses 3 cups of oats to 5 cups of water. Evan’s recipe uses 4 cups of oats to 6 cups of water. Compare the ratio of who makes thicker oatmeal.

Given: Jack’s recipe for oatmeal uses 3 cups of oats to 5 cups of water. Evan’s recipe uses 4 cups of oats to 6 cups of water.

To find: Compare the ratio of who makes thicker oatmeal.

Write the ratio of Jack and Evan of oats to water.

Make a list of equivalent fractions and highlight fractions with the same denominator.

Compare the ratios.

Jack’s recipe for oatmeal uses 3 cups of oats to 5 cups of water.

The ratio of Jack’s recipe of oats to water is 3/5

Evan’s recipe uses 4 cups of oats to 6 cups of water.

The ratio of Jack’s recipe of oats to water is 4/6.

Reducing the ratio by dividing both sides by 2 we get,

The ratio of Jack’s recipe of oats to water is 2/3

List of fraction equivalent to 3/5 : 3/5 ,6/10 ,(9/15) ,12/20,…

List of fraction equivalent to 2/3 : 2/3 ,4/6 ,6/9 ,8/12 ,(10/15),…

We can compare 9/15 and 10/15 : 9/15 < 10/15

So, 3/5 <2/3

Comparing the ratios of oats to the water we say that Evan makes the thicker oatmeal.

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