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

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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.

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