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

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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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