## 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

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

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

We have to draw a graph using the table.

Table is

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

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

The graph formed by using the information in the table is

**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.

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

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

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.

The completed table formed using equivalent ratios is

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

Given a table

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

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 1: Integers Exercise 1.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 1: Integers Exercise 1.2 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 1: Integers Exercise 1.3 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 2: Factors and Multiples Exercise 2.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 2: Factors and Multiples Exercise 2.2 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 3: Rational Numbers Exercise 3.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 3: Rational Numbers Exercise 3.2 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 3: Rational Numbers Exercise 3.3 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 4: Operations with Fractions Exercise 4.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 4: Operations with Fractions Exercise 4.2 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 4: Operations with Fractions Exercise 4.3 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 4: Operations with Fractions Exercise 4.4 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 5: Operations with Decimals Exercise 5.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 5: Operations with Decimals Exercise 5.2 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 Chapter 5: Operations with Decimals Exercise 5.4 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 5: Operations with Decimals Exercise 5.5 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 8: Percents Exercise 8.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 8: Percents Exercise 8.2 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 8: Percents Exercise 8.3 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, Chapter 6: Representing Ratios and Rates Exercise 6.2 Answer Key
- 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, Chapter 7: Applying Ratios and Rates Exercise 7.1 Answer Key
- 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, Chapter 7: Applying Ratios and Rates Exercise 7.3 Answer Key
- Go Math! Practice Fluency Workbook Grade 6, Chapter 7: Applying Ratios and Rates Exercise 7.4 Answer Key