We included **H****MH Into Math Grade 6 Answer Key**** PDF** **Module 5 Lesson 3 Compare Ratios and Rates** to make students experts in learning maths.

## HMH Into Math Grade 6 Module 5 Lesson 3 Answer Key Compare Ratios and Rates

I Can compare ratios and rates using a table or a double number line.

**Step It Out**

1. Amari makes orange juice from cans of frozen concentrate and water. The amounts are shown in the picture.

A. Amari wants to make 4 pitchers of orange juice. Complete the table to find how many cups of water and cups of frozen concentrate she will need.

Answer:

For 1 pitcher he needs 3 cups of water and 2 cups of frozen concentrate.

For 2 pitchers he needs 6 cups of water and 4 cups of frozen concentrate.

For 3 pitchers he needs 9 cups of water and 6 cups of frozen concentrate.

For 4 pitchers he needs 12 cups of water and 8 cups of frozen concentrate.

For 5 pitchers he needs 15 cups of water and 10 cups of frozen concentrate.

Thus the ratio of cups of water to frozen concentrate is 3:2.

B. Amari’s friend Gabriela also makes orange juice from the same frozen concentrate.

Using the table, write a rate to represent Gabriela’s recipe.

Answer:

From the table, we can see that for 4 cups of water she will need 3 cups of frozen concentrate.

C. Whose orange juice has a weaker flavor, Amari’s or Gabriela’s?

Step 1 Find a ratio in Gabriela’s table that has the same first quantity as a ratio in Amari’s table.

Amari: In row ____, she uses cups of concentrate.

Gabriela: In row ___, she uses cups of concentrate.

Step 2 Compare the number of cups of water used in each ratio.

Amari uses ___ cups of water while Gabriela uses ___ cups of water. ___ uses more water than ____. So, ____ orange juice will have a weaker flavor.

Answer:

Step 1 Find a ratio in Gabriela’s table that has the same first quantity as a ratio in Amari’s table.

Amari: In row 1, she uses 2 cups of concentrate.

Gabriela: In row 1, she uses 3 cups of concentrate.

Step 2 Compare the number of cups of water used in each ratio.

Amari uses 3 cups of water while Gabriela uses 4 cups of water. Gabriela uses more water than Amari. So, Gabriela’s orange juice will have a weaker flavor.

**Turn and Talk** Is there another way you could have compared the recipes for orange juice? Explain.

2. Mrs. Morales teaches computer programming. Each student writes an average of 9 lines of code per hour.

A. Complete the double number line to find how many lines of code a student could write in a given number of hours.

Answer:

The ratio of lines per hour is 9 : 1.

9 lines per hour.

18 lines for 2 hours

27 lines for 3 hours

36 lines for 4 hours

45 lines for 5 hours

54 lines for 6 hours

63 lines for 7 hours

B. Ms. Sanchez also teaches computer programming. Each of her students is able to write an average of 4 lines of code every 20 minutes. Write a rate using the quantity 1 hour. Then describe what it means.

Answer:

1 hour = 60 minutes

1/3 × 60 = 20 minutes

2/3 × 60 = 40 minutes

3/3 × 60 = 60 minutes

4/3 × 60 = 80 minutes

5/3 × 60 = 100 minutes

6/3 × 60 = 120 minutes

Students can write 12 line in 1 hour.

C. Two ratios can be compared if both have the same amount of one of the two quantities being compared. Which class writes code faster? Explain.

__________________

Answer:

Ms. Sanchez’s students write 12 lines in 1 hour.

The ratio of Ms. Sanchez’s students is 12 : 1

Mrs. Morales’s students write 9 lines in 1 hour.

The ratio of Mrs. Morales’s students is 9 : 1

Mrs. Morales’s class writes codes faster than Ms. Sanchez’s.

**Check Understanding**

Question 1.

Compare the ratios in the tables. Are they equivalent? Explain.

Answer:

**Sam’s Trail Mix:**

The ratio of Cups of raisins to Cups of peanuts = 3:5

3 Cups of raisins/5 Cups of peanuts

6/10 = 3/5 = 3:5

9/15 = 3/5 = 3:5

**Liams Trail Mix:**

The ratio of Cups of raisins to Cups of peanuts = 2:3

2 Cups of raisins/3 Cups of peanuts

4/6 = 2/3

6/9 = 2/3

Thus the ratios are equivalent.

Question 2.

Ms. Markus also teaches computer programming. Each of her students is able to write an average of 5 lines of code every 30 minutes. Which class, Ms. Markus’ class or Ms. Sanchez’s class, writes code faster? Explain.

Answer:

Given,

Ms. Markus also teaches computer programming.

Each of her students is able to write an average of 5 lines of code every 30 minutes.

Ms. Sanchez’s students write 12 lines in 1 hour.

5 lines for 30 minutes

2/2 × 60 = 2 × 30 = 60

3/2 × 60 = 90 minutes

4/2 × 60 = 120 minutes

5/2 × 60 = 150 minutes

Ms. Markus’s students write 10 lines in 1 hour.

12 is greater than 10.

Thus Ms. Sanchez’s students write faster than Ms. Markus’s students.

**On Your Own**

Question 3.

A track coach has runners perform drills to practice for a track meet. Each runner is supposed to run 5 sprints for every 4 full laps. Megan runs 11 sprints for every 8 full laps. Did Megan use the correct ratio for her running drills?

A. Complete each table.

Answer:

The ratio of each runner is 4:5

The ratio of Megan is 8:11

B. Compare the ratio of sprints to laps that each runner is supposed to run to the ratio of sprints to laps that Megan ran during practice. What row in each table has the same first or second quantity? How can you use that quantity to compare the ratios?

______________________________

______________________________

______________________________

Answer:

The ratio of each runner is 4:5

The ratio of Megan is 8:11

4/5 is greater than 8/11

The ratio of runner is greater than Megan.

C. Did Megan use the same ratio of sprints to laps that her coach asked her to run?

______________________________

______________________________

Answer: Yes

8 : 11

16:22 = 8:11

24:33 = 8:11

32:44 = 8:11

D. **Reason** Suppose that Megan wants to run more sprints and laps. How many of each could she run so that her total sprints and total laps are in the ratio that the coach wanted? Explain.

______________________________

______________________________

______________________________

______________________________

Answer:

Question 4.

Vivian scored 8 out of 10 on a quiz. Ramona scored 3 out of 4. Did Vivian and Ramona get equivalent scores? Explain.

______________________________

Answer:

Question 5.

In art class, Greg makes gray paint by mixing 3 parts black paint to 8 parts white paint, while Tim makes gray paint by mixing 4 parts black paint to 9 parts white paint. Whose paint will be darker? Explain.

Answer:

Given,

In art class, Greg makes gray paint by mixing 3 parts black paint to 8 parts white paint.

The Ratio is 3:8

Tim makes gray paint by mixing 4 parts black paint with 9 parts white paint.

The ratio is 4:9

The ratios can be written in the fraction to find which is greater.

4/9 is greater than 3/8

4/9 > 3/8

The ratio of mixing the paint of Tim’s (4/9 > 3/8) is greater than Greg’s.

Thus Tim’s paint will be darker than Greg’s paint.

Question 6.

Two pet stores both sell canaries and parrots. The ratio of canaries to parrots for each store is shown in the double number lines. Are the ratios equivalent? Explain how you know.

Answer:

Given,

Two pet stores both sell canaries and parrots. The ratio of canaries to parrots for each store is shown in the double number lines.

Pet Store 1:

The ratio of parrots to the Canaries is 6:10 = 3:5

Pet Store 2:

The ratio of parrots to the Canaries is 9:15 = 3:5

Yes the ratios of pet store 1 and pet store 2 are equal.

Thus both are equivalent ratios.

Question 7.

A wildlife manager is stocking fish in several ponds. The manager puts 6 yellow perch for each pair of largemouth bass in the first pond. The manager’s assistant put 54 yellow perch and 16 largemouth bass in a second pond. Did the assistant use the correct ratio of perch to bass in the second pond? Explain your reasoning.

Answer:

Given,

A wildlife manager is stocking fish in several ponds.

The manager puts 6 yellow perch for each pair of largemouth bass in the first pond.

The manager’s assistant put 54 yellow perch and 16 largemouth bass in a second pond.

Manager ratio = 6:2 = 3:1

Assistant ratio = 54:16 = 27:8

No Assistant does not use the correct ratio of perch to bass in the second pond.

**Lesson 5.3 More Practice/Homework**

**Compare Ratios and Rates**

Question 1.

Two farms grow lettuce and tomatoes as shown on the labels.

A. Complete the double number line to find equivalent ratios to 3 acres of lettuce to 7 acres of tomatoes.

Answer:

Explanation:

3 × 2 : 7 × 2 = 6:14

3 × 3 : 7 × 3 = 9:21

3 × 4 : 7 × 4 = 12:28

B. Complete the double number line to find equivalent ratios to 2 acres of lettuce to 5 acres of tomatoes.

Answer:

2:5

2 × 2 : 5 × 2 = 4 : 10

2 × 3 : 5 × 3 = 6 : 15

2 × 4 : 5 × 4 = 8 : 20

C. Which farm has a greater ratio of acres of lettuce to acres of tomatoes? How do you know?

Answer: Madsen farms have a greater ratio of acres of lettuce to acres of tomatoes.

**For Problems 2-3, use the following information.**

Four students in Mr. Morales’ math classes are conducting surveys in their school. They each handed out 100 surveys. The table shows the response rates of each student’s survey.

Question 2.

Did Min-seo and Orlando get the same ratio

Answer:

The ratio of Min-seo is 4:5

The ratio of Orlando is 8:10 = 4:5

Thus Min-Seo and Orlando get the same ratio has the same ratio.

Question 3.

Did Jian and Leona get the same ratio of responses? Explain.

Answer:

The ratio of Jian is 3:4

The ratio of Leona is 10:12 is 5:6

Jian and Leona do not have the same ratio of responses.

Question 4.

At Wild Bill’s Wildlife Sanctuary, there are 3 elephants for every 2 rhinos. At Westside Wildlife Sanctuary, there are 15 elephants for every 8 rhinos. Do the two wildlife sanctuaries have the same ratio of elephants to rhinos? Explain.

Answer:

Given,

At Wild Bill’s Wildlife Sanctuary, there are 3 elephants for every 2 rhinos.

At Westside Wildlife Sanctuary, there are 15 elephants for every 8 rhinos.

As for wild bill’s wildlife sanctuary, it is 3:2

As for westside wildlife sanctuary its 15:8

The ratios are not the same.

**Test Prep**

Question 5.

Mark uses 10 cups of apple juice and 16 cups of orange juice to make fruit punch. Deon uses an equivalent ratio of apple juice to orange juice when he makes fruit punch. Which ratio of apple juice to orange juice could Deon use? Choose all that apply.

A. 5 cups of apple juice for every 8 cups of orange juice

B. 15 cups of apple juice for every 16 cups of orange juice

C. 20 cups of apple juice for every 32 cups of orange juice

D. 30 cups of apple juice for every 48 cups of orange juice

E. 40 cups of apple juice for every 56 cups of orange juice

Answer: A. 5 cups of apple juice for every 8 cups of orange juice

Explanation:

Given,

Mark uses 10 cups of apple juice and 16 cups of orange juice to make fruit punch.

Deon uses an equivalent ratio of apple juice to orange juice when he makes fruit punch.

The ratio is 10/16 = 5/8

Thus option A is the correct answer.

Question 6.

Gabby uses 5 cups of corn and 6 cups of lima beans to make succotash. Robert uses 7 cups of corn and 9 cups of lima beans to make succotash. Are the ratios of corn to lima beans equivalent? Explain why or why not.

Answer:

Given,

Gabby uses 5 cups of corn and 6 cups of lima beans to make succotash.

Robert uses 7 cups of corn and 9 cups of lima beans to make succotash.

The ratio 5:6 and 7:9 are not the same.

No, the ratio of corn to lima beans is not equal because the total amount of succotash is not the same.

Question 7.

Milla ran 3 miles in 21 minutes. Fatima ran 5 miles in 35 minutes. Are the ratios of miles to minutes equivalent? Explain why or why not.

Answer: Yes

Explanation:

Given,

Milla ran 3 miles in 21 minutes.

The ratio is 3 : 21 = 1 : 7

Fatima ran 5 miles in 35 minutes.

5:35 = 1:7

Thus the ratios of miles to minutes are equivalent.

**Spiral Review**

Question 8.

What is the magnitude of -9? ____

Answer: The magnitude of -9 is 9.

Explanation:

The magnitude of a single number is the positive version of that number. It is also known as the absolute value.

|-9| = 9

Question 9.

Write an inequality to compare -10 and |-10|.

Answer:

Inequality is a statement that two quantities are not equal.

We can write the inequality with two numbers to locate the numbers on the number line and mark them.

Here, the positive integer 10 comes to the right of -10.

Therefore “10” is greater than “-10”

It can be written as 10 > -10.

And -10 comes to the left of 10.

Therefore “-10” is smaller than “10”

It can be written as -10 < 10

Question 10.

Find the quotient of \(\frac{3}{7}\) ÷ \(\frac{1}{3}\). __________________

Answer:

Given fractions,

\(\frac{3}{7}\) ÷ \(\frac{1}{3}\)

The denominators of both the fractions are not the same.

Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.

Take the inverse of the second fraction and change the operation.

\(\frac{3}{7}\) × \(\frac{3}{1}\) = \(\frac{9}{7}\)

\(\frac{9}{7}\) is an improper fraction so we have to convert into the mixed fraction.

\(\frac{9}{7}\) = 1 \(\frac{2}{7}\)