We included **HMH Into Math Grade 7 Answer Key PDF** **Module 1 Review **to make students experts in learning maths.

## HMH Into Math Grade 7 Module 1 Review Answer Key

**Vocabulary**

constant of proportionality

proportional relationship

ratio

scale

scale drawing

unit rate

**Choose the correct term from the Vocabulary box.**

Question 1.

the quantity k in a relationship described by an equation of the form y = kx

Answer: **Constant of proportionality** the quantity k in a relationship described by an equation of the form y = kx.

Question 2.

a rate in which the second quantity is one unit

________________

Answer: **Unit rate** is a rate in which the second quantity is one unit.

Question 3.

a relationship between two quantities in which the rate of change or the ratio of one quantity to the other is constant

________________

Answer: A relationship between two quantities in which the rate of change or the ratio of one quantity to the other is constant is called a proportional relationship.

**Concepts and Skills**

Question 4.

Which ratio is equivalent to the scale 3 in.: 1 ft?

Answer:

1/4 ÷ 2/3 = 3/8

2 ÷ 2/3 = ~~2~~ × 3/~~2~~ = 3/1 = 3:1

Option B is the correct answer.

Question 5.

**Use Tools** A news radio program has 3 commercial breaks per half-hour of programming. What is the unit rate of commercials to hours of programming? State what strategy and tool you will use to answer the question, explain your choice, and then find the answer.

Answer:

Given,

A news radio program has 3 commercial breaks per half-hour of programming.

3 breaks = 1/2 hours

For 1 hour

1 = 3 × 2 = 6 breaks

1 hour = 6 breaks

Now for the Unit rate of a break to an hour is

6 breaks = 1 hour

1 break = 1/6 hours

Thus the answer is 1/6 hours

Question 6.

A recipe calls for 2 cups of sugar for \(\frac{1}{4}\) cup of butter. What is the unit rate for sugar to butter? __________

Answer:

A recipe calls for 2 cups of sugar for \(\frac{1}{4}\) cup of butter.

\(\frac{1}{4}\) = 0.25

0.25/2 = 0.125

Unit rate of sugar to butter is 1 to 0.125

Divide both sides by 0.25

0.25/0.25 = 1

2/0.25 = 6

Unit rate of butter to sugar is to

Question 7.

Jana and Jenn are training to run a race. Jana runs 3 miles in \(\frac{1}{3}\) hour. Jenn runs 5 miles in \(\frac{3}{4}\) hour. Who runs faster, and what is the unit rate of her speed in minutes per mile? ________________

Answer:

Given,

Jana and Jenn are training to run a race.

Jana runs 3 miles in \(\frac{1}{3}\) hour. Jenn runs 5 miles in \(\frac{3}{4}\) hour.

1 hour = 60 mins

Jana: 1/3 hour = 1/3 × 60 = 20 minutes

Jana = Time/Distance = 20/3 = 16.7 min/mile

Jenn runs 5 miles in \(\frac{3}{4}\) hour

Jenn: 3/4 hour = 3/4 × 60 = 45 min

Jenn = Time/Distance = 45/5 = 9 min/miles

Jenn runs faster at 9 min/mile

Unit Rate

Jana = 16.7 min/mile

Jenn = 9min/mile

Question 8.

A scale drawing of a rectangular mural has the dimensions 2 inches by 3 inches. The scale is 0.5 inches:5 feet. Find the actual dimensions of the mural. Then find the dimensions of another scale drawing with the scale 0.25 inches:10 feet. ________

Answer:

Given,

A scale drawing of a rectangular mural has the dimensions 2 inches by 3 inches.

The scale is 0.5 inches:5 feet.

2 ÷ (0.5:5) = 20 feet

3 ÷ (0.5:5) = 30 feet

20 × (0.25:10) = 0.5 in

30 × (0.25:10) = 0.75 in.

Question 9.

Write an equation of the form y = kx for the relationship shown in the graph or table.

Answer:

**Write an equation of the form y = kx for the relationship shown in the graph or table.**

Question 10.

__________

Answer:

(2, 8), (4, 12), (6, 16)

Question 11.

Answer:

Question 12.

Use the graph from Problem 10. What is the value of r at the point with coordinates (1, r)? What does this point mean in terms of the proportional relationship shown in the graph?

________________________

________________________

Answer:

Question 13.

A store sells beans for 80tf per pound.

A. Graph the proportional relationship that gives the cost y in dollars of buying x pounds of beans.

________________________

Answer:

B. Write an equation of the form y = kx to represent this relationship.

________________________

Answer: y = 0.8x

C. A farmers’ market sells organic locally grown beans for $1.25 per pound. How much more would it cost to buy 3 pounds of beans at the farmers’ market than at the store?

________________________

Answer:

3 × 1.25 – 3 × 0.8

3.75 – 2.4 = 1.35