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

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?

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.
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? __________
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? ________________
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. ________
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.

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

Question 10.

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

Question 11.

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?
________________________
________________________

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.
________________________