Ratios and Proportional Relationships: math practice, Grade 7

Rate this post

Math practice Grade 7 : Ratios and Proportional Relationships — Zyro the alien explorer of Planète Maths

22 problems graded by difficulty (★ easy, ★★ medium, ★★★ hard). Try first, without looking at the solutions!

1 Price per ounce ★★★

A 15-ounce box of raisins costs $4.20.

Find the unit price in dollars per ounce.
At the same unit price, how much would a 22-ounce box cost?

2 Swimming speed ★★★

Cara swims $ \dfrac{1}{4} $ mile in $ \dfrac{1}{5} $ hour. Find her speed in miles per hour.

3 A proportional table ★★★

Does this table show a proportional relationship? Explain.

x	3	6	9	12
y	7.5	15	22.5	30

4 Not proportional ★★★

Does this table show a proportional relationship? Explain.

x	1	2	3	4
y	4	7	10	13

5 Printer speed ★★★

A printer prints 18 pages in 3 minutes at a steady rate. Let $ x $ be minutes and $ y $ be pages.

Find the constant of proportionality.
Write an equation.
How long does it take to print 42 pages?

6 True or false? ★★★

Decide whether each statement is true or false, and justify.

A straight line through $ (0, 0) $ is the graph of a proportional relationship.
A curve that passes through $ (0, 0) $ is the graph of a proportional relationship.
A straight line through $ (0, 2) $ and $ (4, 10) $ is the graph of a proportional relationship.

7 The point (1, r) ★★★

The graph of a proportional relationship passes through $ (4, 14) $. Here $ x $ is pounds of apples and $ y $ is the cost in dollars.

What is the point on the graph with $ x = 1 $?
Explain what it means.
How much do 10 pounds cost?

8 A slow snail ★★★

A snail crawls $ \dfrac{2}{3} $ foot in $ \dfrac{1}{4} $ hour.

Find its speed in feet per hour.
How far does it crawl in $ 1\dfrac{1}{2} $ hours?

9 Scaling a recipe ★★★

Using $ 2\dfrac{1}{4} $ cups of flour, Jonas makes $ \dfrac{3}{4} $ of a batch of muffins.

How many cups of flour make one full batch?
How many cups are needed for $ 2\dfrac{1}{2} $ batches?

10 Fill in the table ★★★

This table shows a proportional relationship. Find the missing value and write the equation.

x	4	7	10	16
y	14	24.5	35	?

11 Gas mileage ★★★

A car uses 3 gallons of gas to travel 96 miles. Let $ x $ be gallons and $ y $ be miles.

Write the equation $ y = kx $.
How far can the car go on 7.5 gallons?
How many gallons are needed for 400 miles?

12 Better buy ★★★

Store A sells 5 pounds of rice for $13.50. Store B sells 8 pounds of the same rice for $20.80. Which store has the lower unit price?

13 Two runners ★★★

The graph shows the distance in meters run by Ana and Ben after $ x $ seconds.

Find each runner’s speed.
Write an equation for each runner.
After 12 seconds, how much farther has Ben run than Ana?

14 Mixing paint ★★★

Blue and white paint are mixed in the ratio $ 3:5 $. How many liters of each are in 24 liters of the mixture?

15 Jacket on sale ★★★

A $64 jacket is 15% off, and then 5% sales tax is added to the sale price. What is the final cost?

16 Fractions in a table ★★★

The table shows values of $ x $ and $ y $.

x	$ \dfrac{1}{2} $	$ \dfrac{3}{2} $	$ \dfrac{5}{2} $
y	$ \dfrac{3}{4} $	$ \dfrac{9}{4} $	$ \dfrac{15}{4} $

Show that the relationship is proportional.
Write the equation and find $ y $ when $ x = 4 $.

17 Find the error ★★★

Mia says the table below is proportional “because $ y $ goes up by 3 every time.”

x	2	4	6
y	5	8	11

Explain why Mia is wrong.
Change the values of $ y $ for $ x = 4 $ and $ x = 6 $ so that the table is proportional.

18 Two pumps ★★★

Pump A fills $ \dfrac{3}{4} $ of a tank in $ \dfrac{1}{2} $ hour. Pump B fills $ \dfrac{5}{8} $ of an identical tank in $ \dfrac{1}{4} $ hour. Working together at these steady rates, how many minutes do they need to fill one whole tank?

19 Markup then discount ★★★

A store buys a skateboard for $40 and marks the price up by 35%. Later it takes 20% off the marked price.

Find the marked price and the final price.
The final price is what percent more than the $40 the store paid?

20 Reading a map ★★★

On a map, $ \dfrac{3}{4} $ inch represents $ 1\dfrac{1}{2} $ miles.

How many inches on the map represent 1 mile?
Write an equation with $ x $ miles and $ y $ inches.
Two towns are $ 4\dfrac{3}{8} $ inches apart on the map. How many miles apart are they?