Practice Proportions in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

An equation stating that two ratios are equal, used to find an unknown when three of the four values are known.

If 2 candies cost \$1, then 4 candies cost \$2β€”same proportion.

Showing a random 20 of 50 problems.

Example 1

medium
On a map, 1 inch represents 25 miles. What distance is shown by 4.5 inches?

Example 2

easy
In the proportion ab=cd\frac{a}{b} = \frac{c}{d}, which equation expresses the cross-product rule?

Example 3

medium
3 liters of paint cover 24 square meters. How many liters cover 40 square meters?

Example 4

medium
If yy is directly proportional to xx and y=18y = 18 when x=4x = 4, find yy when x=10x = 10.

Example 5

challenge
If ab=cd\frac{a}{b} = \frac{c}{d}, show that a+cb+d=ab\frac{a + c}{b + d} = \frac{a}{b} (assuming b+d≠0b + d \neq 0).

Example 6

easy
Solve: 37=9x\frac{3}{7} = \frac{9}{x}.

Example 7

easy
Solve x5=615\frac{x}{5}=\frac{6}{15}.

Example 8

medium
A car uses 8 gallons of gas to travel 224 miles. How many gallons are needed for 350 miles at the same rate?

Example 9

easy
Solve the proportion 34=x8\frac{3}{4}=\frac{x}{8}.

Example 10

medium
A blueprint uses 2 inches for every 5 feet. How many feet does 7 inches represent?

Example 11

hard
Three pumps fill a tank in 12 hours. How long would 5 pumps take, working at the same rate?

Example 12

easy
Solve 46=x9\frac{4}{6}=\frac{x}{9}.

Example 13

medium
Solve the proportion: x12=58\frac{x}{12} = \frac{5}{8}.

Example 14

easy
A map scale is 1Β cm50Β km\frac{1\text{ cm}}{50\text{ km}}. How many km does 3 cm represent?

Example 15

medium
A recipe calls for 3 cups of sugar to 8 cups of flour. If you have 20 cups of flour, how many cups of sugar do you need?

Example 16

easy
If 6 pencils cost \$1.50, how much do 2 pencils cost at the same rate?

Example 17

medium
If 5 notebooks cost $8.75\$8.75, how much do 12 notebooks cost?

Example 18

easy
Are 46\frac{4}{6} and 1015\frac{10}{15} equal?

Example 19

medium
If 4 workers build a wall in the same time that the ratio predicts, and 4 workers lay 200 bricks, how many bricks do 10 workers lay at the same rate?

Example 20

easy
If 2 pencils cost \$1, how much do 4 pencils cost at the same rate?
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