Practice Ratios in Math

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

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Quick Recap

A ratio compares two or more quantities by showing how many times one contains the other, written as a:ba:b or ab\frac{a}{b}. Unlike fractions, ratios can compare parts to parts, not just parts to wholes.

A recipe that uses 2 cups flour for every 1 cup sugar has a 2:12:1 ratio.

Showing a random 20 of 50 problems.

Example 1

medium
A map has scale 1:50,0001 : 50{,}000. If two cities are 44 cm apart on the map, what is the real distance in km?

Example 2

medium
Simplify the ratio 0.4:1.60.4 : 1.6.

Example 3

easy
Express the ratio 1:41 : 4 as a fraction.

Example 4

easy
Simplify the ratio 36:4836 : 48.

Example 5

hard
A worker can complete a job in 66 days. At the same rate, how many days does it take 33 workers to complete 44 such jobs?

Example 6

easy
If the ratio of red to blue marbles is 4:74 : 7, and there are 2020 red marbles, how many blue?

Example 7

hard
At a concert the ratio of adults to children is 5:25 : 2. There are 8484 more adults than children. How many children are there?

Example 8

easy
If 44 pencils cost $3\$3, what is the unit price per pencil?

Example 9

medium
In a class of 4848 students, the ratio of girls to boys is 5:75 : 7. How many girls are there?

Example 10

medium
If a 55-kg bag of rice costs $8\$8, how much does 1212 kg cost?

Example 11

challenge
Three numbers are in the ratio 2:3:52 : 3 : 5. Their sum is 6060. Find the largest.

Example 12

easy
A class has 1515 boys and 1010 girls. What is the ratio of boys to girls in simplest form?

Example 13

medium
If a:b=2:3a : b = 2 : 3 and b:c=4:5b : c = 4 : 5, find a:b:ca : b : c.

Example 14

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The ratio of cats to dogs in a shelter is 7:57 : 5. If there are 4848 animals total, how many cats?

Example 15

medium
Two numbers are in the ratio 3:73 : 7 and their sum is 5050. Find the two numbers.

Example 16

medium
A class is 25\frac{2}{5} boys. If there are 2020 boys, how many students total?

Example 17

easy
If 33 apples cost $2\$2, how much do 99 apples cost?

Example 18

challenge
Salt water is 20%20\% salt by weight. How much water do I add to 5050 kg of brine to make it 10%10\% salt?

Example 19

hard
A and B share $540\$540 in the ratio 4:54 : 5. Then A gives $x\$x to B so the new ratio is 1:21 : 2. Find xx.

Example 20

medium
Three numbers are in ratio 2:3:52 : 3 : 5 and their sum is 8080. Find each number.
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