Practice Proportional Reasoning in Math

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

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Quick Recap

The ability to recognize and work with multiplicative relationships between quantities. If one quantity doubles, a proportional quantity also doubles — the ratio stays constant.

If 3 pizzas feed 12 people, how many feed 20? Think multiplication, not addition.

Showing a random 20 of 50 problems.

Example 1

easy
A map scale is 1 cm : 5 km. How many km is 4 cm?

Example 2

hard
A car travels 180 miles using 12 gallons. At this rate, how far can it go on 20 gallons?

Example 3

medium
Solve: x+16=53\frac{x + 1}{6} = \frac{5}{3}.

Example 4

medium
If 4 oranges cost \$2.40, how much do 7 oranges cost?

Example 5

challenge
On a map, 3 cm represents 45 km. Two cities are 105 km apart in reality. How far apart on the map?

Example 6

medium
If 7 machines produce 350 widgets per day, how many widgets do 10 machines produce per day?

Example 7

medium
A drink mix uses 3 scoops for 4 cups of water. How many scoops for 10 cups?

Example 8

easy
A recipe ratio of sugar to flour is 1 : 3. If you use 2 cups of sugar, how much flour?

Example 9

medium
A car uses 8 liters of fuel per 100 km. How much fuel for a 250 km trip?

Example 10

medium
A car uses 5 gallons to travel 150 miles. How many gallons to travel 240 miles?

Example 11

hard
If a:b:c=2:3:5a : b : c = 2 : 3 : 5 and the total a+b+c=80a + b + c = 80, find each value.

Example 12

medium
Tip is proportional to bill at a flat 18% rate. If the bill is \$45, find the tip.

Example 13

medium
Three workers paint 60 ft of fence in a day. How much can 5 workers paint in a day (same pace)?

Example 14

easy
A recipe that serves 4 people uses 10 cups of flour. How many cups are needed to serve 10 people?

Example 15

challenge
A 1:50 scale model of a building is 0.4 m tall. How tall is the real building, in meters?

Example 16

easy
If a:b=3:4a : b = 3 : 4 and a=9a = 9, find bb.

Example 17

easy
If 3 pizzas feed 12 people, how many people do 6 pizzas feed?

Example 18

easy
If a photo is enlarged so width goes from 4 in to 12 in, by what factor did it scale?

Example 19

easy
If a recipe for 4 servings uses 2 cups of milk, how many cups for 6 servings?

Example 20

easy
If 6x=25\frac{6}{x} = \frac{2}{5}, find xx.
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