Proportions

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When two ratios have the same value, they can form a

proportion.

A proportion is an equation that shows that two ratios are equal.

For example, the ratio of circles to triangles is the same in both sets of shapes below. The first ratio is 1 circle for every 2 triangles, or

The second ratio is 2 circles for every 4 triangles, or

So, the ratios

and

can form the proportion

Here are some more examples of proportions:

3
4
=
9
12
4:5 = 8:10

How can you tell if two ratios form a proportion?

To tell if two ratios can form a proportion, compare them. It can help to write the ratios as fractions with

common denominators

If the

fractions are equivalent

they can form a proportion.

Let's try it! Determine if

and

form a proportion.

Compare the fractions. Write them to have common denominators. You can use a denominator of 45.

Since

is equivalent to

the ratios

and

can form the following proportion:

Try some practice problems!

Do the ratios form a proportion?

Solving proportions

Some proportions use a variable to stand for an unknown quantity. You can solve for the variable in different ways.

Solving proportions using cross multiplication

You can use cross multiplication to solve proportions. Follow these steps:

Multiply the values across corners of the proportion. Write an equation where the products are equal.
Solve the equation
.

Let's try it for

First, multiply the values across corners of the proportion. Multiply the number in the top left by the number in the bottom right. Then, multiply the number in the bottom left by the number in the top right. Write an equation where the products are equal.

Now, solve for

300

Divide both sides of the equation by 15.

So,

Therefore,

Solving proportions using inverse operations

Another method for solving proportions is to get the variable alone using inverse operations.

Let's try it for

Multiply both sides of the proportion by

Multiply both sides of the proportion by 15.

300

Divide both sides of the equation by 6.

300

Divide both sides of the equation by 6.

So,

Therefore,

Try some practice problems!

Solve the proportion

Real-world proportion problems

Some real-world problems can be solved using proportions.

Let's try it! Kate uses 2 cups of strawberries to make 6 yogurt parfaits. There is a proportional relationship between the number of cups of strawberries Kate uses and number of yogurt parfaits she makes. How many cups of strawberries will Kate need to make 9 yogurt parfaits?

First, set up a proportion. Use a variable for the unknown number of cups of strawberries.

Then, solve the proportion.

Multiply both sides of the proportion by 9.

So, Kate will need 3 cups of strawberries to make 9 yogurt parfaits.

Try some practice problems!

Solve proportions: word problems

Percent problems

You can use proportions to solve

percent

problems. Percentages are parts per hundred, so you can write them as a fraction with a denominator of 100. You can use the proportion below to solve percent problems.

part

whole

percent

100

Let's try it! What is 5% of 48?

You need to find the part of 48 that represents

5%.