# Solving Proportions

#### Grade 7 Math Worksheets

**To solve a proportion, you need to find the value of an unknown variable that makes two ratios equal.**

Table of Contents:

- Solving Proportions
- Solved Example
- FAQs

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## Solving Proportions - Grade 7 Math Worksheet PDF

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## Solving Proportions

To solve a proportion, you need to find the value of an unknown variable that makes two ratios equal. Here are the steps to solve a proportion:

Write the proportion: Use the format “a/b = c/d” to write the proportion. The variables “a” and “c” represent the numerators of the ratios, while “b” and “d” represent the denominators.

**Cross-multiply:** Multiply the numerator of one ratio by the denominator of the other ratio, and vice versa. This gives you two equations that you can use to solve for the unknown variable.

Solve for the unknown variable: Use algebraic techniques to isolate the unknown variable in one of the equations. Then, substitute the value you find into either of the original ratios to check if the proportion is true.

### Here’s an example:

Suppose you have the proportion 3/5 = x/20. To solve for x, you would follow these steps:

**Write the proportion: 3/5 = x/20.**

Cross-multiply: Multiply the numerator of the first ratio by the denominator of the second ratio, and vice versa. This gives you:

3(20) = 5x

60 = 5x

Solve for the unknown variable: Divide both sides of the equation by 5 to isolate x. This gives you:

x = 12

Check the proportion: Substitute the value of x back into either of the original ratios to make sure the proportion is true. For example:

3/5 = 12/20

0.6 = 0.6

Since both sides of the equation are equal, the proportion is true and the value of x is correct.

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## Solved Example

Suppose you have the proportion 2/3 = x/9. To solve for x, you would follow these steps:

**Write the proportion: 2/3 = x/9.**

**Cross-multiply:** Multiply the numerator of the first ratio by the denominator of the second ratio, and vice versa. This gives you:

2(9) = 3x

18 = 3x

Solve for the unknown variable: Divide both sides of the equation by 3 to isolate x. This gives you:

x = 6

Check the proportion: Substitute the value of x back into either of the original ratios to make sure the proportion is true. For example:

2/3 = 6/9

0.666… = 0.666…

Since both sides of the equation are equal, the proportion is true and the value of x is correct. Therefore, x = 6 is the solution to the proportion.

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## Solving Proportions FAQS

##### What is a proportion?

A proportion is a statement that two ratios are equal. It can be written in the form “a/b = c/d”, where “a” and “c” are the numerators of the ratios, and “b” and “d” are the denominators.

##### How do you solve a proportion?

To solve a proportion, you need to find the value of an unknown variable that makes the two ratios equal. This can be done by cross-multiplying and then solving for the unknown variable using algebraic techniques.

##### What does it mean to cross-multiply?

Cross-multiplying means multiplying the numerator of one ratio by the denominator of the other ratio, and vice versa. This results in two equations that can be used to solve for the unknown variable.

##### What are some algebraic techniques used to solve proportions?

Algebraic techniques used to solve proportions include dividing both sides of the equation by the same value, combining like terms, and distributing operations.

##### How do you check if a solution to a proportion is correct?

You can check if a solution to a proportion is correct by substituting the value of the unknown variable back into either of the original ratios and verifying that the two sides of the equation are equal.

##### Can proportions be solved using decimals or fractions?

Yes, proportions can be solved using decimals or fractions. However, it is usually easier to work with fractions or mixed numbers because they can be simplified more easily.

**Gloria Mathew** writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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