Verify Proportions

Proportion says two ratios (or fractions) are equal in value.

Example:

Both 13 and 26 are ratios

We see that 1-out-of-3 is equal to 2-out-of-6

The ratios are the same, so they are in proportion.

Learn more at Proportion. Here we focus on checking or verifying a proportion.

What Are Means and Extremes?

When a proportion is written like this:

a : b = c : d

• a and d are the extremes (the outside numbers)
• b and c are the means (the inside numbers)

Verifying a Proportion

To verify whether two ratios are proportional, we use this rule:

The product of the means equals the product of the extremes

This is cross multiplication. Here we use it to check the proportion.

Checking Proportions Using Equivalent Fractions

Another way to check a proportion is to simplify each fraction.

This method uses number sense and is often quicker when the numbers are small.

Solving vs Verifying a Proportion

It is important to know the difference:

• Verifying a proportion means checking whether two ratios are equal
• Solving a proportion means finding an unknown value

Ratio and Rate

A ratio compares two quantities.

A rate is a special kind of ratio that compares quantities with different units, such as distance and time.

Summary

• Equivalent ratios can be written as a proportion
• The outside numbers are the extremes
• The inside numbers are the means
• If the product of the means equals the product of the extremes, the ratios are proportional
• Proportions can also be checked by simplifying fractions