Equal Ratios: How to Find and Check Them

What Are Equal Ratios?

Two ratios are equal when they express the same relationship between two numbers. Multiplying both sides of a ratio by the same number creates an equal ratio. Starting with 2:3, multiplying both sides by 2 gives 4:6, and multiplying by 3 gives 6:9. All three ratios say the same thing: for every two of the first quantity there are three of the second.

How Do I Check If Two Ratios Are Equal?

The fastest way to check is to simplify both ratios to lowest terms and compare them. If they simplify to the same pair, they are equal. You can also use cross multiplication: two ratios A:B and C:D are equal when A times D equals B times C. For 2:3 and 8:12, 2 times 12 equals 24 and 3 times 8 equals 24, so the ratios are equal.

How Do I Find an Equal Ratio to a Given Ratio?

Multiply both sides of the ratio by any whole number. The ratio 3:5 is equal to 6:10 (multiplied by 2), 9:15 (multiplied by 3), and 12:20 (multiplied by 4). Choose the scale factor based on the total you need. If you need 40 units of the second quantity and the ratio is 1:4, multiply both sides by 10 to get 10:40.

Using Equal Ratios to Scale a Recipe

Equal ratios let you change a batch size without changing the balance of ingredients. A pancake recipe with a flour to milk ratio of 2:1 makes enough for two people. To serve six, multiply both sides by 3 to get 6:3, meaning three times the flour and three times the milk. The ratio stays equal, so the pancakes taste the same.