Ratios & Proportions

A ratio compares two separate quantities or two parts of a whole, and can be written as a:b or a/b. A fraction always represents one part of a whole. For example, if a recipe calls for 2 cups of flour to 3 cups of sugar, the ratio of flour to sugar is 2:3. But the fraction of flour in the total mixture would be 2/5 (since 2+3=5 total cups). Understanding this difference helps you know when to use ratios versus fractions.

Two ratios are equivalent if multiplying or dividing both numbers in one ratio by the same number gives you the other ratio. For example, 2:3 and 4:6 are equivalent because if you multiply both parts of 2:3 by 2, you get 4:6. You can also write both ratios as fractions and check if they simplify to the same number: 2/3 = 4/6 both equal about 0.67.

The order matters because ratios describe relationships between specific quantities. If you say 'the ratio of boys to girls is 3:2,' that's different from saying 'the ratio of girls to boys is 2:3,' even though they use the same numbers. The first number always describes the first quantity mentioned, and the second number describes the second quantity. Always read the problem carefully to make sure you write the ratio in the correct order.

Start by writing out both equivalent ratios, using a box or question mark for the missing number. For example, if 2:3 = ?:9, look at what you multiplied the first ratio by to get the second ratio. Since 3 × 3 = 9, multiply the first number by 3 as well: 2 × 3 = 6. So the missing number is 6. You can also use a ratio table to help organize your thinking.