Ratios Cheat Sheet

Definition

A ratio compares two quantities. It shows how much of one thing there is compared to another.

Example: If there are 3 apples and 2 oranges, the ratio of apples to oranges is 3 to 2.

Ways to Write Ratios

Ratios can be written in three ways: using the word 'to', with a colon (:), or as a fraction.

Example: 3 to 2, 3:2, or 3/2

Order Matters

The order of the numbers in a ratio is important. It tells you which quantity is being compared to which.

Example: The ratio of apples to oranges is different from the ratio of oranges to apples.

Simplifying Ratios

Ratios can be simplified just like fractions. Divide both parts of the ratio by their greatest common factor.

Example: The ratio 6:8 can be simplified to 3:4 by dividing both numbers by 2.

Finding Equivalent Ratios

To find equivalent ratios, multiply or divide both parts of the ratio by the same number.

Example: 2:3 is equivalent to 4:6 (multiply by 2) and 6:9 (multiply by 3).

Solving Ratio Problems

Set up a proportion (two equal ratios) and use cross-multiplication to find the missing value.

Example: If the ratio of boys to girls is 2:3 and there are 8 boys, how many girls are there? 2/3 = 8/x. 2x = 24. x = 12 girls.

Ratio Tables

Ratio tables organize equivalent ratios in a table, making it easier to find relationships between quantities.

Example: A table with columns for 'Apples' and 'Oranges' showing equivalent ratios like 1:2, 2:4, 3:6, etc.

Unit Rate

A unit rate compares a quantity to one unit of another quantity.

Example: If a car travels 100 miles in 2 hours, the unit rate is 50 miles per hour (100 miles / 2 hours).

Ratio as a Fraction

A ratio can be expressed as a fraction, where the first quantity is the numerator and the second quantity is the denominator.

Example: The ratio 1:4 can be written as the fraction 1/4.

Comparing Ratios

To compare ratios, express them as fractions with a common denominator.

Example: To compare 1/2 and 2/5, convert them to 5/10 and 4/10. 5/10 is greater than 4/10, so 1/2 is greater than 2/5.

Ratios and Proportions

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

Example: 1/2 = 2/4 is a proportion.