Simplify ratios to lowest terms, solve the missing value in a proportion, or scale a ratio to a target total.
A ratio compares two or more quantities, showing how many times one value contains another. Ratios are written as A:B and can be simplified, scaled, or used to solve proportions — equations where two ratios are set equal to each other.
To simplify a ratio, divide both numbers by their greatest common factor (GCF). For example, 24:36 shares a GCF of 12, simplifying to 2:3. This is the same process used to reduce a fraction to its lowest terms.
A proportion states that two ratios are equal, such as A:B = C:D. Using cross-multiplication (A × D = B × C), you can solve for any single missing value as long as the other three are known.
To split a total amount according to a ratio, add the parts of the ratio together to find the total number of "shares," then multiply the target total by each part's fraction of that sum. A 2:3 ratio splitting $100 gives $40 and $60, since the ratio has 5 total shares.
A ratio compares two separate quantities (like 2 cups flour : 3 cups sugar), while a fraction represents a part of a single whole. That said, a ratio A:B can always be written as the fraction A/B, and they simplify using the same math.
Keep the ratio between ingredients constant. If a recipe uses a 1:2 ratio of butter to sugar and you want to use 150g of butter, scale the sugar to 300g to keep the same ratio and preserve the recipe's balance.
Yes — ratios can compare three or more quantities, like 1:2:3. The same simplification rule applies: divide every term by the greatest common factor shared across all of them.