Ratio calculator

How the ratio answers are worked out

Simplifying

A ratio stays the same when every part is multiplied or divided by the same number. To simplify, divide every part by the biggest number that goes into all of them (the greatest common factor). 12:18 becomes 2:3 because 6 divides both. If a part has a decimal, the page first multiplies every part by 10, 100 and so on to make whole numbers: 1.5:2.5 becomes 15:25, then 3:5.

Finding a missing number

Two ratios are equal when their cross products match: in A:B = C:D, A × D = B × C. So if 2:3 = 10:D, then D = 3 × 10 ÷ 2 = 15. This is the same idea as scaling a recipe: if 2 cups of flour need 3 eggs, 10 cups need 15 eggs. The page shows the check, 2 × 15 = 3 × 10.

Sharing an amount

Add the parts of the ratio to find how many equal shares there are, work out what one share is worth, then multiply. Sharing 100 in the ratio 2:3 makes 5 shares of 20, so the amounts are 40 and 60. The answers are exact fractions, so when an amount does not divide evenly the page shows it rounded and marked "about"; round money to the cent and check the total.

Ratios and fractions

A ratio of 2:3 means the first part is 2/5 of the whole, not 2/3, because there are 5 parts in all. The simplify card shows these shares.