Simplify a ratio, find the missing number in a proportion, or share an amount in a given ratio — with whole-number answers throughout.
Grade 6–Grade 9 · every refresh draws a new set · answer key included
Ratio and proportion worksheets
Find the missing number in each pair of equal ratios.
Ratio and proportion worksheets — answer key
Find the missing number in each pair of equal ratios.
16 problems · US Letter · answer key — 2 sheets, page breaks marked in the preview
A ratio compares two quantities without saying how big either one is, which is exactly what makes it useful and exactly what pupils find slippery: 2 : 3 describes a mixture, a class, or a map, and the numbers themselves mean nothing until something is measured. The three question types here approach it from different sides — simplifying, scaling up, and dividing an amount — and the third is the one that appears in every exam and in every recipe.
Grade 6 to Grade 9, ages eleven to fifteen. Simplifying ratios follows directly from simplifying fractions and can come as early as Grade 5. Sharing an amount belongs in Grade 7 and up, because it needs the idea of a total number of parts.
Simplifying is the natural first page, because it is the fraction skill in different notation. Move to equivalent ratios next, which is scaling. Sharing an amount is the hardest and deserves working space: the method — add the parts, divide the total, multiply back — is three steps, and pupils who try to shortcut it usually divide by one of the ratio numbers instead of by the total number of parts.
Dividing the total by one side of the ratio rather than by the sum of both is the dominant error in sharing questions. In equivalent ratios, the classic fault is adding rather than multiplying: from 2 : 3 a pupil writes 4 : 5 instead of 4 : 6 — the same misconception that appears in equivalent fractions, and worth naming as such. Simplifying stops halfway for the same reason it does with fractions.