Proportions & Ratios · Grades 6–8

Ratios & Proportions Worksheets

Ratio and proportion worksheets: simplify first, then solve by cross-multiplication. Similar-figure problems included, and the missing value always works out to a whole number.

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What it is

A proportion is two equal ratios. Because the ratios are equal, their cross-products are equal too, which is what lets you solve for a missing value.

Why it matters

Proportional reasoning underlies percentages, scale drawings, unit conversions, similar figures, and rates, one of the most widely used ideas in everyday math.

How to do it

  1. To simplify a ratio, divide both parts by their greatest common factor.
  2. To solve a proportion, cross-multiply, then divide to isolate the unknown.
  3. Keep corresponding parts in the same order on both sides (width to width, cost to cost).

Examples by level

  • Beginner
    228?
    Find the missing side =8
  • Intermediate
    226?
    Find the missing side =6
  • Advanced
    5215?
    Find the missing side =6

Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.

Common mistakes

  • Cross-multiplying the wrong pairs.
  • Not keeping corresponding parts in the same order (width to width, cost to cost).
  • Forgetting to reduce the final ratio to lowest terms.

Tips

  • Cross-multiply, then divide, the same move solves any proportion.
  • Always write the two ratios in the same order.

For parents

Read a proportion as 'this is to that as this is to that', and keep the order consistent on both sides.

For teachers

Have students label the units on each part of the ratio; it prevents the classic 'crossed pairs' error when setting up the proportion.

Key vocabulary

ratio
a comparison of two quantities, written a : b or a/b
proportion
an equation stating that two ratios are equal

Frequently asked questions

How do you solve a proportion?
Cross-multiply (multiply each numerator by the opposite denominator) then divide to isolate the unknown value.
What is the difference between a ratio and a proportion?
A ratio compares two quantities (3 : 4); a proportion is an equation stating that two ratios are equal (3/4 = 6/8).

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