Learning target: A proportion states that two ratios are equal. Use equivalent ratios or cross-products to find an unknown value.
STEP 01
What is a proportion?
Two ratios form a proportion when they describe the same relationship.
Example
2/3 = 8/12
Both ratios equal the same amount. Multiplying the numerator and denominator of 2/3 by 4 produces 8/12.
STEP 02
Solve using multiplication
Look for the scale factor when one pair of corresponding numbers is easy to compare.
Example
3/5 = x/20
Since 5 × 4 = 20, multiply the numerator by 4 as well: x = 12.
STEP 03
Solve using cross-products
In a proportion a/b = c/d, the cross-products are equal: a × d = b × c, provided the denominators are not zero.
Example
4/7 = x/21
- Multiply diagonally: 4 × 21 = 7x.
- Simplify: 84 = 7x.
- Divide by 7: x = 12.
STEP 04
Check your answer
Substitute your value back into the original proportion and confirm that both ratios are equal.
Try it: 5/6 = x/18. Show answer
6 × 3 = 18, so x = 5 × 3 = 15.
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