Solving proportions drills

Solve a/b = c/d for an unknown using cross-multiplication.

Free, timed SHSAT practice sets on solving proportions— every question includes a full worked explanation, and there's no account required.

Loading questions…

How to solve proportions

A proportion says two fractions are equal: \(\dfrac{a}{b} = \dfrac{c}{d}\). Solve it in two steps:

  1. Cross-multiply: multiply each top number by the bottom number on the other side, so \(a \times d = b \times c\).
  2. Divide both sides by the number next to \(x\).

Example: \(\dfrac{x}{12} = \dfrac{10}{15}\). Cross-multiply: \(15x = 12 \times 10 = 120\). Divide by 15: \(x = 8\).

Shortcut: simplify first if you can. \(\dfrac{10}{15} = \dfrac{2}{3}\), and \(\dfrac{x}{12} = \dfrac{2}{3}\) gives \(x = 8\) quickly.

Common traps:

Always check: put your answer back in. \(\dfrac{8}{12} = \dfrac{2}{3}\), so it works.

Worked examples

Example 1.
Solve the proportion for \(x\): \(\dfrac{24}{16} = \dfrac{x}{12}\)
Show answer and explanation
Answer:
D

Cross-multiply: \(24 \times 12 = 16 \times x\), which gives \(x = 18\). (Cross-multiplying the wrong diagonal pair gives 8. Stopping at the cross product without dividing gives 288. Keeping the same difference instead of scaling, \(24 + (12 - 16)\), gives 20.)

Example 2.
Solve the proportion for \(x\): \(\dfrac{12}{20} = \dfrac{x}{15}\)
Show answer and explanation
Answer:
B

Cross-multiply: \(12 \times 15 = 20 \times x\), which gives \(x = 9\). (Cross-multiplying the wrong diagonal pair gives 25. Stopping at the cross product without dividing gives 180. Keeping the same difference instead of scaling, \(12 + (15 - 20)\), gives 7.)

Example 3.
Solve the proportion for \(x\): \(\dfrac{3}{4} = \dfrac{x}{20}\)
Show answer and explanation
Answer:
15

Cross-multiply: \(3 \times 20 = 4 \times x\), so \(60 = 4x\) and \(x = 15\).