How to Solve a Proportion

Step-by-step solution

1. Cross-multiply.

   $$3x = 6 \times 5$$

   Why: Cross-multiplication turns a proportion into a simple equation.

2. Multiply the right side.

   $$3x = 30$$

   Why: 6 times 5 is 30.

3. Divide both sides by 3.

   $$\frac{3x}{3} = \frac{30}{3}$$

   Why: Dividing by the coefficient leaves x alone.

4. Write the answer.

   $$x = 10$$

   Why: 10/6 and 5/3 are equal when both are reduced.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $\frac{x}{4} = \frac{3}{2}$

   Show answer

   $x = 6$

2. 2

   $\frac{2}{5} = \frac{x}{15}$

   Show answer

   $x = 6$

3. 3

   $\frac{x}{8} = \frac{1}{2}$

   Show answer

   $x = 4$

4. 4

   $\frac{3}{7} = \frac{9}{x}$

   Show answer

   $x = 21$

5. 5

   $\frac{x}{10} = \frac{2}{5}$

   Show answer

   $x = 4$