Ratios and Proportions

Solving Proportions

Solve a proportion a/b = x/d using cross- multiplication: x = (a·d) / b.

solve-proportion To solve a/b = x/d: - Cross-multiply: a·d = b·x. - Divide both sides by b: x = (a·d)/b.

Example

Use cross multiplication and inverse operations to solve a proportion.

highlighted = computed this step

Step 1 — Set up

Set up the relationship.

34=x12\frac{3}{4} = \frac{x}{ 12 }
Start with 3/4 = x/12.34left ratiox12right ratio=Cross products compare opposite corners of the equal ratios.

Step 2 — Cross multiply

Cross multiply: 3 x 12 = 36.

3×12=363 \times 12 = \hl{36}
Known cross product: 3 x 12 = 36.34left ratiox12right ratio=3 x 12 = 36Equality means the opposite cross product is also 36.

Step 3 — Write the equation

The other cross product is 4x, so 4x = 36.

4x=364 x= \hl{36}
The other cross product must match: 4x = 36.34left ratiox12right ratio=3 x 12 = 364x = 36Keep the balance level: 4x equals 36.

Step 4 — Divide by coefficient

Divide by 4: x = 36 / 4 = 9.

x=36÷4=9x= 36 \div 4 = \hl{9}
Divide both sides by 4: x = 36 / 4 = 9.34left ratio912right ratio=3 x 12 = 364 x 9 = 36divide both sides by 4x = 9Dividing both sides by 4 leaves one x.

Step 5 — Result

Read the final result.

x=9x= 9
Check with x = 9: both cross products are 36.34left ratio912right ratio=3 x 12 = 364 x 9 = 36divide both sides by 4x = 93 x 12 = 36 and 4 x 9 = 36.