# Cross Multiply

To cross multiply is to go

from this:

To

a × d = b × c

Table of Contents

## How Does it Work?

Multiplying the top (numerator) and bottom (denominator) of a fraction by the same amount doesn’t change its value.

So, To cross multiply:

1. Multiply the top and bottom of the left side fraction by the bottom number of the right side fraction.
2. Multiply the top and bottom of the right side fraction by the bottom number that the left side fraction had.
3. We can get rid of the b × d (as we are dividing both sides by the same amount) and the equation is still true

 Step 1 Step 2 Step 3      a × d = b × c

Example

cross-multiplied form of

Is

4 × 14 = 7 × 8

## Cross multiplication Application

Cross multiplication can help speed up a solution. Like in this

Examples

Find x in Cross Multiply:

x2 = 3 × 12 = 36

x = 6 or x = -6

Substitute both x values to the first form

We cannot use Cross Multiply when a denominator (b or d) is zero, as dividing by zero is undefined.

## Learn More

Multiplication Tables

Fractions

Rationalize the Denominator

Conjugate

Algebra Index