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:

- Multiply the top and bottom of the left side fraction by the bottom number of the right side fraction.
- Multiply the top and bottom of the right side fraction by the bottom number that the left side fraction had.
- 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:

*x*^{2 }= 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.