Cross Multiply - Math Is Fun

Home » How Do You Cross Multiply » Cross Multiply - Math Is Fun

Maybe your like

Math is Fun Cross Multiply

To cross multiply is to go

from this: 8 12 = 2 3 to this: 8 × 3 = 12 × 2

How Does it Work?

Multiplying the top and bottom of a fraction by the same amount doesn't change its value.

Step 1: Multiply the top and bottom of the first fraction by the bottom number of the second fraction.

8 × 3 12 × 3 = 2 3

Step 2: Multiply the top and bottom of the second fraction by the bottom number that the first fraction had.

8 × 3 12 × 3 = 2 × 12 3 × 12

And Magic! The bottom of both fractions is now 12 × 3

Step 3: We can get rid of the 12 × 3 (as we are dividing both sides by the same amount) and the equation is still true:

8 × 3 = 12 × 2

Job Done!

In practice, though, it is easier to skip the steps and go straight to the "cross-multiplied" form.

Using Variables

The general case, using variables instead of numbers, is:

To cross multiply is to go from this: a b = c d To this:ad = bc

To remember think cross (x) multiply: cross multiply illustration

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

Example: Find "x" in x 8 = 2 x

Start with: x 8 = 2 x Cross multiply:x2 = 8 × 2Calculate:x2 = 16And solve:x = 4 or −4

Check: Does 4 8 = 2 4 and −4 8 = 2 −4 ?

Terminology

fraction numerator denominator

I said "top" and "bottom" of the fractions ... but the correct words are numerator and denominator, OK? (I just wanted to keep it simple.)

Caution: Zero

Be careful, though!

We cannot use it when a denominator ("b" or "d" above) is zero, as dividing by zero is illegal.

334,335, 2045, 2046, 3174, 3175, 3176, 3876, 3877, 3878 Algebra Index Fractions Index Mean Proportional Copyright © 2025 Rod Pierce

Tag » How Do You Cross Multiply