Cross Multiply
To cross multiply is to go from this:8=2123To this:8 × 3 = 12 × 2How Does it Work?
Step 1: When you multiply the topandbottom of a fraction by the same amount, it doesn't change its value.
Example (first fraction above):8=8× 31212× 3
In that example I multiplied the top and bottom of the first fractionby the bottom number of the second fraction.
Step 2: We could also multiply the top and bottom of thesecondfraction by the bottom number of thefirstfraction.
Example (second fraction above):2=2× 1233× 12
Step 3: And we would then have:
8× 3=2× 1212× 33× 12
And Magic! The bottom ofbothfractions is now12 × 3... !
Step 4: We can get rid of the12 × 3(because 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
So far I have used numbers, but we can state it more generally using variables:
To cross multiply is to go from this:a=cbdTo this:ad = bc
How to remember: "cross" multiply:
Example
Cross multiplication can help speed up a solution. Like in this example:
Find "x":
x=28xLet's cross multiply:x
2= 8 × 2 = 16And solvex = 4 or -4
Terminology
I have been saying "top" and "bottom" of the fractions ... but the correct words arenumeratoranddenominator, OK?
(I just wanted to keep it simple.)
