CROSS MULTIPLICATION

MATH

When two fractions have the same exact value, multiplying the numerators by the denominators will give the same answer.

for example:
8/12= 2/3
-these two fractions have the same exact value

8×3=24
12×2=24

This proves they are identical in value

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

To this:
ad = bc

Knowing this simple fact is useful. With this we can use a technique called 'cross multiplication'. Cross multiplication has two uses
1. It can tell us which of two fractions is larger
2. It can help us solve variables or the missing piece of information in an equation

WHICH IS THE GREATER FRACTION?

Cross-multiplication is a handy math skill to know. You can use it for a few different purposes. For example, you can compare fractions and find out which is greater.

For example, suppose you want to find out which of the following three fractions is the greatest:

3/5   5/9   6/11

Cross-multiplication works only with two fractions at a time, so pick the first two:

3/5 cross multiply with 5/9

3×9=27
5×5=25

Because 27 is greater than 25, you know now that 3/5 is greater than 5/9. So you can throw out 5/9.

Now do the same thing for 3/5 and 6/11:

3/5 cross multiply with 6/11

3×11=33
6×5=30

Because 33 is greater than 30, 3/5 is greater than 6/11. Pretty straightforward, right?

SOLVING VARIABLES

If a 4ft tree cast an 8ft shadow, how long of a shadow does an 8ft tree cast?

4:8 = 8:x

4x = 8×8
4x = 64
x= 16

Remember the formula?
a:b = c:d

Which is:
ad = bc


KNOWN AS THE RULE OF THREE, WAS UNDERSTOOD BY HEBREWS IN THE 15TH CENTURY