Simplifying Fractions

aNQXhknSwrI

To simplify a fraction, divide the top and bottom by the highest number that can divide into both numbers exactly.

Simplifying (or reducing) fractions means to make the fraction as simple as possible.

Why say four-eighths (48 ) when we really mean half ( 12) ?

How do I Simplify a Fraction ?

There are two ways to simplify a fraction:

Try to exactly divide (only whole number answers) both the top and bottom of the fraction by 2, 3, 5, 7 ,... etc, until we can't go any further.

That is as far as we can go. The fraction simplifies to 2 9

Dividing by 2 doesn't work because 35 can't be exactly divided by 2 (35/2 = 17½)

Likewise we can't divide exactly by 3 (10/3 = 3 1 3 and also 35/3=11 2 3 )

No need to check 4 (we checked 2 already, and 4 is just 2×2).

But 5 does work!

That is as far as we can go. The fraction simplifies to 2 7

Notice that after checking 2 we didn't need to check 4 (4 is 2×2)?

We also don't need to check 6 when we have checked 2 and 3 (6 is 2x3).

In fact, when checking from smallest to largest we use prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...

Divide both the top and bottom of the fraction by the Greatest Common Factor (you have to work it out first!).

The largest number that goes exactly into both 8 and 12 is 4, so the Greatest Common Factor is 4.

Divide both top and bottom by 4:

That is as far as we can go. The fraction simplifies to 2 3

OK, there is a third method, use this tool:

numbers/images/fraction-simplify.js

Also ... see an animation of Fractions on the Number Line where you can see many common fractions and their simpler version.

We also have a chart of fractions with the simplest fraction highlighted.

918,919, 1380, 1381, 3543, 3544, 1379, 3545, 3546, 3547