How do you simplify a fraction?

1. Reduce fractions to the lowest term.
2. Convert the improper fraction to mixed numbers

Think of the highest, common factor (HCF) of both the numerator and the denominator, then divide both by that number, that way, you will get the fraction in its most simplest form.

For example: the H.C.F. of 20/30 is 10, so:

20 / 10 = 2

30 / 10 = 3

So 20/30 in it's simplest form is 2/3.

You are able to simplify a fraction if the numerator and denominator can both be divided by the same number. For example if you had 3/12 you need to ask yourself, can you divide 12 by 3? If yes then how many times does it go? It goes 4 times. Therefore it can be simplified to 1/4

Divide the top (numerator) and bottom (denominator) numbers by factors of the number. The aim is to get it into it's simplest form (where you can't divide it anymore)

EG 10/100 - you can divide the top and bottom by 2 to get 5/50 then again by 5 to get 1/10 or you can simply divide it by 10 to start with and get 1/10

A simplified fraction is a fraction that has the smallest denominator (bottom number) possible.

The rule for simplifying fractions is as follows: whatever mathematical operation you perform on the denominator, you must also do to the numerator (top number).

Let us look at some examples: 24

Simplify 32

As both numbers are even, the easiest method is to halve each number until you can go no lower:

12 6 3

16 8 4

We can also look to see if the numbers are common multiples (if they can be divided by the same number other than two). In this case, they are both in the 8 times table:

24 3

32 divided by 8 4

42

Simplify 49

With these numbers, we cant use the tried and tested method of halving each number until you can go no further. Again we can look if the numbers can be divided by the same number. In this case they are both in the 7 times table, so we should divide both numbers by 7:

42 6

49 divided by 7 7

You find a whole number which can divide evenly into both the numerator and denominator and then divide both sides by that number. For example, if we had 6/12 as a fraction, we know that 6 divides into both 6 and 12. We can then divide both sides by 6 to get 1/2.

You do this by looking to see if there’s a common factor between the numerator and denominator (a number both numbers can be divided by) then dividing both by this number. Then keep doing that until you can’t anymore.

for example 14 and 12 can both be divided by 2, so 12/14 simplified is equal to 6/7.

You can also use one of the numbers in the fraction as the divider; 4 and 16 are both divisible by 4 so 4/16 simplifies to 1/4.

Hope this helps

You need to find a number that can divide into both the numerator and the denominator.

Take for example 2/4. Both these numbers are divisible by 2, and by dividing both by 2 you get 1/2. As 2 divided by 2 is 1, and 4 divided by 2 is 2 hence 1/2.

By dividing both the numerator and the denominator by a common factor.

divide the numerator and denominator by the same number

Divide both the numerator and the denominator by HCF to get the simplified fraction.

The quickest way is to take out the highest common factor from both and then divide - but remember what we do to the top number (numerator) we must do to the bottom number (denominator) so its key the factor fits into both leaving a whole number.

Don't worry if you can't spot the highest number, you can do it in multiple steps as long as you take the same numbers from both sides of the fraction.

Repeat this step until you end up with a fraction that has no common factors that fit into both the numerator or denominator (easy numbers to spot are prime numbers!).

Lets look at an example in two ways:

10/20:

1) Selecting the highest common factors of both numbers would be 10.

Dividing 10 by 10 gives us 1, which is now our new numerator.

Then dividing 20 by 10 gives us 2, which is now our new denominator.

Putting those together now gives us 1/2.

We cannot simplify this further as dividing something by 1 just gives us 1.

2) If you couldn't initially spot that 10 fit into both, start with a much simpler number such as 2.

Dividing both numbers by 2 would get us 5/10.

Look for any other common factors in both, in this case 5 fits into both.

Again divide by the common factor in this case that would get is 1/2.

We cannot simplify this further as dividing something by 1 just gives us 1.

Both give the same answer but one is quicker, but here my top tips would be doing the same to both the numerator and denominator and also ensuring both numbers are divisible by the factor.

Find a common number in which the numerator and denominator are both divisible by and then continue to do this until it the numerator and denominator no longer have a common factor.

You can simplify a fraction if both the top and bottom number can be divided by the same number. For example 8/18... both numbers can be divided separately by 8. If you do this, the top number (numerator) will become 1 and bottom (denominator) 2 = 1/2

Hey Jermain,

This may help: https://www.youtube.com/watch?v=PcEwj5_v75g