How do you simplify a fraction?

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

In order to simplify a fraction, you need to express the both numerator (the number at the top) and denominator (number at the bottom) as a product (so a list of multiplication) of prime factors and then cancel the ten in common between the 2 decomposition. Let's do it together !

Let A = 45/65 be the fraction we want to simplify. We know that :

• 45 = 5*9 and
• 65 = 5*13

Then,

A = 45/65 = 5*9/5*13 = 9/13 since we cancel in the both she of the fraction the in common factor "5".

Do a similar job for every function it works. I give you some exercice to train you :

• 54/85
• 1045/707
• 49/21

If you have more question juste send a message here or book a trial lessons with me !

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

You simplify a fraction by finding the highest common factor that divides both the numerator and the denominator.

The simplest way is to find the HCF (Highest Common Factor), for example 2/4 we know simplifies to 1/2. This is because the HCF of 2 and 4 is 2, divide both 2 and 4 by 2 and you will get 1 and 2 respectively therefore 1/2. Now lets take a much bigger example 640/1024, the highest common factor of these two numbers is 128, divide both of the numbers by 128 and you will reach 5/8. Hopefully this somewhat helps.

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.

To simplify a fraction, you need to find the greatest common divisor or greatest common factor of the numerator (the top number) and the denominator (the bottom number) and then divide both the numerator and denominator by this common factor.

Find a common number between the denominator and numerator, both numbers must be a whole number

Hey Jermain,

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