How do you simplify a fraction?

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.

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

To simplify a fraction, you need to find the common factor of the numerator (top number) and the denominator (bottom number) and then divide both the numerator and the denominator by this common factor. This process reduces the fraction to its simplest form. For example, to simplify the fraction 8/12, you would find that the common factor of 8 and 12 is 4. Dividing both the numerator and denominator by 4 results in the simplified fraction 2/3. (8 divided by 4 = 2 and 12 divided by 4 = 3= 2/3 two thirds). Top tip- whatever you do to the top number, you have to do to the bottom number.

Find the highest common factor (HCF) of the top and bottom number, and then divide the top and bottom number by the HCF, to simplify the fraction.

1) You look for a number that will go into both the top and bottom number:

Example:

40/70

The number 2 can go into both of these - so you divide both of them by 2:

= 20/35

2) After dividing the top and bottom by a number you look to see if it can be further divided by either the same number or a different one

Example:

20 and 35 are both divisible by 5 so now divide 20/35 by 5:

= 4/7

This works for all fractions.

*To do it quicker you can look for the largest number both numbers are divisible by so the 40/70 is also both divisible by 10 which would make it the 4/7 in one step. It is okay to need to break it down slowly though and do it in a few steps!

1. List out the common factors for the numerator and denominator.

The numerator is the number on the top of the fraction. The denominator is the number on the bottom.

Factors are numbers that divide into a number, evenly.

e.g Question: Simplify 8/32.

So factors of 8 are 1, 2 , 4 , 8.

Factors of 32 are 1, 2, 4 , 8 , 16 , 32

2. Find the highest common factor in both.

e.g. 1, 2, 4, 8 are factors in both.... But 8 is the highest one so use this.

3. Divide by the highest common factor.

e.g. 8÷8 = 1

32÷8 = 4

Therefore the answer is 1/4.

4. Then with practise, it won't be necessary to list all the factors. You can stop when you get to the highest common factor.

To simplify a fraction, you must be knowledgeable of your times tables and the idea of the Highest Common Factors.

Look at your fraction and try to, by looking at the numbers, see if they are both in the same times tables. For example:

Simplify 18/54.

Here we can see that 18 and 54 are both in the 9 times tables so we divide both the numerator and denominator by 9.

18/9 = 2 and,

54/9 = 6

so we get 2/6.

BUT we are not done yet because 2 goes into both 2 and 6. We do the same process again and get our final answer as

1/3

Hope this helps :)

Divide both numerator and denominator by the same number I.e 2 if 2 is divisible by both numbers. In order to get the most simplified fraction divide by the highest number that goes into both numbers of the fraction

A fraction is a number with numerator and denominator

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

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.

Take a fraction 15/9

You see different numbers on numerator (top)and denominator (bottom).

Check whether that both the numbers are multiples of common number.

Here 9 and 15 are multiples of 3.

Next step is divide both the numbers by 3.

Or 15/3=5 and 9/3=3 so the answer is 5/3.

Now 5 and 3 are not multiples of common number. So this is the simplified answer. Hope you understand it.

Next example is if 12/13.

You don't have a common number which has 12 and 13 as it multiples. So you can't simplify it.

You use the multiples of the numbers given for example. 6/9 has a multiple of 3 ,therefore we divide both the top and bottom by 3 this would result in 2/3 which is the most simplified form.Top tip : what ever you do to the top , you must do to the bottom.

To simplify a fraction you will need to find the HCF (highest common factor) of the numerator and denominator and divide them by it.

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 !