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# How do you simplify a fraction?

2 years ago

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108 Replies

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6342 views

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Jermain Ankunding

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Asma Aswat
1. Reduce fractions to the lowest term.
2. Convert the improper fraction to mixed numbers
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Qualified Teacher / PhD Researcher

Hi Jermain,

Here's how you can simplify a fraction:

1. Find the Greatest Common Divisor (GCD) of the numerator and the denominator. This is the largest number that divides both the numerator and the denominator evenly.
2. Divide the numerator and the denominator by the GCD:
3. Write the fraction in its simplified form by putting the result of the division as the new numerator and denominator.

Hope this helps :)

I'm available for 1:1 private online tuition!

D
Daisy Gerrard

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

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Fei Yu

You will need to find out the factors shared by the denominator and numerator. Once you can find the shared factors, the fraction can be simplified by dividing the denominator and the numerator by the same factors. It is common that this process might have to be repeated a few times until no more shared factors can be found. For example, 20 / 100 = (20 / 2) / (100 / 2) = (10 / 2) / (50 / 2) = (5 / 5) / (25 / 5).

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Rakshitha

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

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Harry Saxton-Martin

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.

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Ishmael Laurent-Dixon

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

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Arya

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.

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Alina J

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

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Mizba Hussain

To simplify a fractions you must divide both the top and the bottom number by the same amount until your answer is no longer a whole number.

For example: 15/35 simplified is 15 divided by 5 is 3 and 35 divided by 5 is 7. So our answer is 3/7

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Indhuvaruni

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

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Chloe Kirkbright

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.

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Jeremy Franklin

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.﻿

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Alex Bastos

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

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Robyn M

Hey Jermain,