How to Simplify Fractions

Math is very difficult. It can be easy to forget basic concepts when trying to memorize dozens of different principles and methods. This article will remind you of two methods of reducing fractions.

Table of Contents

Use the greatest common factor

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List the factors of the numerator and denominator. Factories are numbers that, when you multiply them together, get a different number. For example, 3 and 4 are two factors of 12, because you can multiply them together to get 12. To list the factors of a number, you only need to list all the numbers that when multiplying in we get the number, and therefore the number can be divisible by.

List the factors of that number from small to large, without forgetting the number 1 or itself. For example, this is how you would list the factors of the numerator and denominator for the fraction 24/32:
- 24: 1, 2, 3, 4, 6, 8, 12, 24.
- 32:1, 2, 4, 8, 16, 32.

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Find the greatest common factor (GCF) of the numerator and denominator. GCF is the largest number that two or more numbers are divisible by. After you have listed all the factors of that number, all you have to do is find the largest number in both lists.

24: 1, 2, 3, 4, 6, 8 , 12, 24.
32: 1, 2, 4, 8 , 16, 32.
The GCF of 24 and 32 is 8, because 8 is the largest number that both 24 and 32 are divisible by.

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Divide the numerator and denominator by the greatest common factor. Once you’ve found the greatest common factor, all you need to do is divide the numerator and denominator by that number to reduce the fraction to its simplest form. Here’s how:

24/8 = 3
32/8 = 4
The reduced fraction is 3/4.

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Check the result. If you want to be sure that you have reduced the fraction correctly, simply multiply the new numerator and the new denominator by GCF to see if the result is the original fraction. Here’s how:

3 * 8 = 24
4 * 8 = 32
You get the original fraction, 24/32.
- You can also check the fraction to make sure it can’t be reduced any further. Since 3 is prime, it can only be divisible by 1 and itself, and four is not divisible by 3, the fraction is already in its simplest form.

Consecutive division by a small number

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Choose a small number. Using this method, you simply choose a small digit such as 2, 3, 4, 5, or 7 to start. Look at the fraction to see if the numerator and denominator are divisible at least once by the number you choose. For example, if you have the fraction 24/108, don’t choose 5, because neither the numerator nor the denominator has a number that is divisible by 5. However, if your fraction is 25/60, 5 would be a reasonable number. thought to use.

For the fraction 24/32, the number 2 is possible. Since both the numerator and denominator are even, they will be divisible by 2.

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Divide both the numerator and denominator of the fraction by that number. The new fraction will have a new numerator and denominator that is the quotient of dividing both the numerator and denominator of the fraction 24/32 by 2. Here’s how:

24/2 = 12
32/2 = 16
The new fraction is 12/16.

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Repeat. Continue this process. Since both numbers are still even, you can continue to divide them by 2. If only one or both numbers are odd, you can try dividing them by a new number. Here’s what to do if you want to reduce the fraction 12/16:

12/2 = 6
16/2 = 8
The new fraction is 6/8.

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Keep dividing by that number until you can’t divide any more. Both the new numerator and denominator are still even, so you can keep dividing them by 2. Here’s how:

6/2 = 3
8/2 = 4
The new fraction is 3/4.

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Make sure the new fraction cannot be reduced any further. In the fraction 3/4, 3 is prime, so it is only divisible by 1 and itself, and 4 is not divisible by three, so the fraction is already in its simplest form. If the numerator or denominator of the fraction is no longer divisible by the number you selected, you can still divide it by a new number.

For example, if you have the fraction 10/40, and you divide the numerator and denominator by 5, you get a fraction of 2/8. You can’t keep dividing the numerator and denominator by 5, but you can divide them by 2 to get a final result of 1/4.

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Check the result. Multiply 3/4 by 2/2 three times to make sure that the original fraction is 24/32. Here’s how to do it:

3/4 * 2/2 = 6/8
6/8 * 2/2 = 12/16
12/16 * 2/2 = 24/32.
Note that you have divided 24/32 by 2 * 2 * 2, which is equivalent to dividing it by 8, which is the greatest common factor (GCF) of 24 and 32.

List the factors

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Write down your fraction. Leave a space on the right side of your page – you will need to write the factors there.

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List the factors of the numerator and denominator. Write them on two different lists. Starting with 1 and subsequent factors, list them in pairs.

For example, if your fraction is 24/60, start with 24. You would write: 24 — 1, 2, 3, 4, 6, 8, 12, 24
Then switch to 60. You would write: 60 — 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

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Find and divide the numerator whose denominator is the greatest common factor. What is the largest number that appears in the factors of both the numerator and the denominator? Divide both numerator and denominator by that number.

For example, the largest number that is a factor of both numbers is 12. So we divide 24 by 12 and 60 by 12, resulting in 2/5 – reduced fraction!

Using a prime factorization tree

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Find the prime factors of the numerator and denominator. A prime number is a number that cannot be divisible by any number other than 1 and itself. 2, 3, 5, 7, and 11 are examples of prime numbers.

Start with the numerator. From 24, branch out into 2 and 12. Since 2 is already a prime, that branch you’re done! Then split 12 into two other numbers, 2 and 6. 2 is prime — done! Now divide 6 into two numbers: 2 and 3. So you have 2, 2, 2, and 3 as prime numbers.
Switch to the denominator. From 60, branch your tree into 2 and 30. 30 is then divided into 2 and 15. Then divide 15 into 3 and 5, both primes. Now you have the primes 2, 2, 3 and 5.

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Write the factorization of each number. Take the list of prime factors you have for each number and write them out as multiplication. This is to make it easier to see.

So with 24, you have 2 x 2 x 2 x 3 = 24.
With 60, you have 2 x 2 x 3 x 5 = 60

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Cross out common factors. Any number that you see appearing in both the numeric and denominator elements is crossed out. In this case, we have two 2s and a 3 that are common.

We’re left with 2 and 5 — or 2/5! The answer is similar to the method above.

Advice

Ask your teacher if you still have questions about it; they will help you.

Steps

Use the greatest common factor

Consecutive division by a small number

List the factors

Using a prime factorization tree

Advice

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