Content

• Steps
• Advice

Math is difficult. You can easily forget the basics when trying to memorize dozens of different principles and methods. This article will remind you of two methods of fraction reduction.

Steps

Method 1 of 4: Use the largest common factor

1. 

   List the factors of the numerator and the denominator. Factors are numbers that, when you multiply them, get a different number. For example, 3 and 4 are factors of 12, because you can multiply them together to get the product 12. To list the factors of a number, you only need to list all the numbers that when multiplying. in we get that number, and so it can be divisible by it.
   • List the factors of the number from small to large, not forgetting the number 1 or itself. For example, here is how you would list the factors of the numerator and the denominator for the fraction 24/32:
     • 24: 1, 2, 3, 4, 6, 8, 12, 24.
     • 32: 1, 2, 4, 8, 16, 32.

2. 

   
   
   Find the largest common factor (GCF) of the numerator and the 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 available 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.

3. 

   
   
   Divide the numerator and denominator by the greatest common factor. Once you have found your greatest common factor, all you need to do is divide the numerator and denominator by that number to return the fraction to its minimal form. Here's how:
   • 24/8 = 3
   • 32/8 = 4
   • The reduced fraction is 3/4.

4. 

   Check the result. If you want to make sure that you have reduced the fraction correctly, simply multiply the new numerator and the new denominator with GCF to see if the result is your first fractions. 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 cannot be reduced any more. Since 3 is a prime number, it can only be divisible by 1 and itself, and four is not divisible by 3, so this fraction is already in its minimal form.
   advertisement

Method 2 of 4: Divide consecutively by a small number

1. 

   
   
   Pick a small number. Using this method, you simply need to choose a small number such as 2, 3, 4, 5, or 7 to get started. Look at the fractions to see if the numerator and sample are divisible by at least once by the number you choose. For example, if you have the fraction 24/108, don't choose the number 5, because neither the numerator nor the denominator has any number that is divisible by 5. However, if your fraction is 25/60, 5 will be a reasonable number. thought to use.
   • For the fraction 24/32, the number 2 is possible. Since both the numerator and the sample are even numbers, they are divisible by 2.

2. 

   Divide both the numerator and the denominator of the fraction by that number. The new fraction will have the numerator and the new denominator is the quotient of the division both the numerator and the denominator of the fraction 24/32 by 2. Here's how:
   • 24/2 = 12
   • 32/2 = 16
   • The new fraction is 12/16.

3. 

   Repeat. Continue this process. Since both numbers are still even numbers, you can continue to divide them by 2. If only one or both of the numbers are odd, you can try dividing them by a new number. Here's what you do if you want to reduce the fraction 12/16:
   • 12/2 = 6
   • 16/2 = 8
   • The new fraction is 6/8.

4. 

   Continue dividing by that number until you cannot divide further. Both the numerator and the new denominator are still even, so you can continue to divide them by 2. Here's how:
   • 6/2 = 3
   • 8/2 = 4
   • The new fraction is 3/4.

5. 

   Make sure that the new fraction cannot be reduced any further. In the fraction 3/4, 3 is a prime number, so it is divisible by only 1 and itself, and 4 is not divisible by three, so the fraction is already in its minimal form. If the numerator or the 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 will divide the numerator and denominator by 5, you will get a fraction of 2/8. You cannot continue to divide the numerator and the sample by 5, but you can divide them by 2 to get a final result of 1/4.

6. 

   Check the result. Multiply 3/4 by 2/2 three times to make sure 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've divided 24/32 by 2 * 2 * 2, which is equivalent to dividing it by 8, which is the largest common factor (GCF) of 24 and 32.
   advertisement

Method 3 of 4: List the factors

1. 

   Write down your fractions. Leave a blank space on the right side of your page - you'll need to write the factors there.

2. 

   List the factors of the numerator and the denominator. Write them down on two different lists. Start with 1 and the next factors, listing 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, move on to 60, and you'll write: 60 - 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

3. 

   Find and divide the whole numerator by the denominator by the greatest common factor. What is the largest number appearing in the factors of both the numerator and the denominator? Divide both the numerator and the denominator by that number.
   • For example, the largest number that is a factor of both numbers is 12. Hence, we divide 24 by 12 and 60 by 12, resulting in 2/5 - the reduced fraction!
   advertisement

Method 4 of 4: Use a prime factor tree

1. 

   Find the prime factors of the numerator and the denominator. A prime number is a number that cannot be divided 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 into 2 and 12. Since 2 is already a prime number, you're done with that branch! Then split 12 into two other numbers 2 and 6. 2 is a prime number - 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 of which are prime. Now you have prime numbers 2, 2, 3 and 5.

2. 

   Write your analysis as a prime factor for each number. Get a list of the prime factors you have for each number and write them down 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

3. 

   Cross out the common factors. Any numbers that you see appear in both the numeric and denominator elements are crossed out. In this case, we have two numbers 2 and a number 3 that are together.
   • We have 2 and 5 - or 2/5! The answer is similar to the method above.
   advertisement

Advice

• Ask your teacher if you're still wondering about it; They will help you.