How to Multiply Fractions Using the GCF Method
Before you can completely understand decimals and percentages, you must know fractions. The basic operations for fractions include addition, subtraction, division and multiplication. If you can multiply two one-digit numbers together, you can easily multiply fractions. But you will often have to reduce the fraction for your final answer. That means you use the lowest numbers possible. Sometimes students have difficulty reducing the answer to the lowest terms. If you can find the greatest common factor, or GCF, of the numerator and denominator, however, you can quickly reduce the fraction.
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Instructions
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Multiply First, Then Reduce
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1
Multiply your numerators together. In the problem 3/4 times 5/6, multiply the 3 and 5. This will give you 15. Write this number on top of your division symbol.
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2
Multiply your denominators together. Using the example problem, multiply the denominators 4 and 6. This will give you 24. Write this number below your division symbol.
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3
List the factors of your numerator. This means the numbers that divide into 15 without a remainder. Factors are also the numbers you multiply together to make a particular number. For example, the factors of 15 are 1, 3, 5 and 15.
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4
List the factors of your denominator. In this case, the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
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5
Look at your list of factors. Find the largest factor that goes into the numerator and denominator. For 15 and 24, the answer is 3.
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6
Divide your numerator by the largest common factor. Write your answer above the division symbol. Next, divide your denominator by the same number, and write your answer below the division symbol. For the sample problem, the answer reduces to 5/8.
Find the Greatest Common Factor, Then Multiply
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7
Find the greatest common factor before you multiply by checking the numerator of one fraction with the denominator of the other fraction. In 3/4 times 5/6, the numerator 3 has a common factor with 6.
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8
Divide the numerator by the largest factor that goes into both numbers. For any number, its largest factor is itself. Three is the largest common factor for both 3 and 6. Three divided by 3 is 1.
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Divide the denominator of the other fraction by the same number. Six divided by 3 equals 2. The other numerator and denominator do not have a common factor, so you will not change these numbers before you multiply.
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Multiply across. Instead of 3/4 times 5/6, the reduced fractions are 1/4 times 5/2. When you multiply the numerators together, then the denominators, you get 5/8. Whether you reduce the fraction by the GCF before or after you multiply, if you do it correctly, you'll get the same answer.
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Tips & Warnings
If you can't find a greatest common factor, don't get discouraged. Some fractions will not have common factors, and you can't reduce them. In this case, simply multiply across.
Always divide the numerator and denominator by the same common factor. For example, in 15/24, you would not divide the 15 by 5 and the 24 by 8. They must both be divided by the same number, or you will get the wrong answer.
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