Divide and Multiply Fractions

To multiply fractions, all you have to do is multiply the numerators and denominators and simplify the result. To divide fractions, you simply have to flip the numerator and denominator of one of the fractions, multiply the result by the other fraction, and simplify. If you want to know how to divide and multiply fractions in no time at all, just follow these steps.

Steps

Multiplying Fractions

  1. Multiply the numerators of the fractions. The numerator is the number on the top of a fraction and the denominator is the number on the bottom. The first step to multiplying fractions is to line them up so that their numerators and denominators are next to each other. If you're multiplying the fraction 1/2 by 12/48, then the first thing you want to do is multiply the numerators, 1 and 12. 1 x 12 = 12. Write the product, 12, in the numerator of the answer.
  2. Multiply the denominators of the fractions. Now, you'll just have to do the same thing with the denominators. Multiply 2 and 48 to find the new denominator. 2 x 48 = 96. Write this answer in the denominator of the new fraction. Therefore, the new fraction is 12/96.
  3. Simplify the fraction. The last step is to simplify the result if it can be done. To simplify a fraction, you have to find the greatest common factor (GCF) of both the numerator and the denominator. The GCF is the largest number that can be evenly divided into both numbers. In the case of 12 and 96, 12 happens to evenly divide into 96. So, divide 12 by 12 to get 1, and divide 96 by 12 to get 8. Therefore, 12/96 ÷ 12/12 = 1/8.
    • If both numbers are even, you can also start by dividing them both by 2 and keep going. 12/96 ÷ 2/2 = 6/48 ÷ 2/2 = 3/24. Then you may notice that 3 goes evenly into 24, so you can divide both the numerator and denominator by 3 to get 1/8. 3/24 ÷ 3/3 = 1/8.

Dividing Fractions

  1. Reverse the numerator and denominator of the second fraction and change the division sign to a multiplication sign. Let's say you're dividing the fraction 1/2 by 18/20. Now, find the reciprocal of 18/20 which is 20/18 and change the division sign to a multiplication sign. So, 1/2 ÷ 18/20 = 1/2 x 20/18.
  2. Multiply the numerators and denominators of the fractions and simplify your answer. Now, do the same thing you would do to multiply. If you multiply the numerators, 1 and 20, you get the result of 20 in the numerator. If you multiply the denominators, 2 and 18, you get 36 in the numerator. The product of the fractions is 20/36. 4 is the largest number that is evenly divisible by both the numerator and the denominator of this fraction, so divide each by 4 to get the simplified answer. 20/36 ÷ 4/4 = 5/9.



Tips

  • Double check your work.
  • Don't ever forget to simplify.
  • Remember: Whole numbers can be expressed as a fraction: 2 is the same as 2/1 .
  • Cross-cancelling can be used at anytime to save yourself work simplifying. Cross-cancelling is dividing the diagonals by a common factor. For example, the problem (8/20)*(6/12) can be cross-cancelled to (2/10)*(3/3).
  • Always double check your work. Have a doubt ? Ask your teacher .
  • Make sure you cross simplify.

Warnings

  • Do it one step at a time. This will minimize the chances of an error.
  • There is always more than one way to do something in math. However, just because you get the right answer once doing a problem a different way doesn't mean that it will always work. Another way to divide fractions, for example, is cross-multiplication, which is multiplying the diagonals.
  • Remember to simplify completely. An incomplete simplification might as well be no simplification at all.

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