How to Times, Divide & Add Fractions

By Suzanne Akerman
Learning to work with fractions can be daunting, but with a little practice, you'll become confident in your skills.
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A fraction is a number that has two parts, a numerator and a denominator, with a line in between representing division. One half, 3/4 and 25/24 are all fractions. When the number on the top --- the numerator --- is smaller than the number on the bottom --- the denominator --- the fraction is called "proper," which means it is less than 1. When the numerator is the larger of the two numbers, the fraction is improper. Working with fractions can be tricky because each term has two parts, but with a little practice, you can add, multiply and divide fractions easily without a calculator.

Multiplying Fractions

Line up the two fractions that you want multiplied together horizontally on the page with a multiplication sign in between them. The numerators should be positioned directly across from each other, as should the denominators.

Multiply the numerator of the first fraction by the numerator of the second fraction. Write the product in the numerator position (on top) of your answer.

Multiply the denominator of the first fraction by the denominator of the second fraction. Write the product in the denominator position (on the bottom) of your answer. If you have more than two fractions to multiply together, line them all up and multiply all of the numerators together for the numerator of the answer and multiply all of the denominators together to get the denominator of the answer.

Dividing Fractions

Line up the fractions you would like to divide with the number you are diving BY in the second position. Do not line up more than two fractions.

Flip the numerator and denominator of the second fraction. For example, if you previously had 2/5, reverse the fraction to be 5/2 or if you had 56/100, switch the numbers to be 100/56. Line up the resulting fraction with the first fraction, which remains unchanged.

Multiply the numerators together and write the product in the numerator of your answer. Multiply the denominators together and write the product in the denominator of your answer. This is your final answer. If you want to divide more than two fractions, you must do them in order, first dividing by one fraction, then dividing the answer you get by the third fraction. Do not line them all up and work across, as you can do with multiplication of fractions.

Adding Fractions

Compare the denominators of the two fractions you want to add. If they are not the same number, you must first find a common denominator, which is a number that both denominators can evenly divide into. For instance, if you have 2/10 and 3/5, choose the number 10 as the denominator because 10 goes in evenly once and 5 goes in evenly twice.

Multiply the first fraction by the number of times its denominator goes into the common denominator. For 2/10, since 10 is the common denominator, we multiply by 1, which does not change the fraction at all: we still have 2/10 for our first fraction.

Multiply the second fraction by the number of times its denominator goes into the common denominator. For 3/5, since 5 goes into 10 twice, we will multiply the fraction by 2 or 2/1. The resulting fraction is 6/10.

Line up the two resulting fractions, now that their denominators are equal. Add the numerators together and write the sum in the numerator position of your answer. Write the common denominator you chose in the denominator position of the answer. If you want to add more than two fractions, change all of them to have the common denominator, then line them up and add the numerators together.

About the Author

Suzanne Akerman began writing in 2000. She has worked as a consultant at Pacific Lutheran University's Writing Center and her works have been published in the creative arts journal "Saxifrage." Akerman holds a Bachelor of Arts in English and a Master of Arts in education from Pacific Lutheran University.