Computations with Fractions

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Fractions Cheat Sheet

This cheat sheet provides a basic outline of what you need to know about fractions when you are required to perform computations that involve fractions. Computations refer to addition, subtraction, multiplication and division. You should have an understanding of simplifying fractions and calculating common denominators prior to adding, subtracting, multiplying and dividing fractions.

Multiplying Fractions

Once you remember that the numerator refers to the top number and the denominator refers to the bottom number of a fraction, you are on your way to being able to multiply fractions. You will multiply the numerators, then multiply the denominators and will be left with an answer that may require one additional step: simplifying. Let's try one:

1/2 x 3/4
1 x 3 = 3
2 x 4 = 8
Therefore the answer is 3/8

Dividing Fractions

Again, you need to know that the numerator refers to the top number and the denominator refers to the bottom number. In the case of division of fractions, you will invert the divisor and then multiply. Put simply, turn the second fraction upside down (this is called the reciprocal) and then multiply. Let's try one:

1/2 x 1/3
1/2 x 3/1 (we just flipped 1/3 to 3/1)
3/3 which we can simplify to 1

Notice that I began with Multiplication and Division? If you remember the above, you won't have much difficulty with those two operations as they don't involve calculating the like denominators.

However, when subtracting and adding fractions, were are often required to calculate the like or common denominators.

Adding Fractions

When adding fractions with the same denominator, you leave the denominator as it is and add the numerators. Let's try one:
3/4 + 9/4
13/4 Of course, now the numerator is larger than the denominator so you would simplify and have a mixed number:
3 1/4

However, when adding fractions with unlike denominators, a common denominator needs to be found prior to adding the fraction. Let's try one:
2/3 + 1/4 (the lowest common denominator is 12)
8/12 + 3/12 = 11/12

Subtracting Fractions

When subtracting fractions with the same denominator, leave the denominator as it is and subtract the numerators. Let's try one:
9/4 - 8/4 = 1/4
However, when subtracting fractions without the same denominator, a common denominator needs to be found prior to subtracting the fraction. Let's try one:
1/2 - 1/6 (the lowest common denominator is 6) 3/6 - 1/6 = 2/6 which can be reduced to 1/3

There are times when you'll simplify the fractions when it makes sense.

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Your Citation
Russell, Deb. "Computations with Fractions." ThoughtCo, Jan. 6, 2018, thoughtco.com/fractions-cheat-sheet-2312255. Russell, Deb. (2018, January 6). Computations with Fractions. Retrieved from https://www.thoughtco.com/fractions-cheat-sheet-2312255 Russell, Deb. "Computations with Fractions." ThoughtCo. https://www.thoughtco.com/fractions-cheat-sheet-2312255 (accessed May 24, 2018).