Add and Subtract Fractions

Method

Adding and Subtracting Fractions

The first step in adding and subtracting fractions is to check if they share the same denominator. Here, the methods of performing these operations on fractions and how to convert unlike fractions to like fractions will be discussed with examples.

Adding and Subtracting Like Fractions

To add or subtract like fractions, add or subtract the numerators and keep the denominator the same.

a/c + b/c=a + b/c [1.3em] a/c - b/c=a - b/c

Adding and Subtracting Unlike Fractions

Unlike fractions must first be converted to like fractions when adding or subtracting. One way to convert them is to multiply the numerator and denominator of each fraction by the denominator of the other. Then, the given operation can be performed.

a/c + b/d=ad + bc/cd [1.3em] a/c - b/d=ad - bc/cd

Another way is to find the least common denominator (LCD) of the fractions. Consider the example of subtracting 712 from 415. 4/15 - 7/12 The result can be found in four steps.

1
Find the Least Common Denominator
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The least common denominator is the least common multiple of the numbers in the denominators. 4/15 - 7/12 The numbers need to be expressed as a product of their prime factors to find their LCM.

Denominator Prime Factorization
15 3 * 5
12 2^2 * 3

The least common denominator is the product of the highest power of each prime factor. LCD: 2^2 * 3 * 5 = 60

2
Rewrite Each Fraction Using the LCD
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The LCD is 60. Now the fractions will be multiplied by the appropriate factor to make their denominators equal to 60. The first fraction must be multiplied by 4 and the second fraction by 5 to get the LCD.

4/15 - 7/12
4 * 4/15 * 4- 7/12
16/60 - 7/12
16/60 - 7 * 5/12 * 5
16/60 - 35/60

3
Combine the Numerators
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The numbers in the numerators can now be subtracted because both fractions have the same denominator.

16/60 - 35/60
16-35/60
- 19/60
- 19/60

4
Simplify if Possible
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Check if the resulting fraction can be simplified or not. Our fraction cannot be simplified because the numerator and denominator do not have any common factors. - 19/60

Use a similar process to add unlike fractions.

Exercises
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