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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.
The numerators of like fractions are added or subtracted when finding the sum or difference of the like fractions, respectively. The denominator remains the same in these situations.
a/c + b/c=a + b/c [0.8em] a/c - b/c=a - b/c
Unlike fractions must first be converted to like fractions when the operation deals with the sum or difference. 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 [0.8em] 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.
| 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
a/b=a * 4/b * 4
Multiply
a/b=a * 5/b * 5
Multiply
The process for adding unlike fractions is similar to the just performed example of subtracting unlike fractions.