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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.
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
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.
| 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
Subtract fractions
Subtract term
Put minus sign in front of fraction
Use a similar process to add unlike fractions.