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Adding and Subtracting Fractions


Adding or subtracting like fractions -- fractions with the same denominator -- is easy. Just add or subtract the numerators, and write the sum or difference over the common denominator.

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To add or subtract fractions with different denominators, you first must find the least common denominator -- the smallest number that can be divided evenly by both denominators. The easiest way to find the least common denominator is to write the multiples of both denominators until you find a number they have in common. For example, to add the fractions 1/3 and 2/5, begin with some multiples of 3 (3, 6, 9, 12, 15) and some multiples of 5 (5, 10, 15). Youll find that 15 is the lowest number that both numbers divide evenly into. So,15 is the least common denominator of 1/3 and 2/5.

The next step is to rewrite those fractions as like fractions. To re-write fractions as like fractions using the least common denominator,

  1. Divide the least common denominator (15 in the example above) by the denominator of the first fraction. (15 divided by 3 = 5)
  2. Multiple the answer times the numerator of the fraction. (5 x 1 = 5)
  3. Re-write the fraction using the answer from step 2 above (5) as the numerator and the least common denominator (15) as the denominator. (1/3 = 5/15)
  4. Repeat the steps above for all additional fractions in the equation. (15 divided by 5 = 3; 3 x 2 = 6; 2/5 = 6/15)

Finally, use the like fractions to solve the equation by adding or subtracting the numerators and writing the sum or difference above the common denominator: 5/15 + 6/15 = 11/15.

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