Subtracting Fractions

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Subtracting Fractions


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To subtract fractions, you need to find a common denominator first, then subtract the numerators while keeping the denominator the same.


When subtracting fractions, follow these steps:


  1. Find the least common multiple (LCM) of the denominators - this will be your common denominator
  2. Convert each fraction to an equivalent fraction with the common denominator
  3. Subtract the numerators while keeping the denominator the same
  4. Simplify the result if possible

Let's look at some examples:


Example 1: Subtract 3/4 - 1/6
  • First, find the least common multiple of 4 and 6, which is 12.
  • Convert both fractions to equivalent fractions with denominator 12:
    • 3/4 = (3 × 3)/(4 × 3) = 9/12
    • 1/6 = (1 × 2)/(6 × 2) = 2/12
  • Now subtract the numerators: 9/12 - 2/12 = 7/12
  • Since 7 and 12 have no common factors, 7/12 is already in simplest form.

Example 2: Subtract 5/8 - 1/4
  • The LCM of 8 and 4 is 8.
    • 5/8 remains as 5/8
    • 1/4 = (1 × 2)/(4 × 2) = 2/8
  • Now subtract: 5/8 - 2/8 = 3/8

Example 3: Subtract 4 2/3 - 1 5/6
  • For mixed numbers, first convert them to improper fractions:
      4 2/3 = (4 × 3 + 2)/3 = 14/3 1 5/6 = (1 × 6 + 5)/6 = 11/6
  • Now find the LCM of 3 and 6, which is 6:
  • 14/3 = (14 × 2)/(3 × 2) = 28/6
  • 11/6 remains as 11/6
  • Subtract: 28/6 - 11/6 = 17/6
  • Convert back to a mixed number: 17/6 = 2 5/6
  • So 4 2/3 - 1 5/6 = 2 5/6

Remember that when subtracting fractions with different denominators, the key is to find a common denominator first, then perform the subtraction.


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