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how to subtract fractions with different denominators

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Here's how to subtract fractions with different denominators:

1. Find the least common multiple (LCM) of the denominators:

The least common multiple (LCM) is the smallest number that is a multiple of both denominators.

  • List out the multiples of each denominator: Start with the smaller denominator and keep adding it to itself until it's larger than the bigger denominator. Then do the same for the bigger denominator.
  • Identify the first number that appears on both lists: This is the LCM.

2. Convert each fraction to have the LCM as the denominator:

  • Multiply the numerator and denominator of the first fraction by the number needed to get the LCM as the denominator.
  • Multiply the numerator and denominator of the second fraction by the number needed to get the LCM as the denominator.

3. Subtract the numerators and keep the denominator the same:

  • Write the new fractions with the LCM as the denominator one above the other.
  • Subtract the numerators of the two fractions.
  • The answer is the fraction with the resulting difference as the numerator and the LCM as the denominator.

Example:

Problem: Subtract ½ from ¾

1. Find the LCM:

  • Multiples of ½: ½, 1, 1½, 2, ...
  • Multiples of ¾: ¾, 1¼, 1½, ...
  • LCM = 1½

2. Convert fractions:

  • ½ becomes (½ * 3) / (½ * 3) = 3/6
  • ¾ becomes (¾ * 2) / (¾ * 2) = 6/6

3. Subtract:

     3
-   = ---
     6
     3

Therefore, ½ - ¾ = -3/6, which can be simplified to -1/2.

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