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How Do You Add and Subtract Fractions?

Published in Fractions 2 mins read

You add and subtract fractions based on whether they have the same or different denominators. If the denominators are the same, you simply add or subtract the numerators. If the denominators are different, you need to find a common denominator before performing the operation.

Adding and Subtracting Fractions with the Same Denominator (Like Fractions)

When fractions have the same denominator (also known as "like fractions"), the process is straightforward:

  1. Add or subtract the numerators: Perform the addition or subtraction operation on the numbers on top of the fraction bars (the numerators).
  2. Keep the denominator the same: The denominator remains unchanged.
  3. Simplify, if possible: Reduce the resulting fraction to its simplest form.

Example:

  • (3/8) + (2/8) = (3+2)/8 = 5/8
  • (7/10) - (2/10) = (7-2)/10 = 5/10 = 1/2 (simplified)

Adding and Subtracting Fractions with Different Denominators (Unlike Fractions)

When fractions have different denominators ("unlike fractions"), you must first convert them to equivalent fractions with a common denominator. The most common approach involves finding the Least Common Multiple (LCM) of the denominators.

  1. Find the Least Common Multiple (LCM) of the denominators: The LCM is the smallest number that is a multiple of both denominators.
  2. Convert each fraction to an equivalent fraction with the LCM as the denominator: To do this, divide the LCM by the original denominator of each fraction and then multiply both the numerator and denominator of that fraction by the result.
  3. Add or subtract the numerators: Now that the fractions have the same denominator, add or subtract the numerators as described above.
  4. Keep the denominator the same: The common denominator (LCM) remains the same.
  5. Simplify, if possible: Reduce the resulting fraction to its simplest form.

Example:

Let's add (1/3) + (1/4):

  1. Find the LCM of 3 and 4: The LCM of 3 and 4 is 12.
  2. Convert the fractions:
    • (1/3) = (1 4) / (3 4) = 4/12
    • (1/4) = (1 3) / (4 3) = 3/12
  3. Add the numerators: (4/12) + (3/12) = (4+3)/12 = 7/12
  4. The denominator stays the same: The result is 7/12.
  5. Simplify: 7/12 is already in its simplest form.

Therefore, (1/3) + (1/4) = 7/12.

In summary, adding and subtracting fractions requires a common denominator. Find the common denominator, convert the fractions, perform the operation on the numerators, and simplify the result.

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