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Adding and Subtracting Fractions Study Guide (page 2)

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Updated on Oct 4, 2011

Adding and Subtracting Fractions Sample Questions

Solutions to Sample Questions

Question 1

The result of can be reduced to , leaving it as an improper fraction, or it can then be changed to a mixed number, . Both answers ( and ) are correct.

Question 2

  1. Find the LCD: The smallest number that both bottom numbers divide into evenly is 8, the larger of the two bottom numbers.
  2. Raise to 8ths, the LCD:
  3. Add as usual:
  4. Optional: Change to a mixed number.

Question 3

  1. Add the fractional parts of the mixed numbers:
  2. Change the improper fraction into a mixed number:
  3. Add the whole number parts of the original mixed numbers:  4 + 1 = 5
  4. Add the results of steps 2 and 3:

Question 4

, which reduces to

Question 5

  1. Find the LCD: Multiply the bottom numbers: 4 × 5 = 20
  2. Raise each fraction to 20ths, the LCD:  
  3. Subtract as usual:

Question 6

  1. You can't subtract the fractions the way they are because is bigger than , so you have to "borrow":
    • Rewrite the 5 part of as :
    • (Note: Thirds are used because 3 is the bottom number in ; also = 5.)

      5 =

    • Then add back the part of :   
  2. Now you have a different version of the original problem:
  3. Subtract the fractional parts of the two mixed numbers after raising them both to 12ths:
  4. Subtract the whole number parts of the two mixed numbers: 4 – 1 = 3
  5. Add the results of the last two steps together:  3 +

Find practice problems and solutions for these concepts at Adding and Subtracting Fractions Practice Questions.

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