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A complex fraction is a fraction that contains a fraction. To simplify a complex fraction, you need to multiply every term by the smallest number that will clear all fractions in the numerator and denominator.



All four denominators will divide easily into 12. You must multiply all of the fractions by 12 to get rid of the fractions:

Your problem now looks like this: .

Try a subtraction problem.



Again, multiply all terms by 12. Don’t forget about the 1.

Fractions: The Vocabulary

  • The numerator is the number on top of the fraction.
  • The denominator is the number on the bottom of the fraction.
  • A mixed number contains an integer and a fraction.
  • An improper fraction is larger on the top than on the bottom.
  • To find the multiplicative inverse, switch around the top and bottom numbers.
  • A complex number is a fraction containing fractions.

Fractions: The Rules

To add or subtract two simple fractions:

  • Cross-multiply and perform the function on top.
  • Multiply across the bottom. Simplify if necessary.

Addition or subtraction of multiple fractions may require common denominators:

  • Find the smallest integer the denominators divide into.
  • Multiply each numerator by the same number the denominator is multiplied by to get to the common denominator.
  • Perform addition or subtraction on top. Use common denominator as the denominator.