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notes on the difference of 2 squares
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powers and roots
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rationalizing denominators
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roots
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simplifying complex fractions
simplifying fractions
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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.

Example:

Solution:

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.

Example:

Solution:

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.