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Chapter 9 · Questions · page 45 of 68

How do you add fractions with different denominators?

Short answerRewrite both fractions over a common denominator, then add the numerators and keep that denominator. Simplify at the end.

levelPre-algebra
standard5.NF.A.1
practiceFraction operations

You can only add pieces of the same size. Quarters and thirds are different sizes, so you cut both into twelfths first. Twelve works because both 4 and 3 divide into it.

How to use it

  1. Find the least common multiple of the denominators.
  2. Scale each fraction so its denominator is that number, multiplying top and bottom by the same amount.
  3. Add the numerators. The denominator stays.
  4. Simplify if you can.

Example

14+23=312+812=1112\frac{1}{4} + \frac{2}{3} = \frac{3}{12} + \frac{8}{12} = \frac{11}{12}
56−14=1012−312=712\frac{5}{6} - \frac{1}{4} = \frac{10}{12} - \frac{3}{12} = \frac{7}{12}
12+16=36+16=46=23\frac{1}{2} + \frac{1}{6} = \frac{3}{6} + \frac{1}{6} = \frac{4}{6} = \frac{2}{3}

Where it goes wrong

  • Adding the bottoms: 1/4 + 2/3 is not 3/7.
  • Scaling the bottom but forgetting to scale the top by the same number.

Related

Adding and subtracting fractionsEquivalent fractions and simplest formWhat a fraction is
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