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Subtract fractions and mixed numbers.

Mathematics

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Answers

4 parts
a

1914\frac{19}{14}

b

119\frac{11}{9}

d

514\frac{5}{14}

e

4213\frac{42}{13}

Step-by-step solution

12 steps

Part a· 3 steps

Subtract 17\frac{1}{7} from 32\frac{3}{2}.

  1. Set up the subtraction.

    32−17\frac{3}{2} - \frac{1}{7}

  2. Find a common denominator, which is 14.

    3×72×7−1×27×2=2114−214\frac{3 \times 7}{2 \times 7} - \frac{1 \times 2}{7 \times 2} = \frac{21}{14} - \frac{2}{14}

  3. Perform the subtraction.

    21−214=1914\frac{21 - 2}{14} = \frac{19}{14}

    The answer is 1914\boxed{\frac{19}{14}}.

Part b

119\frac{11}{9}

Subtract −59\frac{-5}{9} from 23\frac{2}{3}.

  1. Set up the subtraction.

    23−(−59)=23+59\frac{2}{3} - \left(\frac{-5}{9}\right) = \frac{2}{3} + \frac{5}{9}

  2. Find a common denominator, which is 9.

    2×33×3+59=69+59\frac{2 \times 3}{3 \times 3} + \frac{5}{9} = \frac{6}{9} + \frac{5}{9}

  3. Perform the addition.

    6+59=119\frac{6 + 5}{9} = \frac{11}{9}

    The answer is 119\boxed{\frac{11}{9}}.

Part d

514\frac{5}{14}

Subtract −27\frac{-2}{7} from 114\frac{1}{14}.

  1. Set up the subtraction.

    114−(−27)=114+27\frac{1}{14} - \left(\frac{-2}{7}\right) = \frac{1}{14} + \frac{2}{7}

  2. Find a common denominator, which is 14.

    114+2×27×2=114+414\frac{1}{14} + \frac{2 \times 2}{7 \times 2} = \frac{1}{14} + \frac{4}{14}

  3. Perform the addition.

    1+414=514\frac{1 + 4}{14} = \frac{5}{14}

    The answer is 514\boxed{\frac{5}{14}}.

Part e

4213\frac{42}{13}

Subtract −3-3 from 313\frac{3}{13}.

  1. Set up the subtraction.

    313−(−3)=313+3\frac{3}{13} - (-3) = \frac{3}{13} + 3

  2. Convert the whole number to a fraction with the same denominator.

    313+3×1313=313+3913\frac{3}{13} + \frac{3 \times 13}{13} = \frac{3}{13} + \frac{39}{13}

  3. Perform the addition.

    3+3913=4213\frac{3 + 39}{13} = \frac{42}{13}

    The answer is 4213\boxed{\frac{42}{13}}.

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