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How do you subtract unlike fractions? Give examples.

Mathematics

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36 steps

Here are the solutions for subtracting the unlike fractions:

Part a· 3 steps

To subtract 49−13\frac{4}{9} - \frac{1}{3}

  1. Find a common denominator.

    The least common multiple of 9 and 3 is 9.

  2. Convert 13\frac{1}{3} to an equivalent fraction with a denominator of 9.

    13=1×33×3=39\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}

  3. Subtract the fractions.

    49−39=4−39=19\frac{4}{9} - \frac{3}{9} = \frac{4-3}{9} = \frac{1}{9}

    The answer is 19\boxed{\frac{1}{9}}.

Part b· 3 steps

To subtract 34−516\frac{3}{4} - \frac{5}{16}

  1. Find a common denominator.

    The least common multiple of 4 and 16 is 16.

  2. Convert 34\frac{3}{4} to an equivalent fraction with a denominator of 16.

    34=3×44×4=1216\frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16}

  3. Subtract the fractions.

    1216−516=12−516=716\frac{12}{16} - \frac{5}{16} = \frac{12-5}{16} = \frac{7}{16}

    The answer is 716\boxed{\frac{7}{16}}.

Part c· 3 steps

To subtract 38−14\frac{3}{8} - \frac{1}{4}

  1. Find a common denominator.

    The least common multiple of 8 and 4 is 8.

  2. Convert 14\frac{1}{4} to an equivalent fraction with a denominator of 8.

    14=1×24×2=28\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}

  3. Subtract the fractions.

    38−28=3−28=18\frac{3}{8} - \frac{2}{8} = \frac{3-2}{8} = \frac{1}{8}

    The answer is 18\boxed{\frac{1}{8}}.

Part d· 3 steps

To subtract 57−13\frac{5}{7} - \frac{1}{3}

  1. Find a common denominator.

    The least common multiple of 7 and 3 is 21.

  2. Convert both fractions to equivalent fractions with a denominator of 21.

    57=5×37×3=1521\frac{5}{7} = \frac{5 \times 3}{7 \times 3} = \frac{15}{21} 13=1×73×7=721\frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21}

  3. Subtract the fractions.

    1521−721=15−721=821\frac{15}{21} - \frac{7}{21} = \frac{15-7}{21} = \frac{8}{21}

    The answer is 821\boxed{\frac{8}{21}}.

Part e· 3 steps

To subtract 78−25\frac{7}{8} - \frac{2}{5}

  1. Find a common denominator.

    The least common multiple of 8 and 5 is 40.

  2. Convert both fractions to equivalent fractions with a denominator of 40.

    78=7×58×5=3540\frac{7}{8} = \frac{7 \times 5}{8 \times 5} = \frac{35}{40} 25=2×85×8=1640\frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40}

  3. Subtract the fractions.

    3540−1640=35−1640=1940\frac{35}{40} - \frac{16}{40} = \frac{35-16}{40} = \frac{19}{40}

    The answer is 1940\boxed{\frac{19}{40}}.

Part f· 3 steps

To subtract 79−12\frac{7}{9} - \frac{1}{2}

  1. Find a common denominator.

    The least common multiple of 9 and 2 is 18.

  2. Convert both fractions to equivalent fractions with a denominator of 18.

    79=7×29×2=1418\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18} 12=1×92×9=918\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}

  3. Subtract the fractions.

    1418−918=14−918=518\frac{14}{18} - \frac{9}{18} = \frac{14-9}{18} = \frac{5}{18}

    The answer is 518\boxed{\frac{5}{18}}.

Part g· 3 steps

To subtract 34−35\frac{3}{4} - \frac{3}{5}

  1. Find a common denominator.

    The least common multiple of 4 and 5 is 20.

  2. Convert both fractions to equivalent fractions with a denominator of 20.

    34=3×54×5=1520\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} 35=3×45×4=1220\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}

  3. Subtract the fractions.

    1520−1220=15−1220=320\frac{15}{20} - \frac{12}{20} = \frac{15-12}{20} = \frac{3}{20}

    The answer is 320\boxed{\frac{3}{20}}.

Part h· 3 steps

To subtract 12−27\frac{1}{2} - \frac{2}{7}

  1. Find a common denominator.

    The least common multiple of 2 and 7 is 14.

  2. Convert both fractions to equivalent fractions with a denominator of 14.

    12=1×72×7=714\frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14} 27=2×27×2=414\frac{2}{7} = \frac{2 \times 2}{7 \times 2} = \frac{4}{14}

  3. Subtract the fractions.

    714−414=7−414=314\frac{7}{14} - \frac{4}{14} = \frac{7-4}{14} = \frac{3}{14}

    The answer is 314\boxed{\frac{3}{14}}.

Part h(i)· 12 steps

To subtract 34−59\frac{3}{4} - \frac{5}{9}

  1. Find a common denominator.

    The least common multiple of 4 and 9 is 36.

  2. Convert both fractions to equivalent fractions with a denominator of 36.

    34=3×94×9=2736\frac{3}{4} = \frac{3 \times 9}{4 \times 9} = \frac{27}{36} 59=5×49×4=2036\frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36}

  3. Subtract the fractions.

    2736−2036=27−2036=736\frac{27}{36} - \frac{20}{36} = \frac{27-20}{36} = \frac{7}{36}

    The answer is 736\boxed{\frac{7}{36}}.

    *j) To subtract 56−34\frac{5}{6} - \frac{3}{4}:

  4. Find a common denominator.

    The least common multiple of 6 and 4 is 12.

  5. Convert both fractions to equivalent fractions with a denominator of 12.

    56=5×26×2=1012\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} 34=3×34×3=912\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}

  6. Subtract the fractions.

    1012−912=10−912=112\frac{10}{12} - \frac{9}{12} = \frac{10-9}{12} = \frac{1}{12}

    The answer is 112\boxed{\frac{1}{12}}.

    *k) To subtract 49−25\frac{4}{9} - \frac{2}{5}:

  7. Find a common denominator.

    The least common multiple of 9 and 5 is 45.

  8. Convert both fractions to equivalent fractions with a denominator of 45.

    49=4×59×5=2045\frac{4}{9} = \frac{4 \times 5}{9 \times 5} = \frac{20}{45} 25=2×95×9=1845\frac{2}{5} = \frac{2 \times 9}{5 \times 9} = \frac{18}{45}

  9. Subtract the fractions.

    2045−1845=20−1845=245\frac{20}{45} - \frac{18}{45} = \frac{20-18}{45} = \frac{2}{45}

    The answer is 245\boxed{\frac{2}{45}}.

    *l) To subtract 23−58\frac{2}{3} - \frac{5}{8}:

  10. Find a common denominator.

    The least common multiple of 3 and 8 is 24.

  11. Convert both fractions to equivalent fractions with a denominator of 24.

    23=2×83×8=1624\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24} 58=5×38×3=1524\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}

  12. Subtract the fractions.

    1624−1524=16−1524=124\frac{16}{24} - \frac{15}{24} = \frac{16-15}{24} = \frac{1}{24}

    The answer is 124\boxed{\frac{1}{24}}.

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