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Solve the following fraction problems: a) 1/4 + 1/2 b) 7/8 - 1/2 c) 7/10 + 2/5 d) 5/7 + 2/21

Mathematics

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Here are the solutions to the fraction problems:

Part a· 3 steps

14+12\frac{1}{4} + \frac{1}{2}

  1. Find a common denominator.

    The least common multiple of 4 and 2 is 4.

  2. Convert 12\frac{1}{2} to an equivalent fraction with a denominator of 4.

    12=1×22×2=24\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}

  3. Add the fractions.

    14+24=1+24=34\frac{1}{4} + \frac{2}{4} = \frac{1+2}{4} = \boxed{\frac{3}{4}}

Part b· 3 steps

78−12\frac{7}{8} - \frac{1}{2}

  1. Find a common denominator.

    The least common multiple of 8 and 2 is 8.

  2. Convert 12\frac{1}{2} to an equivalent fraction with a denominator of 8.

    12=1×42×4=48\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}

  3. Subtract the fractions.

    78−48=7−48=38\frac{7}{8} - \frac{4}{8} = \frac{7-4}{8} = \boxed{\frac{3}{8}}

Part c· 3 steps

710+25\frac{7}{10} + \frac{2}{5}

  1. Find a common denominator.

    The least common multiple of 10 and 5 is 10.

  2. Convert 25\frac{2}{5} to an equivalent fraction with a denominator of 10.

    25=2×25×2=410\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}

  3. Add the fractions.

    710+410=7+410=1110\frac{7}{10} + \frac{4}{10} = \frac{7+4}{10} = \boxed{\frac{11}{10}}

Part d· 3 steps

57+221\frac{5}{7} + \frac{2}{21}

  1. Find a common denominator.

    The least common multiple of 7 and 21 is 21.

  2. Convert 57\frac{5}{7} to an equivalent fraction with a denominator of 21.

    57=5×37×3=1521\frac{5}{7} = \frac{5 \times 3}{7 \times 3} = \frac{15}{21}

  3. Add the fractions.

    1521+221=15+221=1721\frac{15}{21} + \frac{2}{21} = \frac{15+2}{21} = \boxed{\frac{17}{21}}

Part e· 3 steps

912−16\frac{9}{12} - \frac{1}{6}

  1. Find a common denominator.

    The least common multiple of 12 and 6 is 12.

  2. Convert 16\frac{1}{6} to an equivalent fraction with a denominator of 12.

    16=1×26×2=212\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}

  3. Subtract the fractions.

    912−212=9−212=712\frac{9}{12} - \frac{2}{12} = \frac{9-2}{12} = \boxed{\frac{7}{12}}

Part f· 3 steps

1724−36\frac{17}{24} - \frac{3}{6}

  1. Find a common denominator.

    The least common multiple of 24 and 6 is 24.

  2. Convert 36\frac{3}{6} to an equivalent fraction with a denominator of 24.

    36=3×46×4=1224\frac{3}{6} = \frac{3 \times 4}{6 \times 4} = \frac{12}{24}

  3. Subtract the fractions.

    1724−1224=17−1224=524\frac{17}{24} - \frac{12}{24} = \frac{17-12}{24} = \boxed{\frac{5}{24}}

Part g· 3 steps

78−316\frac{7}{8} - \frac{3}{16}

  1. Find a common denominator.

    The least common multiple of 8 and 16 is 16.

  2. Convert 78\frac{7}{8} to an equivalent fraction with a denominator of 16.

    78=7×28×2=1416\frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16}

  3. Subtract the fractions.

    1416−316=14−316=1116\frac{14}{16} - \frac{3}{16} = \frac{14-3}{16} = \boxed{\frac{11}{16}}

Part h· 6 steps

34−12\frac{3}{4} - \frac{1}{2}

  1. Find a common denominator.

    The least common multiple of 4 and 2 is 4.

  2. Convert 12\frac{1}{2} to an equivalent fraction with a denominator of 4.

    12=1×22×2=24\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}

  3. Subtract the fractions.

    34−24=3−24=14\frac{3}{4} - \frac{2}{4} = \frac{3-2}{4} = \boxed{\frac{1}{4}}

    Additional problem (a) on the right side: 34+12\frac{3}{4} + \frac{1}{2}

  4. Find a common denominator.

    The least common multiple of 4 and 2 is 4.

  5. Convert 12\frac{1}{2} to an equivalent fraction with a denominator of 4.

    12=1×22×2=24\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}

  6. Add the fractions.

    34+24=3+24=54\frac{3}{4} + \frac{2}{4} = \frac{3+2}{4} = \boxed{\frac{5}{4}}
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