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Describe how you would help your learner to add the following mixed fractions: a) 8 2/3 + 1 5/6, b) 5 2/5 + 9 3/7, c) 3 7/10 + 6 4/5

Mathematics

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Answers

3 parts
a

517305\frac{17}{30}

b

1651216\frac{5}{12}

c

10192010\frac{19}{20}

Step-by-step solution

11 steps

Part a· 3 steps

325+2163\frac{2}{5} + 2\frac{1}{6}

  1. Add the whole numbers.

    3+2=53 + 2 = 5

  2. Add the fractions 25+16\frac{2}{5} + \frac{1}{6}.

    Find the least common multiple (LCM) of 5 and 6: LCM = 30.

    25=2×65×6=1230\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30} 16=1×56×5=530\frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30} 1230+530=1730\frac{12}{30} + \frac{5}{30} = \frac{17}{30}

  3. Combine the results.

    Since 1730<1\frac{17}{30} < 1, the sum is 517305\frac{17}{30}.

    5\frac{17}{30}

Part b

1651216\frac{5}{12}

634+9236\frac{3}{4} + 9\frac{2}{3}

  1. Add the whole numbers.

    6+9=156 + 9 = 15

  2. Add the fractions 34+23\frac{3}{4} + \frac{2}{3}.

    Find the LCM of 4 and 3: LCM = 12.

    34=3×34×3=912\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} 23=2×43×4=812\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} 912+812=1712\frac{9}{12} + \frac{8}{12} = \frac{17}{12}

  3. Convert 1712\frac{17}{12} to a mixed number.

    17÷12=117 \div 12 = 1 remainder 5, since 12×1=1212 \times 1 = 12 and 17−12=517 - 12 = 5.
    So, 1712=1512\frac{17}{12} = 1\frac{5}{12}.

  4. Combine the results.

    15+1512=1651215 + 1\frac{5}{12} = 16\frac{5}{12}.

    16\frac{5}{12}

Part c

10192010\frac{19}{20}

3710+6543\frac{7}{10} + 6\frac{5}{4}

  1. Add the whole numbers.

    3+6=93 + 6 = 9

  2. Add the fractions 710+54\frac{7}{10} + \frac{5}{4}.

    Find the LCM of 10 and 4: LCM = 20.

    710=7×210×2=1420\frac{7}{10} = \frac{7 \times 2}{10 \times 2} = \frac{14}{20} 54=5×54×5=2520\frac{5}{4} = \frac{5 \times 5}{4 \times 5} = \frac{25}{20} 1420+2520=3920\frac{14}{20} + \frac{25}{20} = \frac{39}{20}

  3. Convert 3920\frac{39}{20} to a mixed number.

    39÷20=139 \div 20 = 1 remainder 19, since 20×1=2020 \times 1 = 20 and 39−20=1939 - 20 = 19.
    So, 3920=11920\frac{39}{20} = 1\frac{19}{20}.

  4. Combine the results.

    9+11920=1019209 + 1\frac{19}{20} = 10\frac{19}{20}.

    10\frac{19}{20}

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