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Solve the following mixed number addition problems: a) 6(3)/(10) + 10(1)/(10) b) 2(5)/(12) + 9(8)/(12) c) 1(1)/(6) + 2(2)/(6) + 3(1)/(6) d) 4(2)/(8) + 4(5)/(8) + 4(3)/(8)

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Answers

4 parts
a

1625\mathbf{16\frac{2}{5}}

b

12112\mathbf{12\frac{1}{12}}

c

623\mathbf{6\frac{2}{3}}

d

1314\mathbf{13\frac{1}{4}}

Step-by-step solution

17 steps

Here are the solutions to the mixed number problems.

Part a· 3 steps

  1. Add the whole numbers and the fractions separately.

    6310+10110=(6+10)+(310+110)6\frac{3}{10} + 10\frac{1}{10} = (6+10) + \left(\frac{3}{10} + \frac{1}{10}\right)

  2. Perform the additions.

    16+41016 + \frac{4}{10}

  3. Simplify the fraction.

    16+25=162516 + \frac{2}{5} = 16\frac{2}{5}

    The sum is 1625\boxed{\mathbf{16\frac{2}{5}}}.

Part b

12112\mathbf{12\frac{1}{12}}

  1. Add the whole numbers and the fractions separately.

    2512+9812=(2+9)+(512+812)2\frac{5}{12} + 9\frac{8}{12} = (2+9) + \left(\frac{5}{12} + \frac{8}{12}\right)

  2. Perform the additions.

    11+131211 + \frac{13}{12}

  3. Convert the improper fraction to a mixed number and add it to the whole number.

    11+1112=1211211 + 1\frac{1}{12} = 12\frac{1}{12}

    The sum is 12112\boxed{\mathbf{12\frac{1}{12}}}.

Part c

623\mathbf{6\frac{2}{3}}

  1. Add the whole numbers and the fractions separately.

    116+226+316=(1+2+3)+(16+26+16)1\frac{1}{6} + 2\frac{2}{6} + 3\frac{1}{6} = (1+2+3) + \left(\frac{1}{6} + \frac{2}{6} + \frac{1}{6}\right)

  2. Perform the additions.

    6+466 + \frac{4}{6}

  3. Simplify the fraction.

    6+23=6236 + \frac{2}{3} = 6\frac{2}{3}

    The sum is 623\boxed{\mathbf{6\frac{2}{3}}}.

Part d

1314\mathbf{13\frac{1}{4}}

  1. Add the whole numbers and the fractions separately.

    428+458+438=(4+4+4)+(28+58+38)4\frac{2}{8} + 4\frac{5}{8} + 4\frac{3}{8} = (4+4+4) + \left(\frac{2}{8} + \frac{5}{8} + \frac{3}{8}\right)

  2. Perform the additions.

    12+10812 + \frac{10}{8}

  3. Convert the improper fraction to a mixed number.

    12+12812 + 1\frac{2}{8}

  4. Simplify the fraction and add to the whole number.

    12+114=131412 + 1\frac{1}{4} = 13\frac{1}{4}

    The sum is 1314\boxed{\mathbf{13\frac{1}{4}}}.

Part e· 4 steps

The student's work is:

834−214=624=6128\frac{3}{4} - 2\frac{1}{4} = 6\frac{2}{4} = 6\frac{1}{2}

  1. Subtract the whole numbers

    8−2=68 - 2 = 6.

  2. Subtract the fractions

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

  3. Combine the whole number and fraction

    6246\frac{2}{4}.

  4. Simplify the fraction

    24=12\frac{2}{4} = \frac{1}{2}.
    The final answer is 6126\frac{1}{2}.
    ✅ Correct.

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