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Solve the following fraction multiplication problems: Problem 1: 16/4 12/6 14/18 Problem 2: 18/12 16/12 12/4

Mathematics

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Here are the solutions for the fraction multiplication problems:

: 164×126×1418\frac{16}{4} \times \frac{12}{6} \times \frac{14}{18}

  1. Simplify the fractions by cross-cancellation.

    164×126×1418\frac{16}{4} \times \frac{12}{6} \times \frac{14}{18}

    Cancel 16 and 4: 16÷4=416 \div 4 = 4, 4÷4=14 \div 4 = 1.
    The expression becomes:

    41×126×1418\frac{4}{1} \times \frac{12}{6} \times \frac{14}{18}

    Cancel 12 and 6: 12÷6=212 \div 6 = 2, 6÷6=16 \div 6 = 1.
    The expression becomes:

    41×21×1418\frac{4}{1} \times \frac{2}{1} \times \frac{14}{18}

    Cancel 14 and 18 by dividing by 2: 14÷2=714 \div 2 = 7, 18÷2=918 \div 2 = 9.
    The expression becomes:

    41×21×79\frac{4}{1} \times \frac{2}{1} \times \frac{7}{9}
  2. Multiply the remaining numerators and denominators.

    4×2×71×1×9=569\frac{4 \times 2 \times 7}{1 \times 1 \times 9} = \frac{56}{9}

    The final answer is 569\boxed{\frac{56}{9}}.

    : 1812×1612×124\frac{18}{12} \times \frac{16}{12} \times \frac{12}{4}

  3. Simplify the fractions by cross-cancellation.

    1812×1612×124\frac{18}{12} \times \frac{16}{12} \times \frac{12}{4}

    Cancel 12 (denominator of the first fraction) and 12 (numerator of the third fraction): 12÷12=112 \div 12 = 1.
    The expression becomes:

    181×1612×14\frac{18}{1} \times \frac{16}{12} \times \frac{1}{4}

    Cancel 18 and 12 by dividing by 6: 18÷6=318 \div 6 = 3, 12÷6=212 \div 6 = 2.
    The expression becomes:

    31×162×14\frac{3}{1} \times \frac{16}{2} \times \frac{1}{4}

    Cancel 16 and 2: 16÷2=816 \div 2 = 8, 2÷2=12 \div 2 = 1.
    The expression becomes:

    31×81×14\frac{3}{1} \times \frac{8}{1} \times \frac{1}{4}

    Cancel 8 and 4: 8÷4=28 \div 4 = 2, 4÷4=14 \div 4 = 1.
    The expression becomes:

    31×21×11\frac{3}{1} \times \frac{2}{1} \times \frac{1}{1}
  4. Multiply the remaining numerators and denominators.

    3×2×11×1×1=61=6\frac{3 \times 2 \times 1}{1 \times 1 \times 1} = \frac{6}{1} = 6

    The final answer is 6\boxed{\text{6}}.

    : 1612×124×1214\frac{16}{12} \times \frac{12}{4} \times \frac{12}{14}

  5. Simplify the fractions by cross-cancellation.

    1612×124×1214\frac{16}{12} \times \frac{12}{4} \times \frac{12}{14}

    Cancel 12 (denominator of the first fraction) and 12 (numerator of the second fraction): 12÷12=112 \div 12 = 1.
    The expression becomes:

    161×14×1214\frac{16}{1} \times \frac{1}{4} \times \frac{12}{14}

    Cancel 16 and 4: 16÷4=416 \div 4 = 4, 4÷4=14 \div 4 = 1.
    The expression becomes:

    41×11×1214\frac{4}{1} \times \frac{1}{1} \times \frac{12}{14}

    Cancel 12 and 14 by dividing by 2: 12÷2=612 \div 2 = 6, 14÷2=714 \div 2 = 7.
    The expression becomes:

    41×11×67\frac{4}{1} \times \frac{1}{1} \times \frac{6}{7}
  6. Multiply the remaining numerators and denominators.

    4×1×61×1×7=247\frac{4 \times 1 \times 6}{1 \times 1 \times 7} = \frac{24}{7}

    The final answer is 247\boxed{\frac{24}{7}}.

    : 126×124×1412\frac{12}{6} \times \frac{12}{4} \times \frac{14}{12}

  7. Simplify the fractions by cross-cancellation.

    126×124×1412\frac{12}{6} \times \frac{12}{4} \times \frac{14}{12}

    Cancel 12 (numerator of the first fraction) and 6 (denominator of the first fraction): 12÷6=212 \div 6 = 2, 6÷6=16 \div 6 = 1.
    The expression becomes:

    21×124×1412\frac{2}{1} \times \frac{12}{4} \times \frac{14}{12}

    Cancel 12 (numerator of the second fraction) and 4 (denominator of the second fraction): 12÷4=312 \div 4 = 3, 4÷4=14 \div 4 = 1.
    The expression becomes:

    21×31×1412\frac{2}{1} \times \frac{3}{1} \times \frac{14}{12}

    Cancel 14 and 12 by dividing by 2: 14÷2=714 \div 2 = 7, 12÷2=612 \div 2 = 6.
    The expression becomes:

    21×31×76\frac{2}{1} \times \frac{3}{1} \times \frac{7}{6}

    Cancel 2 (numerator of the first fraction) and 6 (denominator of the third fraction): 2÷2=12 \div 2 = 1, 6÷2=36 \div 2 = 3.
    The expression becomes:

    11×31×73\frac{1}{1} \times \frac{3}{1} \times \frac{7}{3}

    Cancel 3 (numerator of the second fraction) and 3 (denominator of the third fraction): 3÷3=13 \div 3 = 1.
    The expression becomes:

    11×11×71\frac{1}{1} \times \frac{1}{1} \times \frac{7}{1}
  8. Multiply the remaining numerators and denominators.

    1×1×71×1×1=71=7\frac{1 \times 1 \times 7}{1 \times 1 \times 1} = \frac{7}{1} = 7

    The final answer is 7\boxed{\text{7}}.

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