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Solve these fraction multiplication problems: 1) 12/4 16/12 4/8 2) 12/6 15/12 12/4

Mathematics

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here are the solutions for the fraction multiplication problems:

: 124×1612×48\frac{12}{4} \times \frac{16}{12} \times \frac{4}{8}

  1. Simplify the fractions by cross-cancellation.

    124×1612×48\frac{12}{4} \times \frac{16}{12} \times \frac{4}{8}

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

    14×161×48\frac{1}{4} \times \frac{16}{1} \times \frac{4}{8}

    Cancel 16 (numerator of the second fraction) and 4 (denominator of the first fraction): 16÷4=416 \div 4 = 4, 4÷4=14 \div 4 = 1.
    The expression becomes:

    11×41×48\frac{1}{1} \times \frac{4}{1} \times \frac{4}{8}

    Cancel 4 (numerator of the second fraction) and 8 (denominator of the third fraction): 4÷4=14 \div 4 = 1, 8÷4=28 \div 4 = 2.
    The expression becomes:

    11×11×42\frac{1}{1} \times \frac{1}{1} \times \frac{4}{2}

    Simplify 42\frac{4}{2} to 21\frac{2}{1}.

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

    1×1×21×1×1=21=2\frac{1 \times 1 \times 2}{1 \times 1 \times 1} = \frac{2}{1} = 2

    The final answer is 2\boxed{\text{2}}.

    : 126×1512×124\frac{12}{6} \times \frac{15}{12} \times \frac{12}{4}

  3. Simplify the fractions by cross-cancellation.

    126×1512×124\frac{12}{6} \times \frac{15}{12} \times \frac{12}{4}

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

    16×151×124\frac{1}{6} \times \frac{15}{1} \times \frac{12}{4}

    Cancel 15 (numerator of the second fraction) and 6 (denominator of the first fraction) by dividing by 3: 15÷3=515 \div 3 = 5, 6÷3=26 \div 3 = 2.
    The expression becomes:

    12×51×124\frac{1}{2} \times \frac{5}{1} \times \frac{12}{4}

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

    12×51×31\frac{1}{2} \times \frac{5}{1} \times \frac{3}{1}
  4. Multiply the remaining numerators and denominators.

    1×5×32×1×1=152\frac{1 \times 5 \times 3}{2 \times 1 \times 1} = \frac{15}{2}

    The final answer is 152\boxed{\frac{15}{2}}.

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