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

Mathematics

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Step-by-step solution

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Here are the solutions for the fraction multiplication problems:

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

  1. Simplify the fractions by cross-cancellation.

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

    14×161×124\frac{1}{4} \times \frac{16}{1} \times \frac{12}{4}

    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:

    11×41×124\frac{1}{1} \times \frac{4}{1} \times \frac{12}{4}

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

    11×11×121\frac{1}{1} \times \frac{1}{1} \times \frac{12}{1}
  2. Multiply the remaining numerators and denominators.

    1×1×121×1×1=121=12\frac{1 \times 1 \times 12}{1 \times 1 \times 1} = \frac{12}{1} = 12

    The final answer is 12\boxed{\text{12}}.

    : 1612×164×124\frac{16}{12} \times \frac{16}{4} \times \frac{12}{4}

  3. Simplify the fractions by cross-cancellation.

    1612×164×124\frac{16}{12} \times \frac{16}{4} \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:

    161×164×14\frac{16}{1} \times \frac{16}{4} \times \frac{1}{4}

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

    41×161×14\frac{4}{1} \times \frac{16}{1} \times \frac{1}{4}

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

    11×161×11\frac{1}{1} \times \frac{16}{1} \times \frac{1}{1}
  4. Multiply the remaining numerators and denominators.

    1×16×11×1×1=161=16\frac{1 \times 16 \times 1}{1 \times 1 \times 1} = \frac{16}{1} = 16

    The final answer is 16\boxed{\text{16}}.

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