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How do you divide fractions? Show your work for 12/4 divided by 2/14.

Mathematics

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Answer

21\text{21}

Step-by-step solution

3 steps

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

  1. Rewrite the division as multiplication.

    The reciprocal of 214\frac{2}{14} is 142\frac{14}{2}.

    124÷214=124×142\frac{12}{4} \div \frac{2}{14} = \frac{12}{4} \times \frac{14}{2}
  2. Simplify by cross-cancellation.

    We can simplify 12 and 2 by dividing both by 2.
    We can simplify 14 and 4 by dividing both by 2.

    12÷24×142÷2=64×141\frac{12^{\div 2}}{4} \times \frac{14}{2^{\div 2}} = \frac{6}{4} \times \frac{14}{1}

    Now, simplify 6 and 4 by dividing both by 2:

    6÷24÷2×141=32×141\frac{6^{\div 2}}{4^{\div 2}} \times \frac{14}{1} = \frac{3}{2} \times \frac{14}{1}

    Finally, simplify 14 and 2 by dividing both by 2:

    32÷2×14÷21=31×71\frac{3}{2^{\div 2}} \times \frac{14^{\div 2}}{1} = \frac{3}{1} \times \frac{7}{1}
  3. Multiply the simplified fractions.

    31×71=3×71×1=211=21\frac{3}{1} \times \frac{7}{1} = \frac{3 \times 7}{1 \times 1} = \frac{21}{1} = 21

    The final answer is 21\text{21}.

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