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Multiply the following fractions, simplifying by cross-cancellation where possible: 16/4 14/4 16/18

Mathematics

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Answer

1129\frac{112}{9}

Step-by-step solution

3 steps

To multiply fractions, we multiply the numerators together and the denominators together. We can simplify the fractions by cross-cancellation before multiplying.

  1. Write the expression.

    164×144×1618\frac{16}{4} \times \frac{14}{4} \times \frac{16}{18}
  2. Simplify by cross-cancellation.

    First, simplify 164\frac{16}{4} to 41\frac{4}{1}.

    41×144×1618\frac{4}{1} \times \frac{14}{4} \times \frac{16}{18}

    Next, simplify 144\frac{14}{4} by dividing both numerator and denominator by 2, resulting in 72\frac{7}{2}.

    41×72×1618\frac{4}{1} \times \frac{7}{2} \times \frac{16}{18}

    Then, simplify 1618\frac{16}{18} by dividing both numerator and denominator by 2, resulting in 89\frac{8}{9}.

    41×72×89\frac{4}{1} \times \frac{7}{2} \times \frac{8}{9}

    Now, we can cross-cancel 4 (numerator of the first fraction) with 2 (denominator of the second fraction). Divide 4 by 2 to get 2, and 2 by 2 to get 1.

    21×71×89\frac{2}{1} \times \frac{7}{1} \times \frac{8}{9}

    There are no more common factors for cross-cancellation.

  3. Multiply the simplified fractions.

    Multiply the numerators: 2×7×8=14×8=1122 \times 7 \times 8 = 14 \times 8 = 112.
    Multiply the denominators: 1×1×9=91 \times 1 \times 9 = 9.

    1129\frac{112}{9}

    The fraction 1129\frac{112}{9} cannot be simplified further.

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