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

Mathematics

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3 parts
i

107\frac{10}{7}

iv

−8135-\frac{8}{135}

vii

725\frac{72}{5}

Step-by-step solution

11 steps

Here are the solutions to the given problems:

Part i· 3 steps

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

    56÷712=56×127\frac{5}{6} \div \frac{7}{12} = \frac{5}{6} \times \frac{12}{7}
  2. Multiply the numerators and the denominators.

    Simplify common factors before multiplying.

    561×1227=5×21×7\frac{5}{\cancel{6}_1} \times \frac{\cancel{12}^2}{7} = \frac{5 \times 2}{1 \times 7}
  3. Calculate the product.

    107\frac{10}{7}

    The final answer is 107\boxed{\frac{10}{7}}.

Part iv

−8135-\frac{8}{135}

  1. Write the integer as a fraction and then multiply by its reciprocal.

    1615÷(−18)=1615÷−181\frac{16}{15} \div (-18) = \frac{16}{15} \div \frac{-18}{1}
  2. Multiply the first fraction by the reciprocal of the second fraction.

    1615×1−18\frac{16}{15} \times \frac{1}{-18}
  3. Multiply the numerators and the denominators.

    Simplify common factors (16 and 18 are both divisible by 2).

    16815×1−189=8×115×(−9)\frac{\cancel{16}^8}{15} \times \frac{1}{-\cancel{18}_9} = \frac{8 \times 1}{15 \times (-9)}
  4. Calculate the product.

    8−135=−8135\frac{8}{-135} = -\frac{8}{135}

    The final answer is −8135\boxed{-\frac{8}{135}}.

Part vii

725\frac{72}{5}

  1. Write the integer as a fraction and then multiply by its reciprocal.

    −12÷(−56)=−121÷−56-12 \div \left(\frac{-5}{6}\right) = \frac{-12}{1} \div \frac{-5}{6}
  2. Multiply the first fraction by the reciprocal of the second fraction.

    −121×6−5\frac{-12}{1} \times \frac{6}{-5}
  3. Multiply the numerators and the denominators.

    −12×61×(−5)\frac{-12 \times 6}{1 \times (-5)}
  4. Calculate the product.

    −72−5=725\frac{-72}{-5} = \frac{72}{5}

    The final answer is 725\boxed{\frac{72}{5}}.

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