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Divide fractions using reciprocals

Division of positive fractions, whole numbers, and mixed numbers is understood as finding the factor that, when multiplied by the divisor, produces the dividend; therefore, dividing by a nonzero fraction is equivalent to multiplying by its reciprocal. The reciprocal applies to the divisor, not the dividend, and bar models or number lines can represent the quotient as the number of fractional groups; signed rational numbers and more abstract algebraic generalizations are not included.

Detailed Explanation: Divide fractions using reciprocals

To divide by a fraction, multiply by the reciprocal of the divisor. The reciprocal is found by switching the numerator and denominator.

For example:

34÷25\frac{3}{4}\div\frac{2}{5}

  1. Identify the divisor:
    The divisor is 25\frac{2}{5} because it is the number you are dividing by.

  2. Find its reciprocal:
    The reciprocal of 25\frac{2}{5} is 52\frac{5}{2}.

  3. Keep the dividend, change division to multiplication, and use the reciprocal of the divisor:

34÷25=34×52\frac{3}{4}\div\frac{2}{5} =\frac{3}{4}\times\frac{5}{2}
  1. Multiply across:
3×54×2=158\frac{3\times5}{4\times2}=\frac{15}{8}
  1. Write the improper fraction as a mixed number:
158=178\frac{15}{8}=1\frac{7}{8}

Therefore,

34÷25=178\boxed{\frac{3}{4}\div\frac{2}{5}=1\frac{7}{8}}

Remember: Keep the first fraction, change division to multiplication, and flip only the second fraction.

Learn by doing: Divide fractions using reciprocals

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