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Theory

Division by fraction

If an expression is divided by a fraction, the expression can be simplified by multiplying the numerator by the reciprocal of the fraction in the denominator.

\frac{3}{5 / 4} = 3 \cdot \frac{4}{5} = \frac{3 \cdot 4}{5}

An alternative way to show this rule is to use that the numerator can be rewritten into a fraction,

3 = \frac{3}{1} .

\frac{3}{5 / 4} = \frac{3 / 1}{5 / 4}

Next, the expression can be simplified by dividing the two fractions.

\frac{3 / 1}{5 / 4} = \frac{3}{1} \cdot \frac{4}{5} = \frac{3 \cdot 4}{1 \cdot 5} = \frac{3 \cdot 4}{5}

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