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Divide fractions

Theory

Divide fractions

To divide fractions, the numerator is multiplied by the reciprocal of the denominator. This converts the division to an equivalent multiplication. 4/53/7=4573 \dfrac{\left.4\middle/5\right.}{\left.3\middle/7\right.}=\dfrac{4}{5}\cdot \dfrac{7}{3} This rule can be proven by expanding with the reciprocal of the denominator. 4/53/7=4/53/77/37/3 \dfrac{\left.4\middle/5\right.}{\left.3\middle/7\right.}=\dfrac{\left.4\middle/5\right.}{\left.3\middle/7\right.}\cdot \dfrac{\left.7\middle/3\right.}{\left.7\middle/3\right.} This can now be simplified by performing the multiplications.
4/53/77/37/3\dfrac{\left.4\middle/5\right.}{\left.3\middle/7\right.}\cdot \dfrac{\left.7\middle/3\right.}{\left.7\middle/3\right.}
4/57/33/77/3\dfrac{\left.4\middle/5\right.\cdot \left.7\middle/3\right.}{\left.3\middle/7\right.\cdot \left.7\middle/3\right.}
45733773\dfrac{\dfrac{4}{5}\cdot \dfrac{7}{3}}{\dfrac{3}{7}\cdot \dfrac{7}{3}}
45731\dfrac{\dfrac{4}{5}\cdot \dfrac{7}{3}}{1}
4573\dfrac{4}{5}\cdot \dfrac{7}{3}