Dividing Rational NumbersYou are currentlynot logged in Click here to log in 

To divide two Rational Numbers there is a simple rule:

As to why we do this, that's more complicated. Here's a way of thinking about it.
We can think of a rational number as a stretching by the numerator, and shrinking by the denominator.
We can think of a rational number as a stretching by the numerator, and shrinking by the denominator. We think of dividing as undoing a multiplication. If we multiply by $\frac{c}{d}$ then we stretch by $c$ and shrink by $d.$ To undo that we must shrink by $c$ and stretch by $d.$ In other words, undoing a multiply by $\frac{c}{d}$ is a shrink by $c$ and stretch by $d,$ which we write as a multiply by $\frac{d}{c}.$
Thus dividing by $\frac{c}{d}$ is the same as multiplying by $\frac{d}{c}.$
Hence the rule.
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