Just invert and multiply!
How does one divide a fraction? As it turns out, it's fairly straightforward, just like fraction multiplication. In fact, you can start out by just dividing the numerators and denominators to get your answer, like so:
$$ \frac{2}{3}\div\frac{1}{2} = ? $$ $$ \frac{2\div1}{3\div2} = ? $$ $$ \frac{2}{1.5}=\frac{4}{3} $$While mathematically valid, this process will quickly become unnecessarily complicated. You'll get some ugly fractions and have to do a lot of simplification to get a normal looking answer. The easiest way to divide two fractions is to invert the second fraction and then perform multiplication! This works because division is the inverse operation of multiplication, so by inverting (flipping the fraction) the second fraction and multiplying, we're really doing the exact same thing as dividing!
As I learned it way back in school, "Never mind the reason why, just invert and multiply!" Of course, you know the reason why -- because multiplication is the inverse of division.
I'll show you a few examples where we divide two fractions by inverting one and multiplying:
$$ \frac{2}{3} \div \frac{1}{2} = \frac{2}{3}*\frac{2}{1} = \frac{4}{3} $$ $$ \frac{4}{9} \div \frac{2}{5} = \frac{4}{9}*\frac{5}{2} = \frac{20}{18} = \frac{10}{9} $$ $$ \frac{3}{4} \div \frac{3}{4} = \frac{3}{4}*\frac{4}{3} = \frac{12}{12} = 1 $$ $$ \frac{2x}{3} \div \frac{x}{2} = \frac{2x}{3}*\frac{2}{x} = \frac{4x}{3x} = \frac{4}{3}$$You might try out the fraction calculator below for more practice: