How do I multiply fractions?
Here's some good news -- it's pretty easy to multiply fractions! There's no complicated rules or procedures -- just multiply the numerators together and then multiply the denominators together. Here's a few examples just to make sure you understand:
$$ \frac{1}{3}*\frac{1}{2}=\frac{1*1}{3*2}=\frac{1}{6} $$ $$ \frac{4}{7}*\frac{2}{3}=\frac{4*2}{7*3}=\frac{8}{21} $$ $$ \frac{5}{6}*\frac{4}{3}=\frac{5*4}{6*3}=\frac{20}{18}=\frac{10}{9} $$Of course, you can do the same with more complicated fractions that contain variables. The same rules apply -- just multiply the numerators and multiply the denominators. Then simplify the fraction if necessary.
$$ \frac{x}{3}*\frac{1}{2}=\frac{x}{3*2}=\frac{x}{6} $$ $$ \frac{x}{2}*\frac{1+x}{2-x} = \frac{x(1+x)}{2(2-x)}=\frac{x+x^2}{4-2x} $$Remember -- don't try this with addition or subtraction! It only works this way for multiplication.