Arithmetic/Multiplying Fractions

Multiplying fractions
To multiply two fractions:
 * multiply the numerators to get the new numerator, and
 * multiply the denominators to get the new denominator.

For instance,


 * $$\frac{2}{3} \times \frac{1}{4} = \frac{2 \times 1}{3 \times 4} = \frac{2}{12} = \frac{1}{6}$$.

Dividing fractions
To divide one fraction by another one, flip numerator and denominator of the second one, and then multiply the two fractions. The flipped-over fraction is called the multiplicative inverse or reciprocal.

For instance,


 * $$\left(\frac{2}{3}\right) / \left(\frac{4}{5}\right) = \frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12} = \frac{5}{6}$$.

To simplify a compound fraction, like $$\frac{\left(\frac{3}{5}\right)}{\left(\frac{1}{4}\right)}$$, just remember that a fraction is the same as division, and divide (3/5) &divide; (1/4), which comes to 12/5.