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) ÷ (1/4), which comes to 12/5.