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,

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

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,

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

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