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Multiplying fractions

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To multiply two fractions:

  • multiply the numerators to get the new numerator, and
  • multiply the denominators to get the new denominator.

For instance,

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

Dividing fractions

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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,

( 2 3 ) / ( 4 5 ) = 2 3 × 5 4 = 2 × 5 3 × 4 = 10 12 = 5 6 {\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 ( 3 5 ) ( 1 4 ) {\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.

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