Multiplying & Dividing Fractions (Cambridge International IGCSE Mathematics)

Multiplying Fractions

How do I multiply two fractions?

• Cancel any factors that are common to both the numerator and the denominator

  • The common factors could be in either of the fractions
  • 3 / 25 x 10 / 11 = 3 / / 25 ^ 5 x / 10 ^2 / 11 = 3 / 5 x 2 / 11

• Multiply

  • Multiply the numerators
  • Multiply the denominators
  • $\frac{3}{5}\times\frac{2}{11}=\frac{3\times2}{5\times11}=\frac{6}{55}$

• Cancel any common factors again if possible

  • There should be no common factors if you cancelled them all at the start

How do I multiply two fractions if one is a mixed number?

• Always convert mixed numbers into improper fractions before multiplying

  • Convert improper fractions back into mixed numbers at the end if required

Worked Example Find $\frac{4}{15}\times\frac{25}{11}$.

Answer:

The 15 and 25 can be cancelled before multiplying

$\frac{4}{3 \times 5} \times \frac{5 \times 5}{11} = \frac{4}{3 \times \cancel{5} } \times \frac{ \cancel{5} \times 5}{11} = \frac{4}{3} \times \frac{5}{11}$

Multiply the numerators together and the denominators together

• *$\frac{4\times5}{3\times11}=\frac{20}{33}$

There is no further cancelling that can be done Write down the fraction

$\frac{20}{33}$

Dividing Fractions

How do I divide two fractions?

• Flip the second fraction and change ÷ into × ”

  • $\frac{1}{3}\div\frac{4}{5}$ becomes $\frac{1}{3}\times\frac{5}{4}$
  • The 'flipped' fraction is called a reciprocal fraction

• Cancel any factors that are common to both the numerator and the denominator

• Multiply the fractions

  • Multiply the numerators
  • Multiply the denominators

• Cancel any common factors again if possible

  • There should be no common factors if you cancelled them all at the start

How do I divide two fractions when one of them is a mixed number?

• Always convert mixed numbers into improper fractions before dividing

  • Convert improper fractions back into mixed numbers at the end if required

Exam Hint Remember “flip’n’times":

When dividing fractions you are multiplying by the reciprocal.

Worked Example Divide $3\frac{1}{4}$ by $\frac{3}{8}$, giving your answer as a mixed number.

Answer:

Rewrite $3\frac{1}{4}$ as an improper fraction

$3\frac{1}{4}=\frac{3\times4+1}{4}=\frac{13}{4}$

Turn the division into a multiplication 'Flip' the second fraction and turn ÷ into ×

$\frac{13}{4}\div\frac{3}{8}=\frac{13}{4}\times\frac{8}{3}$

Cancel a factor of 4 from the numerators and denominators

$\frac{13}{4} \times \frac{8}{3} = \frac{13}{ \cancel{4} } \times \frac{ \cancel{4} \times 2}{3} = \frac{13}{1} \times \frac{2}{3}$

Multiply the fractions

$\frac{13\times2}{1\times3}=\frac{26}{3}$

Rewrite as a mixed number

$\frac{26}{3}=\frac{24}{3}+\frac{2}{3}=8\frac{2}{3}$

$8\frac{2}{3}$