Multiplying & Dividing Fractions (Edexcel IGCSE Maths)

Multiplying Fractions

Spec point — 1.2I

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

Exam Hint In most questions, you can just use your calculator to multiply fractions. However, sometimes you get asked to show your working without using a calculator.

Worked Example Show that $\frac{4}{15}\times\frac{25}{11}=\frac{20}{33}$.

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

Spec point — 1.2I

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 Show that $3\frac{1}{4}\div\frac{3}{8}=8\frac{2}{3}$.

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

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

$8\frac{2}{3}$