Multiplying & Dividing Fractions

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

• The common factors could be in either of the fractions

• $\frac{3}{25}\times \frac{10}{11}=\frac{3}{{\cancel{25}}^5}\times \frac{{\cancel{10}}^2}{11}=\frac{3}{5}\times \frac{2}{11}$

Multiply

• Multiply the numerators

• Multiply the denominators

• $\frac{3}{5}\times \frac{2}{11}=\frac{3\times 2}{5\times 11}=\frac{6}{55}$

Cancel any common factors again if possible

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

Always convert mixed numbers into improper fractions before multiplying

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

Flip the second fraction and change ÷ into × ”

• $\frac{1}{3}÷\frac{4}{5}$  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

Always convert mixed numbers into improper fractions before dividing

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