Mixed numbers (AQA GCSE Maths): Revision Notes

Worked Example: Converting $3\frac{1}{4}$ to an improper fraction

Step 1: Multiply the whole number by the denominator $3 \times 4 = 12$

Step 2: Add the result to the numerator $12 + 1 = 13$

Step 3: Keep the same denominator $\frac{13}{4}$

Therefore: $3\frac{1}{4} = \frac{13}{4}$

Worked Example: Converting $\frac{23}{5}$ to a mixed number

Step 1: Divide the numerator by the denominator $23 ÷ 5 = 4$ remainder $3$

Step 2: Write as a mixed number

• Whole number part: $4$
• Remainder as numerator: $3$
• Keep denominator: $5$

Therefore: $\frac{23}{5} = 4\frac{3}{5}$

Worked Example: Calculating $4\frac{1}{2} \times 3$

Step 1: Convert to improper fraction $4\frac{1}{2} = \frac{9}{2}$

Step 2: Multiply $\frac{9}{2} \times 3 = \frac{9 \times 3}{2} = \frac{27}{2}$

Step 3: Convert back to mixed number $\frac{27}{2} = 13\frac{1}{2}$

Worked Example: Calculating $3\frac{2}{5} - 1\frac{1}{5}$

Step 1: Convert both to improper fractions $3\frac{2}{5} = \frac{17}{5}$ and $1\frac{1}{5} = \frac{6}{5}$

Step 2: Subtract $\frac{17}{5} - \frac{6}{5} = \frac{11}{5}$

Step 3: Convert back to mixed number $\frac{11}{5} = 2\frac{1}{5}$

Worked Example: Sharing pizzas equally

Problem: Someone has $2\frac{1}{2}$ pizzas and wants to divide them equally between 3 people.

Step 1: Convert to improper fraction $2\frac{1}{2} = \frac{5}{2}$

Step 2: Divide using "flip and multiply" $\frac{5}{2} ÷ 3 = \frac{5}{2} \times \frac{1}{3} = \frac{5}{6}$

Answer: Each person receives $\frac{5}{6}$ of a pizza.