Mixed numbers (Edexcel GCSE Maths): Revision Notes

Worked Example: Converting Mixed Number to Improper Fraction

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

Worked Example: Converting Improper Fraction to Mixed Number

Convert $\frac{23}{5}$ to a mixed number

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

Step 2: The quotient becomes the whole number part: $4$

Step 3: The remainder becomes the new numerator: $3$

Step 4: Keep the same denominator: $5$

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

Worked Example: Multiplying Mixed Numbers

Calculate $4\frac{1}{2} \times 3$

Step 1: Convert $4\frac{1}{2}$ to improper fraction $(4 \times 2 + 1) \div 2 = \frac{9}{2}$

Step 2: Multiply the fractions $\frac{9}{2} \times \frac{3}{1} = \frac{27}{2}$

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

Worked Example: Subtracting Mixed Numbers

Calculate $3\frac{2}{5} - 1\frac{1}{2}$

Step 1: Convert both to improper fractions

• $3\frac{2}{5} = \frac{17}{5}$
• $1\frac{1}{2} = \frac{3}{2}$

Step 2: Find common denominator and subtract $\frac{17}{5} - \frac{3}{2} = \frac{34}{10} - \frac{15}{10} = \frac{19}{10}$

Step 3: Convert back to mixed number $\frac{19}{10} = 1\frac{9}{10}$