Arithmetic Operations
Multiplying Mixed Numbers
To multiply mixed numbers, always convert them to improper fractions first. This turns the problem into one you already know how to solve.
How to Convert a Mixed Number to an Improper Fraction
2¾ → (2 × 4) + 3 = 11 → 11/4
Multiply the whole number by the denominator, add the numerator, keep the denominator.
Worked Examples
Easy: 2½ × 3
Convert: 2½ = 5/2. Then 5/2 × 3/1 = 15/2 = 7½
Medium: 1⅔ × 2¼
1⅔ = 5/3. 2¼ = 9/4. Multiply: 5/3 × 9/4 = 45/12. Simplify: 45/12 = 15/4 = 3¾
Advanced: 3½ × 2⅔
7/2 × 8/3 = 56/6 = 28/3 = 9⅓
Key Takeaways
- Always convert mixed numbers to improper fractions before multiplying.
- Multiply numerators together and denominators together.
- Simplify and convert back to a mixed number if needed.
- Cancel before multiplying to keep numbers manageable.
Practice: Multiply Mixed Numbers
Give your answer as a fraction (e.g. 15/2)