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 Questions
- Calculate 3½ × 2.
- Calculate 1¼ × 2½.
- Calculate 2⅔ × 1½.
- A piece of wood is 3¾ m long. You need 2½ pieces. What total length do you need?
- Calculate 4¼ × 3⅓.