Multiplying Fractions
Grade 5 · Math · Study Guide
Learn to multiply fractions, whole numbers, and mixed numbers with confidence.
Multiplying fractions is simpler than adding them — you do NOT need a common denominator. Simply multiply the numerators together and multiply the denominators together to get your answer.
When multiplying a fraction by a whole number, write the whole number as a fraction with 1 as the denominator (e.g., 3 = 3/1), then multiply normally. For mixed numbers, first convert them to improper fractions before multiplying.
You can simplify before or after multiplying. Simplifying before (called cross-cancellation) often makes numbers smaller and easier to work with.
| Problem | Step 1 (Multiply) | Simplified Answer |
|---|---|---|
| 1/2 × 3/4 | 3/8 | 3/8 |
| 2/3 × 3/5 | 6/15 | 2/5 |
| 3/4 × 8 | 24/4 | 6 |
| Mixed Number | Conversion | Improper Fraction |
|---|---|---|
| 1 1/2 | (1×2)+1 = 3, keep denominator 2 | 3/2 |
| 2 3/4 | (2×4)+3 = 11, keep denominator 4 | 11/4 |
| 3 1/3 | (3×3)+1 = 10, keep denominator 3 | 10/3 |
Key terms
- Improper Fraction
- A fraction where the numerator is greater than or equal to the denominator, e.g., 7/4.
- Mixed Number
- A number made up of a whole number and a fraction, e.g., 1 3/4.
- Cross-Cancellation
- Simplifying a numerator with a denominator diagonally before multiplying to get smaller numbers.
- Product
- The result of multiplication.
Practice questions
What is 2/3 × 3/4?
- 5/7
- 6/7
- 1/2
- 6/12
Show answer
Answer: 1/2
2×3=6, 3×4=12. 6/12 simplifies to 1/2.
What is 1/4 × 8?
- 8/4
- 4
- 2
- 1/2
Show answer
Answer: 2
1/4 × 8/1 = 8/4 = 2.
3/5 × 2/3 = ___
Show answer
Answer: 2/5
3×2=6, 5×3=15. 6/15 simplifies to 2/5.
Convert 2 1/4 to an improper fraction: ___
Show answer
Answer: 9/4
(2×4)+1=9. Improper fraction is 9/4.
What is 1/2 × 1/2?
- 1/4
- 1
- 2/4
- 1/2
Show answer
Answer: 1/4
1×1=1, 2×2=4. Answer is 1/4.
Fun facts
- Multiplying two proper fractions always gives a product smaller than either original fraction!
- Chefs use fraction multiplication constantly — if a recipe serves 4 but you need it for 6, you multiply every ingredient by 3/2.
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