Fractions: Unlike Denominators, Multiplying and Dividing: Grade 5 Study Guide
Grade 5 completes the arithmetic of fractions that begins in earlier grades.
To add or subtract fractions with unlike denominators, first rewrite them as equivalent fractions with a common denominator. 1/3 + 1/4 becomes 4/12 + 3/12 = 7/12. The common denominator can be the product of the two denominators or, more efficiently, their least common multiple.
Fifth graders also learn that a fraction is a division: 3/4 means 3 ÷ 4. They multiply fractions, interpret multiplication as scaling, and divide a unit fraction by a whole number or a whole number by a unit fraction.
Adding and subtracting
For 2/3 and 3/4, use 12.
8/12 and 9/12.
8/12 + 9/12 = 17/12.
17/12 = 1 5/12.
Multiplying fractions
To multiply fractions, multiply the numerators and multiply the denominators: 2/3 × 3/5 = 6/15 = 2/5. The product of a number and a fraction less than 1 is smaller than the number: 1/2 × 8 = 4. For mixed numbers, convert to improper fractions first: 1 1/2 × 2/3 = 3/2 × 2/3 = 1. An area model makes this concrete: a rectangle 2/3 unit by 3/5 unit has area 6/15 square unit.
| Problem | Working | Answer |
|---|---|---|
| 1/2 × 1/4 | 1 × 1 over 2 × 4 | 1/8 |
| 3/5 × 10 | 30/5 | 6 |
| 2/3 × 3/4 | 6/12 | 1/2 |
| 1 1/2 × 4 | 3/2 × 4 = 12/2 | 6 |
Dividing with unit fractions
Dividing a whole number by a unit fraction asks how many pieces fit. 3 ÷ 1/4 = 12, because each whole has four quarters. Dividing a unit fraction by a whole number splits it into smaller equal parts: 1/2 ÷ 3 = 1/6. Real-life example: 4 pounds of trail mix shared into 1/2-pound bags gives 4 ÷ 1/2 = 8 bags.
Worked examples and common mistakes
Example: A recipe needs 2/3 cup of flour. Making 1 1/2 batches needs 2/3 × 3/2 = 1 cup. Common mistakes: adding denominators (1/3 + 1/4 is not 2/7), forgetting to simplify, and thinking multiplication always makes a number bigger. Estimate with benchmarks such as 0, 1/2 and 1.
Check your understanding: model answers
1. 9/12 − 2/12 = 7/12. 2. 6/40 = 3/20. 3. 4 ÷ 1/3 = 12 scoops.
✨ Key Takeaways
- Use a common denominator to add or subtract.
- Multiply the tops and multiply the bottoms.
- A fraction is also a division.
- Multiplying by a fraction less than 1 gives a smaller number.
💬 Questions for Discussion & Reflection
- Find 3/4 − 1/6.
- Find 2/5 × 3/8.
- How many 1/3-cup scoops are in 4 cups?
Print a fractions equivalence chart →