Dividing Fractions and Operations with Decimals: Grade 6 Study Guide
Grade 6 completes the four operations with fractions and decimals.
To divide by a fraction, multiply by its reciprocal. The reciprocal of 2/3 is 3/2. So 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8 = 1 1/8. This works because dividing asks 'how many of these fit into that?' and a visual model such as a strip diagram shows it: 2 ÷ 1/4 = 8 because each whole holds four quarters.
Students also fluently use the standard algorithm for multi-digit division and add, subtract, multiply and divide decimals. They find the greatest common factor (GCF) and least common multiple (LCM) of two numbers.
Dividing fractions
3/4
3/4 ×
3/2
9/8 = 1 1/8
Word problems
A ribbon 3/4 yard long is cut into pieces 1/8 yard long. 3/4 ÷ 1/8 = 3/4 × 8 = 6 pieces. A trail mix recipe uses 2/3 cup of raisins per batch. With 4 cups of raisins: 4 ÷ 2/3 = 4 × 3/2 = 6 batches. Mixed numbers are converted to improper fractions first: 1 1/2 ÷ 3/4 = 3/2 × 4/3 = 2.
| Problem | Rewrite | Answer |
|---|---|---|
| 1/2 ÷ 1/4 | 1/2 × 4/1 | 2 |
| 2/3 ÷ 4/5 | 2/3 × 5/4 = 10/12 | 5/6 |
| 3 ÷ 3/5 | 3 × 5/3 | 5 |
| 1 1/2 ÷ 1/3 | 3/2 × 3 | 4 1/2 |
Decimals, GCF and LCM
For decimals, line up the points to add or subtract, and count decimal places to place the point in a product. To divide 4.5 ÷ 0.15, shift both numbers two places: 450 ÷ 15 = 30. The GCF of 12 and 18 is 6; use it to simplify or factor: 12 + 18 = 6(2 + 3). The LCM of 4 and 6 is 12; use it for common denominators or repeating events.
Worked examples and common mistakes
Example: Check 2/3 ÷ 1/6 = 4 by multiplication: 4 × 1/6 = 4/6 = 2/3. Common mistakes: flipping the wrong fraction, forgetting to convert mixed numbers and thinking division always makes a number smaller. Dividing by a fraction less than 1 gives a larger result.
Check your understanding: model answers
1. 5/6 × 3 = 15/6 = 2 1/2. 2. 12. 3. 72 ÷ 4 = 18.
✨ Key Takeaways
- Dividing by a fraction means multiplying by its reciprocal.
- Dividing by a fraction less than 1 gives a bigger number.
- Line up decimal points to add or subtract.
- GCF simplifies; LCM finds common denominators.
💬 Questions for Discussion & Reflection
- Find 5/6 ÷ 1/3.
- Find the GCF of 24 and 36.
- Find 7.2 ÷ 0.4.
Print a fractions equivalence chart →