Let's solve each problem step by step using the visual models provided. The task is to
divide whole numbers by unit fractions and explain what the operation means.
---
🔷 Understanding the Concept:
Dividing a whole number by a
unit fraction (like $ \frac{1}{5}, \frac{1}{4}, \frac{1}{2} $, etc.) means:
>
"How many parts of size $ \frac{1}{n} $ fit into the whole number?"
For example:
$ 6 \div \frac{1}{5} $ means: *How many $ \frac{1}{5} $-sized pieces are in 6 wholes?*
Each whole is divided into 5 equal parts ($ \frac{1}{5} $), so we count how many such parts there are across all wholes.
---
✔ Problem 1:
$$
6 \div \frac{1}{5} = ?
$$
Visual Model:
- There are
6 wholes, each divided into
5 equal parts.
- Each part is $ \frac{1}{5} $.
- So total number of $ \frac{1}{5} $ parts = $ 6 \times 5 = 30 $
✔ Answer: $ \boxed{30} $
Means:
*There are 30 one-fifths in 6 wholes.*
---
✔ Problem 2:
$$
7 \div \frac{1}{4} = ?
$$
Visual Model:
- 7 wholes, each divided into
4 parts → each part is $ \frac{1}{4} $
- Total $ \frac{1}{4} $ parts = $ 7 \times 4 = 28 $
✔ Answer: $ \boxed{28} $
Means:
*There are 28 one-fourths in 7 wholes.*
---
✔ Problem 3:
$$
9 \div \frac{1}{2} = ?
$$
Visual Model:
- 9 wholes, each divided into
2 halves → each part is $ \frac{1}{2} $
- Total $ \frac{1}{2} $ parts = $ 9 \times 2 = 18 $
✔ Answer: $ \boxed{18} $
Means:
*There are 18 one-halves in 9 wholes.*
---
✔ Problem 4:
$$
2 \div \frac{1}{7} = ?
$$
Visual Model:
- 2 wholes, each divided into
7 parts → each part is $ \frac{1}{7} $
- Total $ \frac{1}{7} $ parts = $ 2 \times 7 = 14 $
✔ Answer: $ \boxed{14} $
Means:
*There are 14 one-sevenths in 2 wholes.*
---
✔ Problem 5:
$$
5 \div \frac{1}{3} = ?
$$
Visual Model:
- 5 wholes, each divided into
3 parts → each part is $ \frac{1}{3} $
- Total $ \frac{1}{3} $ parts = $ 5 \times 3 = 15 $
✔ Answer: $ \boxed{15} $
Means:
*There are 15 one-thirds in 5 wholes.*
---
📌 General Rule:
When dividing a whole number $ n $ by a unit fraction $ \frac{1}{k} $:
$$
n \div \frac{1}{k} = n \times k
$$
Because you're counting how many $ \frac{1}{k} $-sized pieces fit into $ n $ wholes.
---
✔ Final Answers:
| Problem | Expression | Answer | Meaning |
|--------|--------------------|--------|--------|
| 1 | $ 6 \div \frac{1}{5} $ | 30 | There are 30 fifths in 6 wholes. |
| 2 | $ 7 \div \frac{1}{4} $ | 28 | There are 28 fourths in 7 wholes. |
| 3 | $ 9 \div \frac{1}{2} $ | 18 | There are 18 halves in 9 wholes. |
| 4 | $ 2 \div \frac{1}{7} $ | 14 | There are 14 sevenths in 2 wholes. |
| 5 | $ 5 \div \frac{1}{3} $ | 15 | There are 15 thirds in 5 wholes. |
Let me know if you'd like these written out in your notebook format!
Parent Tip: Review the logic above to help your child master the concept of dividing fractions using models worksheet.
