Let's solve each problem step by step using
visual models and the concept of
dividing a unit fraction by a whole number.
---
🔍 Concept:
When you divide a
unit fraction (like $ \frac{1}{n} $) by a
whole number $ d $, you are splitting that fraction into $ d $ equal parts.
So:
$$
\frac{1}{n} \div d = \frac{1}{n} \times \frac{1}{d} = \frac{1}{n \times d}
$$
We can use this rule and verify it with the models.
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✔ Example Given:
$$
\frac{1}{2} \div 6 = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}
$$
The model shows $ \frac{1}{2} $ split into 6 equal parts → each part is $ \frac{1}{12} $. ✔️
Now let’s solve each problem:
---
Problem 1:
$$
\frac{1}{3} \div 6
$$
- The top bar represents $ \frac{1}{3} $
- It's divided into
6 equal parts (red rectangles)
- So we're splitting $ \frac{1}{3} $ into 6 pieces.
Each piece is:
$$
\frac{1}{3} \div 6 = \frac{1}{3} \times \frac{1}{6} = \frac{1}{18}
$$
✔ Answer: $ \boxed{\frac{1}{18}} $
---
Problem 2:
$$
\frac{1}{9} \div 9
$$
- Top bar: $ \frac{1}{9} $
- Divided into
9 equal parts (purple rectangles)
Each part is:
$$
\frac{1}{9} \div 9 = \frac{1}{9} \times \frac{1}{9} = \frac{1}{81}
$$
✔ Answer: $ \boxed{\frac{1}{81}} $
---
Problem 3:
$$
\frac{1}{7} \div 3
$$
- Top bar: $ \frac{1}{7} $
- Divided into
3 equal parts (blue rectangles)
Each part is:
$$
\frac{1}{7} \div 3 = \frac{1}{7} \times \frac{1}{3} = \frac{1}{21}
$$
✔ Answer: $ \boxed{\frac{1}{21}} $
---
Problem 4:
$$
\frac{1}{5} \div 10
$$
- Top bar: $ \frac{1}{5} $
- Divided into
10 equal parts (green rectangles)
Each part is:
$$
\frac{1}{5} \div 10 = \frac{1}{5} \times \frac{1}{10} = \frac{1}{50}
$$
✔ Answer: $ \boxed{\frac{1}{50}} $
---
Problem 5:
$$
\frac{1}{4} \div 8
$$
- Top bar: $ \frac{1}{4} $
- Divided into
8 equal parts (yellow rectangles)
Each part is:
$$
\frac{1}{4} \div 8 = \frac{1}{4} \times \frac{1}{8} = \frac{1}{32}
$$
✔ Answer: $ \boxed{\frac{1}{32}} $
---
✔ Final Answers:
| Problem | Expression | Answer |
|--------|--------------------|------------|
| 1 | $ \frac{1}{3} \div 6 $ | $ \frac{1}{18} $ |
| 2 | $ \frac{1}{9} \div 9 $ | $ \frac{1}{81} $ |
| 3 | $ \frac{1}{7} \div 3 $ | $ \frac{1}{21} $ |
| 4 | $ \frac{1}{5} \div 10 $ | $ \frac{1}{50} $ |
| 5 | $ \frac{1}{4} \div 8 $ | $ \frac{1}{32} $ |
---
🧠 Summary Rule:
> To divide a unit fraction $ \frac{1}{n} $ by a whole number $ d $, multiply the denominator:
> $$
> \frac{1}{n} \div d = \frac{1}{n \times d}
> $$
This matches what the models show — splitting a smaller piece into even smaller equal parts.
Let me know if you'd like a visual explanation for any specific one!
Parent Tip: Review the logic above to help your child master the concept of dividing fractions with models worksheet.
