Let's solve each problem step by step using the visual models provided in the worksheet. The task is to
divide whole numbers by unit fractions (fractions with numerator 1), and the models help us visualize how many parts of the fraction fit into the whole number.
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🔷 Understanding the Concept
When you divide a whole number by a unit fraction (like $ \frac{1}{3} $), you are asking:
"How many $ \frac{1}{3} $s are in the whole number?"
For example:
- $ 4 \div \frac{1}{3} $ means: How many $ \frac{1}{3} $ pieces are in 4?
We can use the model to count how many $ \frac{1}{3} $ segments fit into the whole number.
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✔ Problem 1: $ 4 \div \frac{1}{3} $
Model:
There are 4 whole bars, each divided into 3 equal parts (each part is $ \frac{1}{3} $).
So total parts = $ 4 \times 3 = 12 $
Each $ \frac{1}{3} $ is one segment.
✔ So, $ 4 \div \frac{1}{3} = 12 $
>
Answer: $ \boxed{12} $
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✔ Problem 2: $ 8 \div \frac{1}{4} $
Model:
8 whole bars, each split into 4 parts ($ \frac{1}{4} $).
Total number of $ \frac{1}{4} $ parts = $ 8 \times 4 = 32 $
✔ So, $ 8 \div \frac{1}{4} = 32 $
>
Answer: $ \boxed{32} $
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✔ Problem 3: $ 2 \div \frac{1}{6} $
Model:
2 whole bars, each divided into 6 parts ($ \frac{1}{6} $).
Total parts = $ 2 \times 6 = 12 $
✔ So, $ 2 \div \frac{1}{6} = 12 $
>
Answer: $ \boxed{12} $
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✔ Problem 4: $ 7 \div \frac{1}{4} $
Model:
7 whole bars, each divided into 4 parts ($ \frac{1}{4} $).
Total parts = $ 7 \times 4 = 28 $
✔ So, $ 7 \div \frac{1}{4} = 28 $
>
Answer: $ \boxed{28} $
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✔ Problem 5: $ 3 \div \frac{1}{9} $
Model:
3 whole bars, each divided into 9 parts ($ \frac{1}{9} $).
Total parts = $ 3 \times 9 = 27 $
✔ So, $ 3 \div \frac{1}{9} = 27 $
>
Answer: $ \boxed{27} $
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📌 General Rule:
Dividing a whole number $ n $ by a unit fraction $ \frac{1}{k} $ gives:
$$
n \div \frac{1}{k} = n \times k
$$
This is because dividing by a fraction is the same as multiplying by its reciprocal.
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✔ Final Answers:
1) $ 4 \div \frac{1}{3} = \boxed{12} $
2) $ 8 \div \frac{1}{4} = \boxed{32} $
3) $ 2 \div \frac{1}{6} = \boxed{12} $
4) $ 7 \div \frac{1}{4} = \boxed{28} $
5) $ 3 \div \frac{1}{9} = \boxed{27} $
Let me know if you'd like this explained further or want to practice more! 😊
Parent Tip: Review the logic above to help your child master the concept of dividing unit fractions worksheet.
