Free Dividing Whole Numbers By Fractions Worksheets [PDFs] - Free Printable

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 part is $ \frac{1}{3} $, so there are 12 parts of $ \frac{1}{3} $ in 4.

✔ Answer: 12

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✔ Problem 2: $ 8 \div \frac{1}{4} $

Model:
8 whole bars, each divided into 4 equal parts ($ \frac{1}{4} $).

Total parts = $ 8 \times 4 = 32 $

So, there are 32 parts of $ \frac{1}{4} $ in 8.

✔ Answer: 32

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✔ Problem 3: $ 2 \div \frac{1}{6} $

Model:
2 whole bars, each divided into 6 equal parts ($ \frac{1}{6} $).

Total parts = $ 2 \times 6 = 12 $

So, there are 12 parts of $ \frac{1}{6} $ in 2.

✔ Answer: 12

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✔ Problem 4: $ 7 \div \frac{1}{4} $

Model:
7 whole bars, each divided into 4 equal parts ($ \frac{1}{4} $).

Total parts = $ 7 \times 4 = 28 $

So, there are 28 parts of $ \frac{1}{4} $ in 7.

✔ Answer: 28

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✔ Problem 5: $ 3 \div \frac{1}{9} $

Model:
3 whole bars, each divided into 9 equal parts ($ \frac{1}{9} $).

Total parts = $ 3 \times 9 = 27 $

So, there are 27 parts of $ \frac{1}{9} $ in 3.

✔ Answer: 27

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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} $

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💡 General Rule:

$$
\text{Whole number} \div \frac{1}{n} = \text{Whole number} \times n
$$

Because dividing by a unit fraction is the same as multiplying by its reciprocal.

For example:
- $ 4 \div \frac{1}{3} = 4 \times 3 = 12 $

This rule matches what we see in the models!

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✔ All answers are consistent with both the visual models and mathematical rules.