Divide Whole Numbers by Fractions - Free Printable

The image you've uploaded is a math worksheet titled "Dividing Whole Numbers by Unit Fractions 3 Answers", which provides solutions to 30 problems involving division of whole numbers by unit fractions.

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🔍 What Is a Unit Fraction?

A unit fraction is a fraction with a numerator of 1, such as $ \frac{1}{2}, \frac{1}{3}, \frac{1}{4} $, etc.

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✔ Key Concept:

When dividing a whole number by a unit fraction, the result is:

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

This is because dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of $ \frac{1}{n} $ is $ n $.

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🧮 Example:

Let’s take problem #1:
$$
3 \div \frac{1}{4} = 3 \times 4 = 12
$$
Which matches the answer shown in red.

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✔ General Rule:

$$
a \div \frac{1}{b} = a \times b
$$

So, for any problem like:
$$
x \div \frac{1}{y} = x \times y
$$

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✔️ Verification of a Few Problems:

| Problem | Calculation | Answer |
|--------|-------------|--------|
| 1) $ 3 \div \frac{1}{4} $ | $ 3 \times 4 = 12 $ | ✔ 12 |
| 5) $ 6 \div \frac{1}{4} $ | $ 6 \times 4 = 24 $ | ✔ 24 |
| 10) $ 6 \div \frac{1}{3} $ | $ 6 \times 3 = 18 $ | ✔ 18 |
| 29) $ 11 \div \frac{1}{6} $ | $ 11 \times 6 = 66 $ | ✔ 66 |

All answers follow this rule consistently.

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✔ Summary:

- This worksheet is correctly solved.
- The rule used:
$$
\text{Whole number} \div \frac{1}{n} = \text{Whole number} \times n
$$
- Each answer is obtained by multiplying the whole number by the denominator of the unit fraction.

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💡 Why Does This Work?

Think about it: If you divide 3 by $ \frac{1}{4} $, you're asking:
"How many $ \frac{1}{4} $s are in 3?"

Since one whole has 4 quarters, then 3 wholes have $ 3 \times 4 = 12 $ quarters.

So, $ 3 \div \frac{1}{4} = 12 $

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📌 Final Note:

This worksheet is from Math-Salamanders.com, a site known for providing free math resources. It's great for practicing division with fractions and reinforcing conceptual understanding.

If you'd like, I can generate a similar worksheet or explain how to teach this concept visually (e.g., using number lines or area models). Let me know!