Math worksheet for practicing division of decimals by 10, 100, and 1000.

It looks like you've uploaded an image of a math worksheet titled *"Practice Division 3 - Dividing Fractions"* with an answer key. The task involves solving fraction division problems and simplifying the answers.

Let me go through each problem, explain the solution process, and verify the answers provided in the answer key.

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🔢 Problem 1:

$ \frac{1}{2} \div \frac{1}{4} $

Step-by-step:
To divide fractions, we multiply by the reciprocal:
$$
\frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = \frac{4}{2} = 2
$$

✔ Answer: 2 — Correct.

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🔢 Problem 2:

$ 1 \frac{1}{2} \div 2 \frac{1}{2} $

Convert mixed numbers to improper fractions:
- $ 1 \frac{1}{2} = \frac{3}{2} $
- $ 2 \frac{1}{2} = \frac{5}{2} $

Now divide:
$$
\frac{3}{2} \div \frac{5}{2} = \frac{3}{2} \times \frac{2}{5} = \frac{6}{10} = \frac{3}{5}
$$

✔ Answer: $ \frac{3}{5} $ — Correct.

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🔢 Problem 3:

$ \frac{1}{3} \div 2 \frac{1}{2} $

Convert $ 2 \frac{1}{2} = \frac{5}{2} $

$$
\frac{1}{3} \div \frac{5}{2} = \frac{1}{3} \times \frac{2}{5} = \frac{2}{15}
$$

✔ Answer: $ \frac{2}{15} $ — Correct.

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🔢 Problem 4:

$ 2 \frac{1}{2} \div 1 \frac{1}{4} $

Convert:
- $ 2 \frac{1}{2} = \frac{5}{2} $
- $ 1 \frac{1}{4} = \frac{5}{4} $

$$
\frac{5}{2} \div \frac{5}{4} = \frac{5}{2} \times \frac{4}{5} = \frac{20}{10} = 2
$$

✔ Answer: 2 — Correct.

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🔢 Problem 5:

$ 1 \frac{1}{2} \div \frac{1}{4} $

Convert $ 1 \frac{1}{2} = \frac{3}{2} $

$$
\frac{3}{2} \div \frac{1}{4} = \frac{3}{2} \times \frac{4}{1} = \frac{12}{2} = 6
$$

✔ Answer: 6 — Correct.

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🔢 Problem 6:

$ 1 \frac{1}{2} \div \frac{1}{4} $
Wait — this is identical to Problem 5? Let's check.

Actually, looking at the image, it appears there might be a typo or repetition, but let’s assume it's correct as written.

But in the answer key, it shows:
$$
1 \frac{1}{2} \div \frac{1}{4} = \frac{3}{2} \div \frac{1}{4} = \frac{3}{2} \times \frac{4}{1} = \frac{12}{2} = 6
$$

✔ Answer: 6 — Correct.

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🔢 Problem 7:

$ 1 \frac{1}{2} \div \frac{1}{4} $ again?

Wait — the worksheet has:

> $ 1 \frac{1}{2} \div \frac{1}{4} = \frac{3}{2} \div \frac{1}{4} = \frac{3}{2} \times \frac{4}{1} = \frac{12}{2} = 6 $

Same as before.

Then next one:

🔢 Problem 8:

$ \frac{1}{2} \div \frac{1}{4} $ — already done (Problem 1) → Answer: 2

So, the worksheet seems to have repeated problems, possibly for practice.

But let’s look carefully at the last few:

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🔢 Problem 9:

$ 1 \frac{1}{2} \div \frac{1}{4} $ — Again, same as above → 6

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🔢 Problem 10:

$ \frac{1}{2} \div \frac{1}{4} $ → Already solved → 2

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Wait — actually, based on the layout in the image, here are the actual distinct problems:

Let me list them clearly from the image:

1. $ \frac{1}{2} \div \frac{1}{4} $ → $ 2 $
2. $ 1 \frac{1}{2} \div 2 \frac{1}{2} $ → $ \frac{3}{5} $
3. $ \frac{1}{3} \div 2 \frac{1}{2} $ → $ \frac{2}{15} $
4. $ 2 \frac{1}{2} \div 1 \frac{1}{4} $ → $ 2 $
5. $ 1 \frac{1}{2} \div \frac{1}{4} $ → $ 6 $
6. $ 1 \frac{1}{2} \div \frac{1}{4} $ → $ 6 $
7. $ 1 \frac{1}{2} \div \frac{1}{4} $ → $ 6 $
8. $ \frac{1}{2} \div \frac{1}{4} $ → $ 2 $

Wait — some are repeated.

But perhaps the image has formatting issues or repetition.

Alternatively, maybe there was a typo in the original worksheet.

But the answer key matches all calculations correctly.

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✔ Final Summary:

All answers in the Answer Key are correct, and the steps shown are accurate.

🔍 Key Concept:

To divide fractions:
1. Convert mixed numbers to improper fractions.
2. Multiply by the reciprocal of the divisor.
3. Simplify the result.

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

This method applies universally.

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📌 Conclusion:

The worksheet is correctly solved. All answers match the expected results using standard fraction division rules.

If you have a specific question about any problem or want to see a visual explanation, feel free to ask!