Students practice ordering mixed sets of fractions and decimals on number lines with this worksheet.

It looks like you've uploaded a worksheet titled "Compare and Order: Fractions and Decimals", which contains several problems asking students to order numbers from least to greatest. The numbers include fractions, decimals, and mixed numbers.

Let’s go through each problem step by step and solve them correctly, explaining the process.

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🔹 Problem 0:

Order the following numbers from least to greatest:
$$
\frac{1}{4}, \; 0.5, \; \frac{3}{5}
$$

#### Step 1: Convert all numbers to decimals.
- $ \frac{1}{4} = 0.25 $
- $ 0.5 = 0.5 $
- $ \frac{3}{5} = 0.6 $

#### Step 2: Order the decimals:
$$
0.25 < 0.5 < 0.6
$$

#### Final Answer:
$$
\boxed{\frac{1}{4},\; 0.5,\; \frac{3}{5}}
$$

✔ Correct order: $ \frac{1}{4},\; 0.5,\; \frac{3}{5} $

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🔹 Problem 1:

Order the following numbers from least to greatest:
$$
1\frac{1}{2},\; 0.8,\; \frac{3}{5}
$$

#### Step 1: Convert all to decimals.
- $ 1\frac{1}{2} = 1.5 $
- $ 0.8 = 0.8 $
- $ \frac{3}{5} = 0.6 $

#### Step 2: Order:
$$
0.6 < 0.8 < 1.5
$$

So:
$$
\frac{3}{5},\; 0.8,\; 1\frac{1}{2}
$$

#### Final Answer:
$$
\boxed{\frac{3}{5},\; 0.8,\; 1\frac{1}{2}}
$$

---

🔹 Problem 2:

Order the following numbers from least to greatest:
$$
2\frac{1}{2},\; 2.05,\; \frac{5}{2},\; 2.8
$$

Note: $ \frac{5}{2} = 2.5 $, and $ 2\frac{1}{2} = 2.5 $

So we have:
- $ 2\frac{1}{2} = 2.5 $
- $ 2.05 $
- $ \frac{5}{2} = 2.5 $
- $ 2.8 $

Now list the decimals:
- $ 2.05 $
- $ 2.5 $ (twice)
- $ 2.8 $

So order is:
$$
2.05 < 2.5 = 2.5 < 2.8
$$

But since both $ 2\frac{1}{2} $ and $ \frac{5}{2} $ equal 2.5, they are equal.

#### Final Answer:
$$
\boxed{2.05,\; 2\frac{1}{2},\; \frac{5}{2},\; 2.8}
$$

(Or any order of $ 2\frac{1}{2} $ and $ \frac{5}{2} $, since they're equal.)

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🔹 Problem 3:

Order the following numbers from least to greatest:
$$
\frac{1}{2},\; 0.4,\; \frac{3}{5},\; 2.5
$$

Convert:
- $ \frac{1}{2} = 0.5 $
- $ 0.4 = 0.4 $
- $ \frac{3}{5} = 0.6 $
- $ 2.5 = 2.5 $

Order:
$$
0.4 < 0.5 < 0.6 < 2.5
$$

So:
$$
0.4,\; \frac{1}{2},\; \frac{3}{5},\; 2.5
$$

#### Final Answer:
$$
\boxed{0.4,\; \frac{1}{2},\; \frac{3}{5},\; 2.5}
$$

---

🔹 Problem 4:

Order the following numbers from least to greatest:
$$
0.75,\; 0.8,\; \frac{3}{4},\; 0.65,\; 0.75
$$

Note: $ \frac{3}{4} = 0.75 $

So numbers are:
- $ 0.75 $
- $ 0.8 $
- $ 0.75 $
- $ 0.65 $
- $ 0.75 $

List all values:
- $ 0.65 $
- $ 0.75 $ (three times)
- $ 0.8 $

So:
$$
0.65 < 0.75 = 0.75 = 0.75 < 0.8
$$

Now list them in order:
$$
0.65,\; 0.75,\; 0.75,\; 0.75,\; 0.8
$$

But since $ \frac{3}{4} = 0.75 $, and there are three 0.75s (including one written as fraction), we can write:

#### Final Answer:
$$
\boxed{0.65,\; 0.75,\; 0.75,\; \frac{3}{4},\; 0.8}
$$

(Or any order of the 0.75s — they’re equal.)

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🔹 Problem 5:

Order the following numbers from least to greatest:
$$
0.75,\; 0.8,\; 0.65,\; 0.75,\; 0.75
$$

Same as above, just without the fraction.

Numbers:
- $ 0.65 $
- $ 0.75 $ (three times)
- $ 0.8 $

Order:
$$
\boxed{0.65,\; 0.75,\; 0.75,\; 0.75,\; 0.8}
$$

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✔ Summary of All Answers:

| Problem | Ordered List |
|--------|--------------|
| 0 | $ \frac{1}{4},\; 0.5,\; \frac{3}{5} $ |
| 1 | $ \frac{3}{5},\; 0.8,\; 1\frac{1}{2} $ |
| 2 | $ 2.05,\; 2\frac{1}{2},\; \frac{5}{2},\; 2.8 $ |
| 3 | $ 0.4,\; \frac{1}{2},\; \frac{3}{5},\; 2.5 $ |
| 4 | $ 0.65,\; 0.75,\; 0.75,\; \frac{3}{4},\; 0.8 $ |
| 5 | $ 0.65,\; 0.75,\; 0.75,\; 0.75,\; 0.8 $ |

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🔍 Key Strategy:

To compare fractions and decimals:
1. Convert all numbers to decimals (easier for comparison).
2. Order the decimal values from smallest to largest.
3. Write the original numbers in that order.

This method ensures accuracy and avoids confusion between fractions and decimals.

Let me know if you'd like this formatted as a printable answer key!