Which number line correctly labels the points between 2 and 3 with mixed numbers and decimals?

We are given four number lines (A, B, C, D), each showing points labeled with values between 2 and 3. We need to determine which number line correctly labels the points in increasing order from left to right.

The values involved are:

- $ 2\frac{1}{3} $
- $ 2.4 $
- $ 2.6 $
- $ 2\frac{1}{2} $
- $ 2\frac{1}{5} $

Let’s convert all these numbers to decimal form for easier comparison.

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Step 1: Convert fractions to decimals

1. $ 2\frac{1}{3} = 2 + \frac{1}{3} \approx 2 + 0.333 = 2.333 $
2. $ 2.4 = 2.4 $
3. $ 2.6 = 2.6 $
4. $ 2\frac{1}{2} = 2 + \frac{1}{2} = 2.5 $
5. $ 2\frac{1}{5} = 2 + \frac{1}{5} = 2 + 0.2 = 2.2 $

So the decimal equivalents are:

- $ 2\frac{1}{5} = 2.2 $
- $ 2\frac{1}{3} \approx 2.333 $
- $ 2.4 = 2.4 $
- $ 2\frac{1}{2} = 2.5 $
- $ 2.6 = 2.6 $

Now list them in ascending order:

$$
2.2 < 2.333 < 2.4 < 2.5 < 2.6
$$

So the correct order is:

$$
2\frac{1}{5} < 2\frac{1}{3} < 2.4 < 2\frac{1}{2} < 2.6
$$

This means, on a number line from left to right, the points should be labeled in this order:

1. $ 2\frac{1}{5} $
2. $ 2\frac{1}{3} $
3. $ 2.4 $
4. $ 2\frac{1}{2} $
5. $ 2.6 $

Now let's check each option.

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Option A:

Labels:
$ 2\frac{1}{3}, 2.4, 2.6, 2\frac{1}{2}, 2\frac{1}{5} $

Order:
2.333, 2.4, 2.6, 2.5, 2.2 → Incorrect, because 2.2 should come first, not last.

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Option B:

Labels:
$ 2.4, 2.6, 2\frac{1}{2}, 2\frac{1}{3}, 2\frac{1}{5} $

Order:
2.4, 2.6, 2.5, 2.333, 2.2 → Not increasing — 2.2 is at the end. Incorrect

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Option C:

Labels:
$ 2\frac{1}{2}, 2\frac{1}{3}, 2.4, 2\frac{1}{5}, 2.6 $

Order:
2.5, 2.333, 2.4, 2.2, 2.6 → Starts with 2.5, then drops to 2.333 — not increasing. Incorrect

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Option D:

Labels:
$ 2\frac{1}{5}, 2\frac{1}{3}, 2.4, 2\frac{1}{2}, 2.6 $

Order:
2.2, 2.333, 2.4, 2.5, 2.6 → This matches our correct ascending order! ✔

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✔ Correct Answer: D

It shows the points in the correct increasing order.

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Final Answer: D ✔