Comparing Fractions worksheet with visual fraction models and answer key.

Let’s solve each problem one by one. We need to find the fraction that goes in the middle so that the inequality is true:
left fraction < middle fraction < right fraction

We’ll compare fractions by converting them to have the same denominator (common denominator) or by thinking about their size using pictures or number sense.

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Problem 1:

3/8 < ? < 5/8

Look at the options:
- 4/8 → this is between 3/8 and 5/8 ✔
- 2/8 → too small
- 6/8 → too big
- 5/6 → bigger than 5/8? Let’s check: 5/6 ≈ 0.83, 5/8 = 0.625 → yes, too big

So only 4/8 fits.

✔ Answer for #1: 4/8

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Problem 2:

1/4 < ? < 2/3

Options:
- 1/6 → 1/6 ≈ 0.166, 1/4 = 0.25 → too small ✘
- 4/8 = 1/2 = 0.5 → Is 0.25 < 0.5 < 0.666? YES ✔
- 5/6 ≈ 0.833 → too big ✘
- 6/8 = 3/4 = 0.75 → also bigger than 2/3 (≈0.666) ✘

So 4/8 works.

✔ Answer for #2: 4/8

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Problem 3:

3/6 < ? < 2/3

Note: 3/6 = 1/2 = 0.5, 2/3 ≈ 0.666

Options:
- 2/8 = 1/4 = 0.25 → too small ✘
- 1/8 = 0.125 → too small ✘
- 5/8 = 0.625 → Is 0.5 < 0.625 < 0.666? YES ✔
- 6/8 = 3/4 = 0.75 → too big ✘

So 5/8 fits.

✔ Answer for #3: 5/8

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Problem 4:

1/8 < ? < 2/4

2/4 = 1/2 = 0.5, 1/8 = 0.125

Options:
- 1/6 ≈ 0.166 → Is 0.125 < 0.166 < 0.5? YES ✔
- 3/4 = 0.75 → too big ✘
- 5/6 ≈ 0.833 → too big ✘
- 5/8 = 0.625 → too big ✘

Wait — let’s double-check: 1/6 ≈ 0.166, which is greater than 1/8 (0.125) and less than 0.5 → YES.

But look at the answer key on the right — it says 1/6 for #4? Wait no — actually in the image’s answer key, #4 is 1/6? Let me recheck.

Actually, looking back at the original image’s answer column:

It shows:

1. 4/8
2. 4/8
3. 5/8
4. 1/6 ← but wait, is that correct?

Hold on — let’s recalculate carefully.

Problem 4: 1/8 < ? < 2/4 → 2/4 = 1/2

Is 1/6 between 1/8 and 1/2?

Convert to 24ths:

1/8 = 3/24
1/6 = 4/24
1/2 = 12/24

Yes! 3/24 < 4/24 < 12/24 → So 1/6 DOES work.

But are there other options? The choices given are:

- 1/6
- 3/4
- 5/6
- 5/8

Only 1/6 is between 1/8 and 1/2.

✔ Answer for #4: 1/6

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Problem 5:

3/8 < ? < 4/6

First, convert to decimals or common denominators.

3/8 = 0.375
4/6 = 2/3 ≈ 0.666

Options:
- 3/6 = 1/2 = 0.5 → Is 0.375 < 0.5 < 0.666? YES ✔
- 3/4 = 0.75 → too big ✘
- 1/4 = 0.25 → too small ✘
- 5/6 ≈ 0.833 → too big ✘

So 3/6 works.

✔ Answer for #5: 3/6

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Problem 6:

2/6 < ? < 4/6

2/6 = 1/3 ≈ 0.333, 4/6 = 2/3 ≈ 0.666

Options:
- 5/6 ≈ 0.833 → too big ✘
- 1/2 = 0.5 → Is 0.333 < 0.5 < 0.666? YES ✔
- 1/8 = 0.125 → too small ✘
- 7/8 = 0.875 → too big ✘

So 1/2 fits.

✔ Answer for #6: 1/2

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Problem 7:

2/8 < ? < 3/6

2/8 = 1/4 = 0.25
3/6 = 1/2 = 0.5

Options:
- 5/6 ≈ 0.833 → too big ✘
- 1/8 = 0.125 → too small ✘
- 1/3 ≈ 0.333 → Is 0.25 < 0.333 < 0.5? YES ✔
- 4/6 = 2/3 ≈ 0.666 → too big ✘

Wait — option is “1/3”? But in the image, the options listed under problem 7 are:

Looking back:
Under problem 7, the choices shown are:

- 5/6
- 1/8
- 1/3
- 4/6

Yes — so 1/3 is an option.

Check: 2/8 = 0.25, 1/3 ≈ 0.333, 3/6 = 0.5 → YES.

✔ Answer for #7: 1/3

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Problem 8:

2/8 < ? < 2/4

2/8 = 1/4 = 0.25
2/4 = 1/2 = 0.5

Options:
- 2/6 = 1/3 ≈ 0.333 → Is 0.25 < 0.333 < 0.5? YES ✔
- 2/3 ≈ 0.666 → too big ✘
- 7/8 = 0.875 → too big ✘
- 1/6 ≈ 0.166 → too small ✘

So 2/6 fits.

✔ Answer for #8: 2/6

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Now let’s list all answers clearly:

1. 4/8
2. 4/8
3. 5/8
4. 1/6
5. 3/6
6. 1/2
7. 1/3
8. 2/6

These match the answer key shown on the right side of the image.

Final Answer:
1. 4/8
2. 4/8
3. 5/8
4. 1/6
5. 3/6
6. 1/2
7. 1/3
8. 2/6