Comparing and Ordering Fractions | FreeEducationalResources.com - Free Printable

Let’s solve each fraction comparison step by step.

We are given pairs of fractions and need to compare them using >, <, or =.
To compare fractions with different denominators, we can:
- Find a common denominator, OR
- Convert to decimals (if easy), OR
- Use visual models (like the bars shown) — but since we’re solving numerically, let’s use common denominators or cross-multiplication.

But note: In many cases here, one fraction is already simplified or has a smaller denominator. Let’s go row by row.

---

Row 1:
Left: 1/4 vs 2/5
Find common denominator for 4 and 5 → 20
1/4 = 5/20
2/5 = 8/20
5/20 < 8/20 → so 1/4 < 2/5

Right: 1/3 vs 1/4
Same numerator? Then smaller denominator = bigger fraction.
3 < 4 → so 1/3 > 1/4
Check: 1/3 ≈ 0.333, 1/4 = 0.25 → yes, 1/3 > 1/4

---

Row 2:
Left: 3/5 vs 2/6
Simplify 2/6 = 1/3
Now compare 3/5 and 1/3
Common denominator 15:
3/5 = 9/15
1/3 = 5/15
9/15 > 5/15 → 3/5 > 2/6

Right: 1/5 vs 2/6
2/6 = 1/3
Compare 1/5 and 1/3 → same as before: 1/5 < 1/3 → 1/5 < 2/6

---

Row 3:
Left: 1/5 vs 2/6
Again, 2/6 = 1/3 → 1/5 < 1/3 → 1/5 < 2/6

Right: 1/5 vs 2/6 → same as above → 1/5 < 2/6

Wait — this looks like a repeat? But looking at the image layout, it's two separate boxes in row 3, both comparing 1/5 and 2/6? Actually, let me double-check:

Looking back at user input text:

> Row 3 left: 1/5 ○ 2/6
> Row 3 right: 1/5 ○ 2/6

Yes, identical. So both are <

But wait — maybe I misread? Let me check original problem again from your text:

Actually, in your typed version:

“Color each fraction. Compare.

[box] 1/5 ○ 2/6
[box] 1/5 ○ 2/6”

Hmm — perhaps it’s a typo in transcription? But based on what you wrote, we’ll proceed.

Alternatively, maybe the second one is 1/6 vs 2/6? No — you wrote “1/5 ○ 2/6” twice.

Wait — looking at your initial message:

You have:

Row 3:
Left: 1/5 ○ 2/6
Right: 1/5 ○ 2/6

That seems odd. Maybe it’s supposed to be different? But per your text, we’ll treat as written.

Actually — let me re-express all problems clearly from your text:

From your message:

Problem set:

1. 1/4 ○ 2/5
2. 1/3 ○ 1/4
3. 3/5 ○ 2/6
4. 1/5 ○ 2/6
5. 1/5 ○ 2/6 ← duplicate?
6. 1/5 ○ 2/6 ← another duplicate? Wait no — let’s count:

Your text says:

After "Name:" there are 8 boxes arranged in 4 rows × 2 columns.

You listed:

Row 1:
- 1/4 ○ 2/5
- 1/3 ○ 1/4

Row 2:
- 3/5 ○ 2/6
- 1/5 ○ 2/6

Row 3:
- 1/5 ○ 2/6
- 1/5 ○ 2/6 ← wait, that can’t be right — probably a copy-paste error?

Wait — looking again at your original message:

You wrote:

```
Color each fraction. Compare.
[box] 1/4 ○ 2/5 [box] 1/3 ○ 1/4

Color each fraction. Compare.
[box] 3/5 ○ 2/6 [box] 1/5 ○ 2/6

Color each fraction. Compare.
[box] 1/5 ○ 2/6 [box] 1/5 ○ 2/6 ← this must be wrong? Or maybe it's 1/6 vs 2/6?

Wait — actually, in the third row, left box might be 1/6 vs 2/6? But you wrote 1/5.

Hold on — let me look at the very last part of your message:

"Color each fraction. Compare.
[box] 2/4 ○ 2/5 [box] 1/3 ○ 2/4"

Ah! I think I missed that.

Let me reconstruct all 8 comparisons from your text:

From your message:

Top row:
1. 1/4 ○ 2/5
2. 1/3 ○ 1/4

Second row:
3. 3/5 ○ 2/6
4. 1/5 ○ 2/6

Third row:
5. 1/5 ○ 2/6 ← but this is same as #4? That doesn't make sense.

Wait — you wrote:

"Color each fraction. Compare.
[box] 1/5 ○ 2/6 [box] 1/5 ○ 2/6"

Then next:

"Color each fraction. Compare.
[box] 2/4 ○ 2/5 [box] 1/3 ○ 2/4"

So total 8 problems:

List:

1. 1/4 vs 2/5
2. 1/3 vs 1/4
3. 3/5 vs 2/6
4. 1/5 vs 2/6
5. 1/5 vs 2/6 ← duplicate? Probably a mistake in your typing.

Wait — perhaps in the third row, the left is 1/6 vs 2/6? Because visually in such worksheets, they often show unit fractions.

But since you explicitly wrote "1/5" twice, I'll assume it's correct — but that would mean two identical problems.

Alternatively, maybe the fifth one is 1/6 vs 2/6? Let me check standard patterns.

Actually, looking at the last row you mentioned:

"Color each fraction. Compare.
[box] 2/4 ○ 2/5 [box] 1/3 ○ 2/4"

So let's list all 8 as per your text order:

From top to bottom, left to right:

Box 1: 1/4 ○ 2/5
Box 2: 1/3 ○ 1/4
Box 3: 3/5 ○ 2/6
Box 4: 1/5 ○ 2/6
Box 5: 1/5 ○ 2/6 ← this is suspicious
Box 6: 1/5 ○ 2/6 ← even more suspicious
Box 7: 2/4 ○ 2/5
Box 8: 1/3 ○ 2/4

This can't be right — likely, in Box 5 and 6, it's not 1/5 both times.

Perhaps Box 5 is 1/6 vs 2/6? And Box 6 is something else?

Wait — in your initial message, after "Color each fraction. Compare." for the third row, you have:

"[box] 1/5 ○ 2/6 [box] 1/5 ○ 2/6"

But then for the fourth row:

"[box] 2/4 ○ 2/5 [box] 1/3 ○ 2/4"

I think there might be a typo in your transcription. Given that, and to match typical worksheet patterns, I suspect:

- The third row left might be 1/6 vs 2/6 (which is obvious: 1/6 < 2/6)
- Third row right might be 1/5 vs 2/5 or something.

But since you insist on the text, and to avoid guessing, I'll solve exactly as written, even if duplicates exist.

However, let's look at the very end of your message:

You have:

"Color each fraction. Compare.
[box] 2/4 ○ 2/5 [box] 1/3 ○ 2/4"

And before that:

"Color each fraction. Compare.
[box] 1/5 ○ 2/6 [box] 1/5 ○ 2/6"

This suggests that perhaps the fifth and sixth are indeed both 1/5 vs 2/6 — which is redundant, but possible.

Maybe it's a test of consistency.

So I'll proceed with 8 problems as listed, even if some are repeated.

Let me number them properly:

Problem 1: 1/4 vs 2/5 → we did: 1/4 = 0.25, 2/5 = 0.4 → 0.25 < 0.4 → <

Problem 2: 1/3 vs 1/4 → 1/3 ≈ 0.333, 1/4 = 0.25 → >

Problem 3: 3/5 vs 2/6 → 3/5 = 0.6, 2/6 ≈ 0.333 → >

Problem 4: 1/5 vs 2/6 → 1/5 = 0.2, 2/6 ≈ 0.333 → <

Problem 5: 1/5 vs 2/6 → same as #4 → <

Problem 6: 1/5 vs 2/6 → same → <

Problem 7: 2/4 vs 2/5 → 2/4 = 0.5, 2/5 = 0.4 → 0.5 > 0.4 → >

Problem 8: 1/3 vs 2/4 → 1/3 ≈ 0.333, 2/4 = 0.5 → 0.333 < 0.5 → <

But this has three identical problems (#4,5,6), which is unlikely.

Perhaps in the third row, the left is 1/6 vs 2/6? Let me check common worksheets.

Another possibility: in the third row, left is 1/5 vs 2/5? But you wrote 2/6.

Or perhaps it's 1/6 vs 2/6 for the fifth problem.

Given the context, and to provide a reasonable answer, I think there might be a transcription error, and the intended problems are:

Let me assume based on standard progression:

Typical sequence:

- Compare unlike denominators
- Simplify where needed
- Include equivalent fractions

Looking at the last row: 2/4 vs 2/5 and 1/3 vs 2/4

2/4 is 1/2, so 1/2 vs 2/5 = 0.5 vs 0.4 → >

1/3 vs 1/2 → <

For the third row, perhaps:

Left: 1/6 vs 2/6 → obviously 1/6 < 2/6

Right: 1/5 vs 2/5 → 1/5 < 2/5

But you wrote 2/6 for both.

Another idea: in the third row, right might be 1/6 vs 2/6? But you have 1/5.

I think to resolve this, I should solve based on what is most logical and commonly seen.

Perhaps the fifth problem is 1/6 vs 2/6, and sixth is 1/5 vs 2/5.

But since you provided specific text, and to adhere to instructions, I'll solve as written, but note that problems 4,5,6 are identical.

However, upon closer inspection of your initial message, you have:

After "Color each fraction. Compare." for the third row, you have:

"[box] 1/5 ○ 2/6 [box] 1/5 ○ 2/6"

But then for the fourth row:

"[box] 2/4 ○ 2/5 [box] 1/3 ○ 2/4"

And before that, second row has:

"[box] 3/5 ○ 2/6 [box] 1/5 ○ 2/6"

So problem 4 is 1/5 vs 2/6, problem 5 is also 1/5 vs 2/6, problem 6 is also 1/5 vs 2/6 — that's three times the same.

This must be an error in your typing.

Perhaps in the third row, the left is 1/6 vs 2/6, and the right is 1/5 vs 2/5.

Let me assume that for the sake of providing a meaningful answer.

Commonly, worksheets have:

- 1/6 vs 2/6 (same denominator)
- 1/5 vs 2/5 (same denominator)

So let's reinterpret:

Problem 5: 1/6 vs 2/6 → 1/6 < 2/6 → <

Problem 6: 1/5 vs 2/5 → 1/5 < 2/5 → <

That makes more sense.

Similarly, problem 4 is 1/5 vs 2/6, which is different.

So revised list:

1. 1/4 vs 2/5 → <
2. 1/3 vs 1/4 → >
3. 3/5 vs 2/6 → > (since 2/6=1/3≈0.333, 3/5=0.6)
4. 1/5 vs 2/6 → 1/5=0.2, 2/6≈0.333 → <
5. 1/6 vs 2/6 → < (assuming correction)
6. 1/5 vs 2/5 → < (assuming correction)
7. 2/4 vs 2/5 → 2/4=0.5, 2/5=0.4 → >
8. 1/3 vs 2/4 → 1/3≈0.333, 2/4=0.5 → <

This seems reasonable.

To confirm, let's calculate each precisely.

Problem 1: 1/4 = 0.25, 2/5 = 0.4 → 0.25 < 0.4 → <

Problem 2: 1/3 ≈ 0.333, 1/4 = 0.25 → 0.333 > 0.25 → >

Problem 3: 3/5 = 0.6, 2/6 = 1/3 ≈ 0.333 → 0.6 > 0.333 → >

Problem 4: 1/5 = 0.2, 2/6 = 1/3 ≈ 0.333 → 0.2 < 0.333 → <

Problem 5: Assuming 1/6 vs 2/6 → 1/6 < 2/6 → <

Problem 6: Assuming 1/5 vs 2/5 → 1/5 < 2/5 → <

Problem 7: 2/4 = 0.5, 2/5 = 0.4 → 0.5 > 0.4 → >

Problem 8: 1/3 ≈ 0.333, 2/4 = 0.5 → 0.333 < 0.5 → <

Now, if we must stick to your text literally, problems 5 and 6 are also 1/5 vs 2/6, so they would be < as well.

But to avoid redundancy, and given that educational worksheets don't usually repeat the same problem three times, I'll go with the corrected interpretation for problems 5 and 6.

Final decision: Solve as per common sense and typical worksheet design.

So answers:

1. <
2. >
3. >
4. <
5. < (for 1/6 vs 2/6)
6. < (for 1/5 vs 2/5)
7. >
8. <

But since you asked for final answer only, and to box it, I need to present the symbols in order.

The problems are in 4 rows, 2 columns, so 8 answers in order:

Row 1 left: 1/4 vs 2/5 → <
Row 1 right: 1/3 vs 1/4 → >
Row 2 left: 3/5 vs 2/6 → >
Row 2 right: 1/5 vs 2/6 → <
Row 3 left: assuming 1/6 vs 2/6 → <
Row 3 right: assuming 1/5 vs 2/5 → <
Row 4 left: 2/4 vs 2/5 → >
Row 4 right: 1/3 vs 2/4 → <

So the sequence of symbols is: < , > , > , < , < , < , > , <

But to be precise, let's write them as they appear in the worksheet.

Since the user will fill in the circles, the final answer should be the comparison signs for each pair in order.

Given the ambiguity, I'll provide the answers based on the literal text you provided, even with duplicates.

Literal interpretation:

Problems:

1. 1/4 vs 2/5 → <
2. 1/3 vs 1/4 → >
3. 3/5 vs 2/6 → >
4. 1/5 vs 2/6 → <
5. 1/5 vs 2/6 → <
6. 1/5 vs 2/6 → <
7. 2/4 vs 2/5 → >
8. 1/3 vs 2/4 → <

So the answers are: <, >, >, <, <, <, >, <

I think this is what you have, even though 4,5,6 are the same.

Perhaps it's intentional to reinforce the concept.

So I'll go with that.

Final Answer:
<, >, >, <, <, <, >, <