Printable worksheet for comparing fractions with answers.

Let’s solve each fraction comparison step by step. We’ll use <, >, or = to show how the fractions compare.

We can compare fractions by:
- Finding a common denominator (if denominators are different)
- Converting to decimals (if needed)
- Or using cross-multiplication: For a/b vs c/d → compare a×d and b×c

But since these are simple fractions, we’ll often just find equivalent fractions with same denominator or think about their size.

---

1) 5/9 ___ 2/3

Convert 2/3 to ninths: 2/3 = 6/9
So 5/9 < 6/9 → <

2) 2/3 ___ 3/7

Cross multiply: 2×7=14, 3×3=9 → 14 > 9 → so 2/3 > 3/7 → >

Wait — actually, cross multiplication for comparing a/b and c/d: if a×d > b×c then a/b > c/d.

Here: 2/3 vs 3/7 → 2×7 = 14, 3×3 = 9 → 14 > 9 → so 2/3 > 3/7 → >

3) 7/10 ___ 7/8

Same numerator? Then smaller denominator means bigger fraction.
8 < 10 → so 7/8 > 7/10 → so 7/10 < 7/8 → <

4) 4/11 ___ 4/6

Same numerator → smaller denominator is bigger → 6 < 11 → 4/6 > 4/11 → so 4/11 < 4/6 → <

5) 5/6 ___ 5/15

Same numerator → 6 < 15 → 5/6 > 5/15 → >

6) 6/11 ___ 8/9

Cross multiply: 6×9=54, 11×8=88 → 54 < 88 → so 6/11 < 8/9 → <

7) 2/9 ___ 5/6

Cross multiply: 2×6=12, 9×5=45 → 12 < 45 → 2/9 < 5/6 → <

8) 4/9 ___ 5/5

5/5 = 1 → 4/9 < 1 → <

9) 5/5 ___ 4/12

5/5 = 1, 4/12 = 1/3 → 1 > 1/3 → >

10) 1/2 ___ 1/3

Half is bigger than third → >

11) 5/9 ___ 4/10

Simplify 4/10 = 2/5
Compare 5/9 and 2/5 → cross multiply: 5×5=25, 9×2=18 → 25 > 18 → 5/9 > 2/5 → >

Or convert to decimals: 5/9 ≈ 0.555, 4/10 = 0.4 → yes, greater.

12) 1/3 ___ 1/3

Equal → =

13) 5/9 ___ 4/10 ← Wait, this is duplicate of #11? Let me check original sheet.

Looking back at user input:

Actually in the list it's:

11) 5/9 ___ 4/10 → we did that as >

12) 1/3 ___ 1/3 → =

Then 13) 5/9 ___ 4/10 again? No — let me re-read the original problem list from user:

User wrote:

1) 5/9 _ 2/3
2) 2/3 _ 3/7
3) 7/10 _ 7/8
4) 4/11 _ 4/6
5) 5/6 _ 5/15
6) 6/11 _ 8/9
7) 2/9 _ 5/6
8) 4/9 _ 5/5
9) 5/5 _ 4/12
10) 1/2 _ 1/3
11) 5/9 _ 4/10
12) 1/3 _ 1/3
13) 5/9 _ 4/10 ← wait no — looking at user’s text:

Actually in the user’s message, after 12) it says:

13) 5/9 _ 4/10 — but that’s same as 11? That must be typo.

Wait — let me copy exactly what user provided:

From user:

```
1) 5/9 _ 2/3 13) 5/9 _ 4/10
2) 2/3 _ 3/7 14) 9/11 _ 4/5
3) 7/10 _ 7/8 15) 9/12 _ 4/4
...
```

Ah! I misread earlier. So 13) is 5/9 vs 4/10 — which is same as 11)? But 11) was also 5/9 vs 4/10? That can’t be.

Wait — looking again:

In user’s input:

Line 11: “11) 5/9 _ 4/10”

Line 13: “13) 5/9 _ 4/10” — oh, it’s duplicated? Or maybe typo?

Wait — let me check full list as given:

User wrote:

```
1) 5/9 _ 2/3 13) 5/9 _ 4/10
2) 2/3 _ 3/7 14) 9/11 _ 4/5
3) 7/10 _ 7/8 15) 9/12 _ 4/4
4) 4/11 _ 4/6 16) 4/5 _ 3/4
5) 5/6 _ 5/15 17) 5/12 _ 5/9
6) 6/11 _ 8/9 18) 3/7 _ 11/11
7) 2/9 _ 5/6 19) 5/5 _ 3/3
8) 4/9 _ 5/5 20) 6/11 _ 2/3
9) 5/5 _ 4/12 21) 6/9 _ 2/3
10) 1/2 _ 1/3 22) 3/4 _ 2/3
11) 5/9 _ 4/10 23) 6/11 _ 1/3
12) 1/3 _ 1/3 24) 1/4 _ 4/5
```

Oh! So 11) and 13) are both 5/9 vs 4/10? That seems like a mistake in the worksheet, but we’ll do both as written.

But 13) is listed as “5/9 _ 4/10” — same as 11). Maybe it’s a copy-paste error? Or perhaps 13) is meant to be something else? But based on what’s written, we’ll proceed.

Actually, looking carefully: in the user’s text, line 13 says “13) 5/9 _ 4/10” — but in the initial block, it might be formatted differently. To avoid confusion, I’ll go by the numbers as labeled.

So let’s continue properly numbered:

We did up to 12.

Now:

13) 5/9 ___ 4/10 → same as 11 → we said > → >

But let’s confirm: 5/9 ≈ 0.555, 4/10=0.4 → yes >

14) 9/11 ___ 4/5

Cross multiply: 9×5=45, 11×4=44 → 45 > 44 → so 9/11 > 4/5 → >

15) 9/12 ___ 4/4

4/4 = 1
9/12 = 3/4 = 0.75 < 1 → <

16) 4/5 ___ 3/4

Cross multiply: 4×4=16, 5×3=15 → 16 > 15 → 4/5 > 3/4 → >

17) 5/12 ___ 5/9

Same numerator → smaller denominator is bigger → 9 < 12 → 5/9 > 5/12 → so 5/12 < 5/9 → <

18) 3/7 ___ 11/11

11/11 = 1 → 3/7 < 1 → <

19) 5/5 ___ 3/3

Both equal 1 → =

20) 6/11 ___ 2/3

Cross multiply: 6×3=18, 11×2=22 → 18 < 22 → so 6/11 < 2/3 → <

21) 6/9 ___ 2/3

6/9 simplifies to 2/3 → so equal → =

22) 3/4 ___ 2/3

Cross multiply: 3×3=9, 4×2=8 → 9 > 8 → 3/4 > 2/3 → >

23) 6/11 ___ 1/3

Cross multiply: 6×3=18, 11×1=11 → 18 > 11 → 6/11 > 1/3 → >

24) 1/4 ___ 4/5

1/4 = 0.25, 4/5=0.8 → clearly 1/4 < 4/5 → <

Now let’s compile all answers in order:

1) <
2) >
3) <
4) <
5) >
6) <
7) <
8) <
9) >
10) >
11) >
12) =
13) > (same as 11)
14) >
15) <
16) >
17) <
18) <
19) =
20) <
21) =
22) >
23) >
24) <

I notice that 11 and 13 are identical — probably a typo in the worksheet, but we answered as given.

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