Comparing Fractions With Unlike Denominators Worksheet - Free Printable

Explanation:
Let’s go through each problem step by step.

Comparing fractions (Problems 1–9):
To compare two fractions, we can either:
- Find a common denominator and compare numerators, or
- Convert to decimals (if easy), or
- Use logic: for same numerator, bigger denominator = smaller fraction; for same denominator, bigger numerator = bigger fraction.

1. 2/5 vs 2/3
Same numerator (2). Denominators: 5 > 3 → so 2/5 < 2/3
✔ Answer: <

2. 3/4 vs 1/6
Find common denominator: LCM of 4 and 6 is 12.
3/4 = 9/12, 1/6 = 2/12 → 9/12 > 2/12
✔ Answer: >

3. 7/8 vs 2/6
Simplify 2/6 = 1/3.
Compare 7/8 and 1/3. Common denominator = 24.
7/8 = 21/24, 1/3 = 8/24 → 21 > 8
✔ Answer: >

4. 2/3 vs 1/4
Common denominator = 12.
2/3 = 8/12, 1/4 = 3/12 → 8 > 3
✔ Answer: >

5. 1/5 vs 2/8
Simplify 2/8 = 1/4.
Now compare 1/5 and 1/4. Same numerator, bigger denominator = smaller.
5 > 4 → 1/5 < 1/4
✔ Answer: <

6. 1/4 vs 4/6
Simplify 4/6 = 2/3.
Compare 1/4 and 2/3. Common denominator = 12.
1/4 = 3/12, 2/3 = 8/12 → 3 < 8
✔ Answer: <

7. 1/3 vs 3/5
Common denominator = 15.
1/3 = 5/15, 3/5 = 9/15 → 5 < 9
✔ Answer: <

8. 1/8 vs 1/4
Same numerator (1). Denominator 8 > 4 → 1/8 < 1/4
✔ Answer: <

9. 2/3 vs 1/8
Common denominator = 24.
2/3 = 16/24, 1/8 = 3/24 → 16 > 3
✔ Answer: >

Color the fraction (Problems 10–13):
These are visual representations — you’re supposed to shade the correct number of parts.

10. 1/6 → 6 boxes total → shade 1 box
11. 1/2 → 6 boxes total → half of 6 = 3 boxes shaded
12. 3/4 → 4 boxes total → shade 3 boxes
13. 1/2 → 2 boxes total → shade 1 box

So for coloring:
- #10: shade 1 out of 6
- #11: shade 3 out of 6
- #12: shade 3 out of 4
- #13: shade 1 out of 2

But since the question asks only for the comparison symbols and the coloring is just instruction (no answer format needed beyond that), and the final answer should reflect what’s fillable (the <, >, = signs), we list those.

Let me double-check all comparisons:

1. 2/5 = 0.4, 2/3 ≈ 0.666 → < ✔
2. 3/4 = 0.75, 1/6 ≈ 0.166 → > ✔
3. 7/8 = 0.875, 2/6 ≈ 0.333 → > ✔
4. 2/3 ≈ 0.666, 1/4 = 0.25 → > ✔
5. 1/5 = 0.2, 2/8 = 0.25 → < ✔
6. 1/4 = 0.25, 4/6 ≈ 0.666 → < ✔
7. 1/3 ≈ 0.333, 3/5 = 0.6 → < ✔
8. 1/8 = 0.125, 1/4 = 0.25 → < ✔
9. 2/3 ≈ 0.666, 1/8 = 0.125 → > ✔

All correct.

Final Answer:
1. <
2. >
3. >
4. >
5. <
6. <
7. <
8. <
9. >
10. Shade 1 of 6 boxes
11. Shade 3 of 6 boxes
12. Shade 3 of 4 boxes
13. Shade 1 of 2 boxes