We are given 18 fraction comparison problems. For each, we must write “>”, “<”, or “=” to compare the two fractions.
The key idea: when denominators are the same, just compare numerators.
When denominators are different, we can either:
- Find a common denominator and compare numerators, or
- Convert both to decimals (carefully), or
- Cross-multiply: for a/b vs c/d, compare a·d vs b·c.
Let’s solve each one carefully.
---
1. 3/15 ___ 9/15
Same denominator → compare numerators: 3 < 9
→
<
2. 2/3 ___ 1/3
Same denominator: 2 > 1
→
>
3. 1/2 ___ 1/2
Same fraction
→
=
4. 4/4 ___ 1/4
4/4 = 1, 1/4 = 0.25 → 1 > 0.25
Or same denominator: 4 > 1
→
>
5. 2/6 ___ 3/6
Same denominator: 2 < 3
→
<
6. 5/25 ___ 9/25
Same denominator: 5 < 9
→
<
7. 12/24 ___ 3/24
Same denominator: 12 > 3
→
>
8. 1/10 ___ 7/10
Same denominator: 1 < 7
→
<
9. 10/16 ___ 2/16
Same denominator: 10 > 2
→
>
10. 5/10 ___ 8/10
Same denominator: 5 < 8
→
<
11. 5/6 ___ 5/6
Same fraction
→
=
12. 1/3 ___ 2/3
Same denominator: 1 < 2
→
<
13. 3/5 ___ 2/5
Same denominator: 3 > 2
→
>
14. 4/10 ___ 5/10
Same denominator: 4 < 5
→
<
15. 7/8 ___ 7/8
Same fraction
→
=
16. 20/24 ___ 22/24
Same denominator: 20 < 22
→
<
17. 6/10 ___ 13/18
Different denominators. Let’s cross-multiply:
6 × 18 = 108
10 × 13 = 130
Since 108 < 130, then 6/10 < 13/18
→
<
Double-check:
6/10 = 0.6
13/18 ≈ 0.722… → yes, 0.6 < 0.722
→
<
18. 28/40 ___ 21/40
Same denominator: 28 > 21
→
>
Let me list all answers in order:
1. <
2. >
3. =
4. >
5. <
6. <
7. >
8. <
9. >
10. <
11. =
12. <
13. >
14. <
15. =
16. <
17. <
18. >
Final Answer:
<, >, =, >, <, <, >, <, >, <, =, <, >, <, =, <, <, >
Parent Tip: Review the logic above to help your child master the concept of comparing fractions with like numerators worksheet.
