Let’s solve each fraction comparison step by step using cross multiplication.
We’ll compare the two fractions in each problem by multiplying:
- Top left × Bottom right
- Top right × Bottom left
Then we compare those two products to decide if the first fraction is less than (<), greater than (>), or equal to (=) the second fraction.
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Problem 1: 3/4 ___ 5/6
Cross multiply:
- 3 × 6 = 18
- 5 × 4 = 20
Compare: 18 < 20 → So,
3/4 < 5/6
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Problem 2: 2/8 ___ 3/8
Same denominator! But let’s cross multiply anyway:
- 2 × 8 = 16
- 3 × 8 = 24
16 < 24 → So,
2/8 < 3/8
(Also, since denominators are same, just compare numerators: 2 < 3 → same result.)
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Problem 3: 5/8 ___ 3/8
Again, same denominator.
Cross multiply:
- 5 × 8 = 40
- 3 × 8 = 24
40 > 24 → So,
5/8 > 3/8
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Problem 4: 2/6 ___ 4/4
Cross multiply:
- 2 × 4 = 8
- 4 × 6 = 24
8 < 24 → So,
2/6 < 4/4
(Note: 4/4 = 1, and 2/6 is about 0.33 — so yes, less than 1.)
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Problem 5: 3/8 ___ 4/6
Cross multiply:
- 3 × 6 = 18
- 4 × 8 = 32
18 < 32 → So,
3/8 < 4/6
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Problem 6: 3/4 ___ 8/2
Wait — 8/2 is actually 4 (a whole number). Let’s cross multiply:
- 3 × 2 = 6
- 8 × 4 = 32
6 < 32 → So,
3/4 < 8/2
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Problem 7: 6/4 ___ 2/3
Cross multiply:
- 6 × 3 = 18
- 2 × 4 = 8
18 > 8 → So,
6/4 > 2/3
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Problem 8: 1/5 ___ 6/10
Cross multiply:
- 1 × 10 = 10
- 6 × 5 = 30
10 < 30 → So,
1/5 < 6/10
(Note: 6/10 simplifies to 3/5, which is bigger than 1/5.)
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Problem 9: 5/3 ___ 3/5
Cross multiply:
- 5 × 5 = 25
- 3 × 3 = 9
25 > 9 → So,
5/3 > 3/5
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Problem 10: 2/6 ___ 1/2
Cross multiply:
- 2 × 2 = 4
- 1 × 6 = 6
4 < 6 → So,
2/6 < 1/2
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Problem 11: 3/4 ___ 5/2
Cross multiply:
- 3 × 2 = 6
- 5 × 4 = 20
6 < 20 → So,
3/4 < 5/2
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Problem 12: 1/4 ___ 8/2
Cross multiply:
- 1 × 2 = 2
- 8 × 4 = 32
2 < 32 → So,
1/4 < 8/2
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Final Answer:
1. <
2. <
3. >
4. <
5. <
6. <
7. >
8. <
9. >
10. <
11. <
12. <
Parent Tip: Review the logic above to help your child master the concept of comparing fractions worksheets.
