Let’s solve each fraction comparison step by step. We’ll compare the two fractions in each problem and decide whether to use >, <, or =.
We can do this by:
- Finding a common denominator (if needed)
- Or cross-multiplying: multiply top of first × bottom of second, and top of second × bottom of first — then compare those products.
- Or converting to decimals (but we’ll avoid that unless necessary).
Let’s go one by one:
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1) 1/5 vs 3/8
Cross-multiply:
1 × 8 = 8
3 × 5 = 15
8 < 15 → so 1/5 < 3/8
Answer: <
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2) 2/3 vs 3/7
2 × 7 = 14
3 × 3 = 9
14 > 9 → so 2/3 > 3/7
Answer: >
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3) 9/10 vs 7/8
9 × 8 = 72
7 × 10 = 70
72 > 70 → so 9/10 > 7/8
Answer: >
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4) 2/5 vs 3/11
2 × 11 = 22
3 × 5 = 15
22 > 15 → so 2/5 > 3/11
Answer: >
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5) 5/6 vs 7/9
5 × 9 = 45
7 × 6 = 42
45 > 42 → so 5/6 > 7/9
Answer: >
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6) 4/5 vs 12/15
Note: 12/15 simplifies to 4/5 (divide numerator and denominator by 3). So they are equal.
Answer: =
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7) 6/11 vs 5/8
6 × 8 = 48
5 × 11 = 55
48 < 55 → so 6/11 < 5/8
Answer: <
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8) 2/9 vs 1/5
2 × 5 = 10
1 × 9 = 9
10 > 9 → so 2/9 > 1/5
Answer: >
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9) 8/9 vs 4/5
8 × 5 = 40
4 × 9 = 36
40 > 36 → so 8/9 > 4/5
Answer: >
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10) 5/7 vs 7/12
5 × 12 = 60
7 × 7 = 49
60 > 49 → so 5/7 > 7/12
Answer: >
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11) 3/8 vs 4/9
3 × 9 = 27
4 × 8 = 32
27 < 32 → so 3/8 < 4/9
Answer: <
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12) 1/3 vs 3/9
3/9 = 1/3 → so they are equal.
Answer: =
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Now the right column:
13) 5/9 vs 4/7
5 × 7 = 35
4 × 9 = 36
35 < 36 → so 5/9 < 4/7
Answer: <
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14) 9/11 vs 4/5
9 × 5 = 45
4 × 11 = 44
45 > 44 → so 9/11 > 4/5
Answer: >
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15) 9/12 vs 3/4
9/12 simplifies to 3/4 → equal.
Answer: =
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16) 4/9 vs 3/8
4 × 8 = 32
3 × 9 = 27
32 > 27 → so 4/9 > 3/8
Answer: >
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17) 5/12 vs 3/7
5 × 7 = 35
3 × 12 = 36
35 < 36 → so 5/12 < 3/7
Answer: <
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18) 2/3 vs 9/11
2 × 11 = 22
9 × 3 = 27
22 < 27 → so 2/3 < 9/11
Answer: <
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19) 5/7 vs 3/5
5 × 5 = 25
3 × 7 = 21
25 > 21 → so 5/7 > 3/5
Answer: >
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20) 6/11 vs 3/5
6 × 5 = 30
3 × 11 = 33
30 < 33 → so 6/11 < 3/5
Answer: <
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21) 4/9 vs 2/3
4 × 3 = 12
2 × 9 = 18
12 < 18 → so 4/9 < 2/3
Answer: <
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22) 2/3 vs 10/15
10/15 = 2/3 → equal.
Answer: =
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23) 6/11 vs 4/9
6 × 9 = 54
4 × 11 = 44
54 > 44 → so 6/11 > 4/9
Answer: >
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24) 3/4 vs 7/9
3 × 9 = 27
7 × 4 = 28
27 < 28 → so 3/4 < 7/9
Answer: <
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Final Answer:
1) <
2) >
3) >
4) >
5) >
6) =
7) <
8) >
9) >
10) >
11) <
12) =
13) <
14) >
15) =
16) >
17) <
18) <
19) >
20) <
21) <
22) =
23) >
24) <
Parent Tip: Review the logic above to help your child master the concept of comparing fractions with pictures worksheet.
