Let’s go through each problem one by one. We’ll compare the fractions and decide whether to put >, <, or = in the box.
We can compare fractions by:
- Making them have the same denominator (bottom number), OR
- Simplifying them first if possible, OR
- Thinking about what they mean — like “half” or “almost all”.
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1a. 4/6 vs 12/12
→ 12/12 = 1 whole
→ 4/6 is less than 1 (it’s about two-thirds)
So:
4/6 < 12/12
1b. 6/9 vs 6/9
→ They are exactly the same!
So:
6/9 = 6/9
1c. 10/10 vs 6/6
→ Both equal 1 whole
So:
10/10 = 6/6
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2a. 12/12 vs 10/11
→ 12/12 = 1
→ 10/11 is almost 1, but not quite
So:
12/12 > 10/11
2b. 7/7 vs 8/8
→ Both equal 1
So:
7/7 = 8/8
2c. 7/11 vs 9/11
→ Same bottom number → bigger top number wins
9 > 7 → so 9/11 is bigger
So:
7/11 < 9/11
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3a. 11/12 vs 10/12
→ Same bottom → 11 > 10
So:
11/12 > 10/12
3b. 3/3 vs 3/6
→ 3/3 = 1
→ 3/6 = half (or 1/2)
So:
3/3 > 3/6
3c. 5/6 vs 8/8
→ 8/8 = 1
→ 5/6 is less than 1
So:
5/6 < 8/8
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4a. 1/11 vs 1/6
→ Same top number → smaller bottom means BIGGER fraction
Because dividing into fewer pieces makes each piece larger
6 < 11 → so 1/6 > 1/11
So:
1/11 < 1/6
4b. 1/11 vs 6/11
→ Same bottom → 6 > 1
So:
1/11 < 6/11
4c. 1/2 vs 8/11
→ Let’s think: 1/2 = 0.5
→ 8/11 ≈ 0.72 (since 8 ÷ 11 is more than half)
Or cross-multiply: 1×11=11, 2×8=16 → 11 < 16 → so 1/2 < 8/11
So:
1/2 < 8/11
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5a. 2/9 vs 2/2
→ 2/2 = 1
→ 2/9 is small (less than 1)
So:
2/9 < 2/2
5b. 1/12 vs 2/12
→ Same bottom → 2 > 1
So:
1/12 < 2/12
5c. 6/7 vs 6/6
→ 6/6 = 1
→ 6/7 is less than 1
So:
6/7 < 6/6
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6a. 2/9 vs 1/2
→ 1/2 = 0.5
→ 2/9 ≈ 0.22 (less than half)
Cross-multiply: 2×2=4, 9×1=9 → 4 < 9 → so 2/9 < 1/2
So:
2/9 < 1/2
6b. 5/11 vs 1/2
→ Half of 11 is 5.5 → 5/11 is just under half
So:
5/11 < 1/2
6c. 2/3 vs 2/5
→ Same top → smaller bottom = bigger fraction
5 > 3 → so 2/5 is smaller than 2/3
So:
2/3 > 2/5
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7a. 2/8 vs 1/2
→ 2/8 simplifies to 1/4
→ 1/4 = 0.25, 1/2 = 0.5
So:
2/8 < 1/2
7b. 1/1 vs 9/9
→ Both equal 1
So:
1/1 = 9/9
7c. 11/11 vs 4/10
→ 11/11 = 1
→ 4/10 = 0.4
So:
11/11 > 4/10
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8a. 7/7 vs 3/10
→ 7/7 = 1
→ 3/10 = 0.3
So:
7/7 > 3/10
8b. 5/5 vs 10/12
→ 5/5 = 1
→ 10/12 ≈ 0.83 (less than 1)
So:
5/5 > 10/12
8c. 7/10 vs 1/2
→ 1/2 = 5/10
→ 7/10 > 5/10
So:
7/10 > 1/2
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Final Answer:
1a. <
1b. =
1c. =
2a. >
2b. =
2c. <
3a. >
3b. >
3c. <
4a. <
4b. <
4c. <
5a. <
5b. <
5c. <
6a. <
6b. <
6c. >
7a. <
7b. =
7c. >
8a. >
8b. >
8c. >
Parent Tip: Review the logic above to help your child master the concept of equivalent fractions questions.
