Let's solve each of these fraction comparison problems step by step, following the method shown in the example:
Method Recap:
1.
Find a common denominator (you can multiply denominators).
2.
Cross multiply or convert both fractions to have the same denominator.
3.
Compare the numerators.
4.
Write the correct symbol: >, <, or =.
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We'll go through each problem one by one.
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1) ½ □ ⅙
- Common denominator: 6
- Convert:
½ = 3/6
⅙ = 1/6
- Compare: 3/6 > 1/6 →
>
✔ Answer: >
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2) ⅗ □ ½
- Common denominator: 10
- Convert:
⅗ = 6/10
½ = 5/10
- Compare: 6/10 > 5/10 →
>
✔ Answer: >
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3) ½ □ ⅙
- Same as #1:
½ = 3/6, ⅙ = 1/6 → 3/6 > 1/6 →
>
✔ Answer: >
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4) ⅖ □ ⅜
- Common denominator: 30
- Convert:
⅖ = (2×6)/(5×6) = 12/30
⅜ = (3×5)/(6×5) = 15/30
- Compare: 12/30 < 15/30 →
<
✔ Answer: <
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5) ⅚ □ ¼
- Common denominator: 12
- Convert:
⅚ = (5×2)/(6×2) = 10/12
¼ = 3/12
- Compare: 10/12 > 3/12 →
>
✔ Answer: >
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6) ⅖ □ ½
- ⅖ = 2/4, and ½ = 2/4 → So they are equal
- Or: ⅖ = 2/4, ½ = 2/4 →
=
✔ Answer: =
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11) ⅔ □ ½
- Common denominator: 6
- ⅔ = 4/6, ½ = 3/6 → 4/6 > 3/6 →
>
✔ Answer: >
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12) ⅝ □ ⅘
- Common denominator: 30
- ⅝ = (5×5)/(6×5) = 25/30
⅘ = (6×3)/(10×3) = 18/30
- Compare: 25/30 > 18/30 →
>
✔ Answer: >
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13) ⁵⁄₁₀ □ ⁴⁄₁₀
- Same denominator: 10
- 5/10 > 4/10 →
>
✔ Answer: >
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14) ¾ □ ⅗
- Common denominator: 20
- ¾ = 15/20
⅗ = 12/20
- 15/20 > 12/20 →
>
✔ Answer: >
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15) ²⁄₇ □ ²⁄₄
- Different denominators: 7 and 4 → LCM = 28
- ²⁄₇ = 8/28
²⁄₄ = 14/28
- 8/28 < 14/28 →
<
✔ Answer: <
---
16) ⁴⁄₇ □ ⁴⁄₇
- Same fraction →
=
✔ Answer: =
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✔ Final Answers:
1)
>
2)
>
3)
>
4)
<
5)
>
6)
=
11)
>
12)
>
13)
>
14)
>
15)
<
16)
=
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📌 Summary:
To compare fractions with unlike denominators:
- Use cross multiplication or find a common denominator.
- Compare the resulting numerators.
- Fill in the correct symbol.
Let me know if you'd like this as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of comparing fractions with unlike denominators.
