Comparing fractions with unlike denominators worksheet with examples and practice problems.

You're comparing fractions with unlike denominators. The worksheet gives you a method:

1. Find a common denominator (often by multiplying the two denominators).
2. Cross multiply to find equivalent fractions.
3. Compare the numerators.
4. Smile and be happy 😊

Let’s solve each problem step-by-step using this method.

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🔢 Problem 1: ½ □ ²⁄₆

- Denominators: 2 and 6 → common denominator = 2×6 = 12
- Cross multiply:
- ½ → (1 × 6) = 6 → ⁶⁄₁₂
- ²⁄₆ → (2 × 2) = 4 → ⁴⁄₁₂
- Compare: 6 > 4 → ½ > ²⁄₆

✔ Answer: >

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🔢 Problem 2: ³⁄₅ □ ½

- Denominators: 5 and 2 → common denominator = 10
- Cross multiply:
- ³⁄₅ → (3 × 2) = 6 → ⁶⁄₁₀
- ½ → (1 × 5) = 5 → ⁵⁄₁₀
- Compare: 6 > 5 → ³⁄₅ > ½

✔ Answer: >

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🔢 Problem 3: ½ □ ¹⁄₆

- Denominators: 2 and 6 → common denominator = 12
- Cross multiply:
- ½ → (1 × 6) = 6 → ⁶⁄₁₂
- ¹⁄₆ → (1 × 2) = 2 → ²⁄₁₂
- Compare: 6 > 2 → ½ > ¹⁄₆

✔ Answer: >

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🔢 Problem 4: ²⁄₅ □ ³⁄₆

- Denominators: 5 and 6 → common denominator = 30
- Cross multiply:
- ²⁄₅ → (2 × 6) = 12 → ¹²⁄₃₀
- ³⁄₆ → (3 × 5) = 15 → ¹⁵⁄₃₀
- Compare: 12 < 15 → ²⁄₅ < ³⁄₆

✔ Answer: <

*(Note: ³⁄₆ simplifies to ½, so you could also compare ²⁄₅ vs ½ — ²⁄₅ = 0.4, ½ = 0.5 → still ²⁄₅ < ½)*

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🔢 Problem 5: ⁵⁄₆ □ ¼

- Denominators: 6 and 4 → common denominator = 24
- Cross multiply:
- ⁵⁄₆ → (5 × 4) = 20 → ²⁰⁄₂₄
- ¼ → (1 × 6) = 6 → ⁶⁄₂₄
- Compare: 20 > 6 → ⁵⁄₆ > ¼

✔ Answer: >

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🔢 Problem 6: ²⁄₄ □ ½

- Denominators: 4 and 2 → common denominator = 8
- Cross multiply:
- ²⁄₄ → (2 × 2) = 4 → ⁴⁄₈
- ½ → (1 × 4) = 4 → ⁴⁄₈
- Compare: 4 = 4 → ²⁄₄ = ½

✔ Answer: =

*(Also, ²⁄₄ simplifies to ½, so they’re equal.)*

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🔢 Problem 7: ²⁄₃ □ ½

- Denominators: 3 and 2 → common denominator = 6
- Cross multiply:
- ²⁄₃ → (2 × 2) = 4 → ⁴⁄₆
- ½ → (1 × 3) = 3 → ³⁄₆
- Compare: 4 > 3 → ²⁄₃ > ½

✔ Answer: >

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🔢 Problem 8: ⁵⁄₆ □ ⁶⁄₁₀

- Denominators: 6 and 10 → common denominator = 60
- Cross multiply:
- ⁵⁄₆ → (5 × 10) = 50 → ⁵⁰⁄₆₀
- ⁶⁄₁₀ → (6 × 6) = 36 → ³⁶⁄₆₀
- Compare: 50 > 36 → ⁵⁄₆ > ⁶⁄₁₀

✔ Answer: >

*(Note: ⁶⁄₁₀ = ³⁄₅ = 0.6; ⁵⁄₆ ≈ 0.833 → confirms ⁵⁄₆ > ⁶⁄₁₀)*

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🔢 Problem 9: ⁵⁄₁₀ □ ⁴⁄₁₀

- Denominators are the same! No need to cross multiply.
- Compare numerators: 5 > 4 → ⁵⁄₁₀ > ⁴⁄₁₀

✔ Answer: >

*(Simplifies to ½ > ²⁄₅ — which is true since 0.5 > 0.4)*

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🔢 Problem 10: ¾ □ ³⁄₅

- Denominators: 4 and 5 → common denominator = 20
- Cross multiply:
- ¾ → (3 × 5) = 15 → ¹⁵⁄₂₀
- ³⁄₅ → (3 × 4) = 12 → ¹²⁄₂₀
- Compare: 15 > 12 → ¾ > ³⁄₅

✔ Answer: >

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🔢 Problem 11: ²⁄₇ □ ²⁄₄

- Denominators: 7 and 4 → common denominator = 28
- Cross multiply:
- ²⁄₇ → (2 × 4) = 8 → ⁸⁄₂₈
- ²⁄₄ → (2 × 7) = 14 → ¹⁴⁄₂₈
- Compare: 8 < 14 → ²⁄₇ < ²⁄₄

✔ Answer: <

*(Also, ²⁄₄ = ½ = 0.5; ²⁄₇ ≈ 0.285 → confirms ²⁄₇ < ½)*

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🔢 Problem 12: ⁴⁄₇ □ ⁴⁄₇

- Same fraction! So obviously equal.

✔ Answer: =

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## ✔ Final Answers:

1) >
2) >
3) >
4) <
5) >
6) =
7) >
8) >
9) >
10) >
11) <
12) =

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💡 Tip: You can also simplify fractions first if possible (like ²⁄₄ = ½, ⁵⁄₁₀ = ½), which sometimes makes comparison easier!

Let me know if you want to see visual models or decimal equivalents too! 😊