Let’s solve each problem one by one. We need to order the fractions from
least to greatest.
To compare fractions, we can either:
- Find a common denominator and rewrite all fractions with that denominator, then compare numerators.
- Or convert them to decimals (if allowed) — but since this is likely for practice with fractions, we’ll use common denominators.
We’ll go step by step for each set.
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Problem 1: ½, ¹⁄₁₀, ⅛
Find a common denominator for 2, 10, and 8.
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38,
40
Check if 40 works for 10 and 8 → yes!
Convert:
- ½ = 20/40
- ¹⁄₁₀ = 4/40
- ⅛ = 5/40
Now order: 4/40 < 5/40 < 20/40 → so ¹⁄₁₀ < ⅛ < ½
✔ Answer for #1: ¹⁄₁₀, ⅛, ½
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Problem 2: ²⁄₅, ³⁄₄,
Denominators: 5, 4, 3 → LCM?
List multiples:
- 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55,
60
- 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56,
60
- 3: 3, 6, 9, 12, ..., 57,
60
Use 60.
Convert:
- ²⁄₅ = (2×12)/(5×12) = 24/60
- ³⁄₄ = (3×15)/(4×15) = 45/60
- ⅓ = (1×20)/(3×20) = 20/60
Order: 20/60 < 24/60 < 45/60 → so ⅓ < ²⁄₅ < ³⁄₄
✔ Answer for #2: ⅓, ²⁄₅, ³⁄₄
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Problem 3: ¹⁄₁₀, ⁴⁄, ³⁄₈
Denominators: 10, 5, 8 → LCM?
10: 10, 20, 30, 40
5: 5, 10, 15, 20, 25, 30, 35,
40
8: 8, 16, 24, 32,
40
Use 40.
Convert:
- ¹⁄₁₀ = 4/40
- ⁴⁄₅ = (4×8)/(5×8) = 32/40
- ³⁄₈ = (3×5)/(8×5) = 15/40
Order: 4/40 < 15/40 < 32/40 → so ¹⁄₁₀ < ³⁄₈ < ⁄₅
✔ Answer for #3: ¹⁄₁₀, ³⁄₈, ⁄₅
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Problem 4: ⅕, ⁷⁄₈, ⅓
Denominators: 5, 8, 3 → LCM?
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115,
120
8: 8, 16, ..., 120 → yes
3: 3, 6, ..., 120 → yes
Use 120.
Convert:
- ⅕ = 24/120
- ⁷⁄₈ = (7×15)/120 = 105/120
- ⅓ = 40/120
Order: 24/120 < 40/120 < 105/120 → so ⅕ < < ⁷⁄
✔ Answer for #4: ⅕, ⅓, ⁷⁄
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Problem 5: ³⁄₈, ¼, ²⁄₃
Denominators: 8, 4, 3 → LCM?
8: 8, 16, 24
4: 4, 8, 12, 16, 20,
24
3: 3, 6, 9, 12, 15, 18, 21,
24
Use 24.
Convert:
- ³⁄₈ = (3×3)/24 = 9/24
- ¼ = 6/24
- ²⁄₃ = (2×8)/24 = 16/24
Order: 6/24 < 9/24 < 16/24 → so ¼ < ³⁄₈ < ²⁄₃
✔ Answer for #5: ¼, ³⁄₈, ²⁄₃
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Problem 6: ³⁄₁₀, ⅓,
Denominators: 10, 3, 5 → LCM?
10: 10, 20, 30
3: 3, 6, 9, 12, 15, 18, 21, 24, 27,
30
5: 5, 10, 15, 20, 25,
30
Use 30.
Convert:
- ³⁄₁₀ = 9/30
- ⅓ = 10/30
- ⅕ = 6/30
Order: 6/30 < 9/30 < 10/30 → so ⅕ < ³⁄₁₀ < ⅓
✔ Answer for #6: ⅕, ³⁄₁₀, ⅓
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Final Answer:
1) ¹⁄₁₀, ⅛, ½
2) ⅓, ²⁄₅, ³⁄₄
3) ¹⁄₁₀, ³⁄₈, ⁴⁄₅
4) ⅕, , ⁷⁄
5) ¼, ³⁄₈, ²⁄₃
6) ⅕, ³⁄₁₀, ⅓
Parent Tip: Review the logic above to help your child master the concept of ordering fraction worksheet.
