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Ordering Fractions — placing each set of fractions correctly on a number line from 0 to 1. Let’s solve each problem step by step, explaining how to compare and order the fractions.
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🔢 General Strategy:
To order fractions:
-
Find a common denominator (LCM) to compare numerators.
- Or convert to
decimals for easy comparison.
- Or use
benchmark fractions like 0, ½, 1 to estimate positions.
We’ll use decimals here for clarity and speed.
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##
✔ Problem 1: `3/4`, `2/4`, `1/4`
Convert to decimals:
- 3/4 = 0.75
- 2/4 = 0.5
- 1/4 = 0.25
✔ Order from least to greatest:
1/4 → 2/4 → 3/4
On the number line:
0 —— [1/4] —— [2/4] —— [3/4] —— 1
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✔ Problem 2: `4/8`, `4/10`, `4/5`
Convert to decimals:
- 4/8 = 0.5
- 4/10 = 0.4
- 4/5 = 0.8
✔ Order from least to greatest:
4/10 → 4/8 → 4/5
On the number line:
0 —— [4/10] —— [4/8] —— [4/5] —— 1
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✔ Problem 3: `3/6`, `1/4`, `2/3`
Convert to decimals:
- 3/6 = 0.5
- 1/4 = 0.25
- 2/3 ≈ 0.666...
✔ Order from least to greatest:
1/4 → 3/6 → 2/3
On the number line:
0 —— [1/4] —— [3/6] —— [2/3] —— 1
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✔ Problem 4: `1/10`, `1/2`, `1/5`
Convert to decimals:
- 1/10 = 0.1
- 1/2 = 0.5
- 1/5 = 0.2
✔ Order from least to greatest:
1/10 → 1/5 → 1/2
On the number line:
0 —— [1/10] —— [1/5] —— [1/2] —— 1
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✔ Problem 5: `5/7`, `1/3`, `5/10`
Convert to decimals:
- 5/7 ≈ 0.714
- 1/3 ≈ 0.333
- 5/10 = 0.5
✔ Order from least to greatest:
1/3 → 5/10 → 5/7
On the number line:
0 —— [1/3] —— [5/10] —— [5/7] —— 1
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✔ Problem 6: `2/10`, `3/4`, `2/8`
Convert to decimals:
- 2/10 = 0.2
- 3/4 = 0.75
- 2/8 = 0.25
✔ Order from least to greatest:
2/10 → 2/8 → 3/4
On the number line:
0 —— [2/10] —— [2/8] —— [3/4] —— 1
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## 📝 Final Answers (for writing on number lines):
1.
1/4, 2/4, 3/4
2.
4/10, 4/8, 4/5
3.
1/4, 3/6, 2/3
4.
1/10, 1/5, 1/2
5.
1/3, 5/10, 5/7
6.
2/10, 2/8, 3/4
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## 💡 Teaching Tip:
This activity is great for building
fraction sense. Encourage students to:
- Visualize fractions as parts of a whole.
- Use benchmarks (like 0, ½, 1).
- Practice converting to decimals or finding common denominators.
If working with a partner, they can discuss *why* one fraction is larger/smaller — this builds deeper understanding!
Let me know if you’d like printable answer keys or visual diagrams for each number line! 😊
Parent Tip: Review the logic above to help your child master the concept of ordering fractions on a number line worksheet.
