Ordering Fractions Worksheets - Free Printable
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Step-by-step solution for: Ordering Fractions Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Ordering Fractions Worksheets
Let’s solve each part step by step. We’ll compare fractions by finding a common denominator or converting them to decimals — whichever is easier for each set.
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Part A: Order in increasing order (smallest to largest)
We have 6 sets. Let’s do one at a time.
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A1: 3/5, 4/9, 7/10
Find decimal values:
- 3/5 = 0.6
- 4/9 ≈ 0.444...
- 7/10 = 0.7
Order: 0.444 < 0.6 < 0.7 → 4/9, 3/5, 7/10
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A2: 2/3, 5/8, 1/4, 3/5
Decimals:
- 2/3 ≈ 0.666...
- 5/8 = 0.625
- 1/4 = 0.25
- 3/5 = 0.6
Order: 0.25 < 0.6 < 0.625 < 0.666... → 1/4, 3/5, 5/8, 2/3
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A3: 11/12, 7/8, 5/6
Decimals:
- 11/12 ≈ 0.9167
- 7/8 = 0.875
- 5/6 ≈ 0.8333
Order: 0.8333 < 0.875 < 0.9167 → 5/6, 7/8, 11/12
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A4: 3/4, 2/5, 1/3, 2/7
Decimals:
- 3/4 = 0.75
- 2/5 = 0.4
- 1/3 ≈ 0.333...
- 2/7 ≈ 0.2857
Order: 0.2857 < 0.333 < 0.4 < 0.75 → 2/7, 1/3, 2/5, 3/4
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A5: 5/6, 7/9, 11/12, 3/4
Decimals:
- 5/6 ≈ 0.8333
- 7/9 ≈ 0.777...
- 11/12 ≈ 0.9167
- 3/4 = 0.75
Order: 0.75 < 0.777 < 0.8333 < 0.9167 → 3/4, 7/9, 5/6, 11/12
---
A6: 1/2, 3/8, 5/12, 7/16
Decimals:
- 1/2 = 0.5
- 3/8 = 0.375
- 5/12 ≈ 0.4167
- 7/16 = 0.4375
Order: 0.375 < 0.4167 < 0.4375 < 0.5 → 3/8, 5/12, 7/16, 1/2
---
Part B: Order in decreasing order (largest to smallest)
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B1: 2/3, 3/5, 4/7, 5/9
Decimals:
- 2/3 ≈ 0.666...
- 3/5 = 0.6
- 4/7 ≈ 0.5714
- 5/9 ≈ 0.555...
Order: 0.666 > 0.6 > 0.5714 > 0.555 → 2/3, 3/5, 4/7, 5/9
---
B2: 5/6, 7/8, 3/4, 11/12
Decimals:
- 5/6 ≈ 0.8333
- 7/8 = 0.875
- 3/4 = 0.75
- 11/12 ≈ 0.9167
Order: 0.9167 > 0.875 > 0.8333 > 0.75 → 11/12, 7/8, 5/6, 3/4
---
B3: 2/5, 3/8, 5/12, 7/16
Decimals:
- 2/5 = 0.4
- 3/8 = 0.375
- 5/12 ≈ 0.4167
- 7/16 = 0.4375
Order: 0.4375 > 0.4167 > 0.4 > 0.375 → 7/16, 5/12, 2/5, 3/8
---
B4: 1/2, 3/7, 4/9, 5/11
Decimals:
- 1/2 = 0.5
- 3/7 ≈ 0.4286
- 4/9 ≈ 0.444...
- 5/11 ≈ 0.4545
Order: 0.5 > 0.4545 > 0.444 > 0.4286 → 1/2, 5/11, 4/9, 3/7
---
B5: 3/4, 5/6, 7/8, 9/10
Decimals:
- 3/4 = 0.75
- 5/6 ≈ 0.8333
- 7/8 = 0.875
- 9/10 = 0.9
Order: 0.9 > 0.875 > 0.8333 > 0.75 → 9/10, 7/8, 5/6, 3/4
---
B6: 2/3, 3/5, 4/7, 5/9 ← Same as B1? Wait, let me check the image again.
Actually, looking back — B6 is: 2/3, 3/5, 4/7, 5/9 — same as B1? That can’t be right. Let me double-check the original problem.
Wait — in the user’s image, B6 is actually:
2/3, 3/5, 4/7, 5/9 — yes, same as B1. But that seems odd. Maybe it's a typo? Or perhaps I misread.
Looking again — no, in the original image, B6 is written as:
> b) Write each set of fractions in decreasing order
> ...
> 6) 2/3, 3/5, 4/7, 5/9
Yes, same as B1. So we already solved it: 2/3, 3/5, 4/7, 5/9
But wait — maybe it’s different? Let me check the numerators and denominators again.
No — it’s identical to B1. Perhaps it’s intentional for practice? Or maybe I made a mistake.
Alternatively, perhaps in B6 it’s meant to be different? Let me re-express all with common denominators to verify.
But since decimals matched, and it’s the same set, we’ll go with that.
Actually — wait! Looking more carefully at the original image transcription:
In Part B, question 6 is:
2/3, 3/5, 4/7, 5/9 — same as B1.
So answer is same: 2/3, 3/5, 4/7, 5/9
But that feels redundant. Maybe it’s a copy-paste error in the worksheet? Anyway, we’ll proceed.
---
Now, compiling all answers clearly.
Final Answer:
A1: 4/9, 3/5, 7/10
A2: 1/4, 3/5, 5/8, 2/3
A3: 5/6, 7/8, 11/12
A4: 2/7, 1/3, 2/5, 3/4
A5: 3/4, 7/9, 5/6, 11/12
A6: 3/8, 5/12, 7/16, 1/2
B1: 2/3, 3/5, 4/7, 5/9
B2: 11/12, 7/8, 5/6, 3/4
B3: 7/16, 5/12, 2/5, 3/8
B4: 1/2, 5/11, 4/9, 3/7
B5: 9/10, 7/8, 5/6, 3/4
B6: 2/3, 3/5, 4/7, 5/9
---
Part A: Order in increasing order (smallest to largest)
We have 6 sets. Let’s do one at a time.
---
A1: 3/5, 4/9, 7/10
Find decimal values:
- 3/5 = 0.6
- 4/9 ≈ 0.444...
- 7/10 = 0.7
Order: 0.444 < 0.6 < 0.7 → 4/9, 3/5, 7/10
---
A2: 2/3, 5/8, 1/4, 3/5
Decimals:
- 2/3 ≈ 0.666...
- 5/8 = 0.625
- 1/4 = 0.25
- 3/5 = 0.6
Order: 0.25 < 0.6 < 0.625 < 0.666... → 1/4, 3/5, 5/8, 2/3
---
A3: 11/12, 7/8, 5/6
Decimals:
- 11/12 ≈ 0.9167
- 7/8 = 0.875
- 5/6 ≈ 0.8333
Order: 0.8333 < 0.875 < 0.9167 → 5/6, 7/8, 11/12
---
A4: 3/4, 2/5, 1/3, 2/7
Decimals:
- 3/4 = 0.75
- 2/5 = 0.4
- 1/3 ≈ 0.333...
- 2/7 ≈ 0.2857
Order: 0.2857 < 0.333 < 0.4 < 0.75 → 2/7, 1/3, 2/5, 3/4
---
A5: 5/6, 7/9, 11/12, 3/4
Decimals:
- 5/6 ≈ 0.8333
- 7/9 ≈ 0.777...
- 11/12 ≈ 0.9167
- 3/4 = 0.75
Order: 0.75 < 0.777 < 0.8333 < 0.9167 → 3/4, 7/9, 5/6, 11/12
---
A6: 1/2, 3/8, 5/12, 7/16
Decimals:
- 1/2 = 0.5
- 3/8 = 0.375
- 5/12 ≈ 0.4167
- 7/16 = 0.4375
Order: 0.375 < 0.4167 < 0.4375 < 0.5 → 3/8, 5/12, 7/16, 1/2
---
Part B: Order in decreasing order (largest to smallest)
---
B1: 2/3, 3/5, 4/7, 5/9
Decimals:
- 2/3 ≈ 0.666...
- 3/5 = 0.6
- 4/7 ≈ 0.5714
- 5/9 ≈ 0.555...
Order: 0.666 > 0.6 > 0.5714 > 0.555 → 2/3, 3/5, 4/7, 5/9
---
B2: 5/6, 7/8, 3/4, 11/12
Decimals:
- 5/6 ≈ 0.8333
- 7/8 = 0.875
- 3/4 = 0.75
- 11/12 ≈ 0.9167
Order: 0.9167 > 0.875 > 0.8333 > 0.75 → 11/12, 7/8, 5/6, 3/4
---
B3: 2/5, 3/8, 5/12, 7/16
Decimals:
- 2/5 = 0.4
- 3/8 = 0.375
- 5/12 ≈ 0.4167
- 7/16 = 0.4375
Order: 0.4375 > 0.4167 > 0.4 > 0.375 → 7/16, 5/12, 2/5, 3/8
---
B4: 1/2, 3/7, 4/9, 5/11
Decimals:
- 1/2 = 0.5
- 3/7 ≈ 0.4286
- 4/9 ≈ 0.444...
- 5/11 ≈ 0.4545
Order: 0.5 > 0.4545 > 0.444 > 0.4286 → 1/2, 5/11, 4/9, 3/7
---
B5: 3/4, 5/6, 7/8, 9/10
Decimals:
- 3/4 = 0.75
- 5/6 ≈ 0.8333
- 7/8 = 0.875
- 9/10 = 0.9
Order: 0.9 > 0.875 > 0.8333 > 0.75 → 9/10, 7/8, 5/6, 3/4
---
B6: 2/3, 3/5, 4/7, 5/9 ← Same as B1? Wait, let me check the image again.
Actually, looking back — B6 is: 2/3, 3/5, 4/7, 5/9 — same as B1? That can’t be right. Let me double-check the original problem.
Wait — in the user’s image, B6 is actually:
2/3, 3/5, 4/7, 5/9 — yes, same as B1. But that seems odd. Maybe it's a typo? Or perhaps I misread.
Looking again — no, in the original image, B6 is written as:
> b) Write each set of fractions in decreasing order
> ...
> 6) 2/3, 3/5, 4/7, 5/9
Yes, same as B1. So we already solved it: 2/3, 3/5, 4/7, 5/9
But wait — maybe it’s different? Let me check the numerators and denominators again.
No — it’s identical to B1. Perhaps it’s intentional for practice? Or maybe I made a mistake.
Alternatively, perhaps in B6 it’s meant to be different? Let me re-express all with common denominators to verify.
But since decimals matched, and it’s the same set, we’ll go with that.
Actually — wait! Looking more carefully at the original image transcription:
In Part B, question 6 is:
2/3, 3/5, 4/7, 5/9 — same as B1.
So answer is same: 2/3, 3/5, 4/7, 5/9
But that feels redundant. Maybe it’s a copy-paste error in the worksheet? Anyway, we’ll proceed.
---
Now, compiling all answers clearly.
Final Answer:
A1: 4/9, 3/5, 7/10
A2: 1/4, 3/5, 5/8, 2/3
A3: 5/6, 7/8, 11/12
A4: 2/7, 1/3, 2/5, 3/4
A5: 3/4, 7/9, 5/6, 11/12
A6: 3/8, 5/12, 7/16, 1/2
B1: 2/3, 3/5, 4/7, 5/9
B2: 11/12, 7/8, 5/6, 3/4
B3: 7/16, 5/12, 2/5, 3/8
B4: 1/2, 5/11, 4/9, 3/7
B5: 9/10, 7/8, 5/6, 3/4
B6: 2/3, 3/5, 4/7, 5/9
Parent Tip: Review the logic above to help your child master the concept of ordering fraction worksheet.
