Let’s solve each problem step by step. We need to order the fractions from smallest to largest. To compare fractions, we can either find a common denominator or convert them to decimals. I’ll use decimals because it’s easier for quick comparison — but I’ll double-check with common denominators if needed.
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Problem 1:
Fractions:
4/15, 1/3, 3/5, 4/9, 11/15
Convert to decimals:
- 4 ÷ 15 = 0.266...
- 1 ÷ 3 = 0.333...
- 3 ÷ 5 = 0.6
- 4 ÷ 9 = 0.444...
- 11 ÷ 15 = 0.733...
Order from smallest to largest:
0.266 → 0.333 → 0.444 → 0.6 → 0.733
So:
4/15, 1/3, 4/9, 3/5, 11/15
✔ Double-check using common denominator (LCM of 15,3,5,9 is 45):
- 4/15 = 12/45
- 1/3 = 15/45
- 3/5 = 27/45
- 4/9 = 20/45
- 11/15 = 33/45
Order: 12, 15, 20, 27, 33 → same as above! ✔️
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Problem 2:
Fractions:
5/8, 2/3, 3/4, 9/16, 1/4
Decimals:
- 5 ÷ 8 = 0.625
- 2 ÷ 3 ≈ 0.666...
- 3 ÷ 4 = 0.75
- 9 ÷ 16 = 0.5625
- 1 ÷ 4 = 0.25
Order:
0.25 → 0.5625 → 0.625 → 0.666 → 0.75
So:
1/4, 9/16, 5/8, 2/3, 3/4
✔ Check with common denominator (LCM of 8,3,4,16 is 48):
- 5/8 = 30/48
- 2/3 = 32/48
- 3/4 = 36/48
- 9/16 = 27/48
- 1/4 = 12/48
Order: 12, 27, 30, 32, 36 → same! ✔️
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Problem 3:
Fractions:
3/5, 4/7, 1/2, 2/5, 2/7
Decimals:
- 3 ÷ 5 = 0.6
- 4 ÷ 7 ≈ 0.571
- 1 ÷ 2 = 0.5
- 2 ÷ 5 = 0.4
- 2 ÷ 7 ≈ 0.2857
Order:
0.2857 → 0.4 → 0.5 → 0.571 → 0.6
So:
2/7, 2/5, 1/2, 4/7, 3/5
✔ Common denominator? LCM of 5,7,2 is 70:
- 3/5 = 42/70
- 4/7 = 40/70
- 1/2 = 35/70
- 2/5 = 28/70
- 2/7 = 20/70
Order: 20, 28, 35, 40, 42 → same! ✔️
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Problem 4:
Fractions:
5/16, 3/4, 1/2, 11/16, 2/3
Wait — there’s also “1/5” written under “smallest”? That seems like a typo in the worksheet. Looking at the layout, the fractions given are:
Top row: 5/16, 3/4, 1/2, 11/16, 2/3
Then below “smallest” it says “1/5” — that must be a mistake. Probably meant to list only the five fractions above. Let me check the original image description again… Actually, looking back, in Problem 4, the user wrote:
> 4) | 5/16 | 3/4 | 1/2 | 11/16 | 2/3 |
> | smallest | | | | largest |
> | 1/5 | | | | |
That “1/5” under “smallest” is likely an error — maybe copied from another problem? Because the instruction says “Put these fractions in order”, and the five fractions listed are 5/16, 3/4, 1/2, 11/16, 2/3. So I will ignore the “1/5” — it doesn’t belong here.
So fractions: 5/16, 3/4, 1/2, 11/16, 2/3
Decimals:
- 5 ÷ 16 = 0.3125
- 3 ÷ 4 = 0.75
- 1 ÷ 2 = 0.5
- 11 ÷ 16 = 0.6875
- 2 ÷ 3 ≈ 0.666...
Order:
0.3125 → 0.5 → 0.666 → 0.6875 → 0.75
So:
5/16, 1/2, 2/3, 11/16, 3/4
✔ Common denominator? LCM of 16,4,2,3 is 48:
- 5/16 = 15/48
- 3/4 = 36/48
- 1/2 = 24/48
- 11/16 = 33/48
- 2/3 = 32/48
Order: 15, 24, 32, 33, 36 → same! ✔️
*(Note: If “1/5” was intentionally included, then we’d have six fractions — but since the box has only five slots and the top row lists five, I’m confident “1/5” is a misprint.)*
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Problem 5:
Fractions:
5/9, 2/3, 3/5, 1/2, 4/9
Decimals:
- 5 ÷ 9 ≈ 0.555...
- 2 ÷ 3 ≈ 0.666...
- 3 ÷ 5 = 0.6
- 1 ÷ 2 = 0.5
- 4 ÷ 9 ≈ 0.444...
Order:
0.444 → 0.5 → 0.555 → 0.6 → 0.666
So:
4/9, 1/2, 5/9, 3/5, 2/3
✔ Common denominator? LCM of 9,3,5,2 is 90:
- 5/9 = 50/90
- 2/3 = 60/90
- 3/5 = 54/90
- 1/2 = 45/90
- 4/9 = 40/90
Order: 40, 45, 50, 54, 60 → same! ✔️
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Final Answer:
1) 4/15, 1/3, 4/9, 3/5, 11/15
2) 1/4, 9/16, 5/8, 2/3, 3/4
3) 2/7, 2/5, 1/2, 4/7, 3/5
4) 5/16, 1/2, 2/3, 11/16, 3/4
5) 4/9, 1/2, 5/9, 3/5, 2/3
Parent Tip: Review the logic above to help your child master the concept of comparing unlike fractions worksheet.
