Let’s solve each problem step by step. We’ll find equivalent fractions with the same denominator, then order them from least to greatest.
---
Problem 1):
Fractions: 5/6, 1/2, 2/3
We need a common denominator for 6, 2, and 3 → LCM is 6.
- 5/6 = 5/6 (already over 6)
- 1/2 = 3/6 (multiply numerator and denominator by 3)
- 2/3 = 4/6 (multiply numerator and denominator by 2)
So equivalent fractions: 5/6, 3/6, 4/6
Order from least to greatest: 3/6, 4/6, 5/6 → which is 1/2, 2/3, 5/6
✔ Final Answer for #1:
1/2, 2/3, 5/6
---
Problem 2):
Fractions: 3/4, 9/10, 17/20
LCM of 4, 10, 20 → 20
- 3/4 = 15/20 (×5)
- 9/10 = 18/20 (×2)
- 17/20 = 17/20 (already)
Equivalent: 15/20, 18/20, 17/20
Order: 15/20, 17/20, 18/20 → 3/4, 17/20, 9/10
✔ Final Answer for #2:
3/4, 17/20, 9/10
---
Problem 3):
Fractions: 10/12, 3/4, 2/3
LCM of 12, 4, 3 → 12
- 10/12 = 10/12
- 3/4 = 9/12 (×3)
- 2/3 = 8/12 (×4)
Equivalent: 10/12, 9/12, 8/12
Order: 8/12, 9/12, 10/12 → 2/3, 3/4, 10/12
✔ Final Answer for #3:
2/3, 3/4, 10/12
---
Problem 4):
Fractions: 5/9, 2/3, 5/6
LCM of 9, 3, 6 → 18
- 5/9 = 10/18 (×2)
- 2/3 = 12/18 (×6)
- 5/6 = 15/18 (×3)
Equivalent: 10/18, 12/18, 15/18
Order: 10/18, 12/18, 15/18 → 5/9, 2/3, 5/6
✔ Final Answer for #4:
5/9, 2/3, 5/6
---
Problem 5):
Fractions: 13/20, 19/25, 31/50
LCM of 20, 25, 50 → 100
- 13/20 = 65/100 (×5)
- 19/25 = 76/100 (×4)
- 31/50 = 62/100 (×2)
Equivalent: 65/100, 76/100, 62/100
Order: 62/100, 65/100, 76/100 → 31/50, 13/20, 19/25
✔ Final Answer for #5:
31/50, 13/20, 19/25
---
Problem 6):
Fractions: 7/12, 11/20, 16/30
First simplify 16/30 → divide top and bottom by 2 → 8/15
Now we have: 7/12, 11/20, 8/15
LCM of 12, 20, 15 → 60
- 7/12 = 35/60 (×5)
- 11/20 = 33/60 (×3)
- 8/15 = 32/60 (×4)
Equivalent: 35/60, 33/60, 32/60
Order: 32/60, 33/60, 35/60 → 8/15, 11/20, 7/12
But original was 16/30, so write as 16/30 in answer.
✔ Final Answer for #6:
16/30, 11/20, 7/12
*(Note: 16/30 simplifies to 8/15, but since the problem gave 16/30, we keep it unless told to simplify. The ordering is correct.)*
---
Problem 7):
Fractions: 1/3, 5/12, 3/8
LCM of 3, 12, 8 → 24
- 1/3 = 8/24 (×8)
- 5/12 = 10/24 (×2)
- 3/8 = 9/24 (×3)
Equivalent: 8/24, 10/24, 9/24
Order: 8/24, 9/24, 10/24 → 1/3, 3/8, 5/12
✔ Final Answer for #7:
1/3, 3/8, 5/12
---
Final Answer:
1) 1/2, 2/3, 5/6
2) 3/4, 17/20, 9/10
3) 2/3, 3/4, 10/12
4) 5/9, 2/3, 5/6
5) 31/50, 13/20, 19/25
6) 16/30, 11/20, 7/12
7) 1/3, 3/8, 5/12
Parent Tip: Review the logic above to help your child master the concept of order fractions worksheet.
