Understanding Fractions as Division Worksheet / Worksheet - Free Printable
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Step-by-step solution for: Understanding Fractions as Division Worksheet / Worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Understanding Fractions as Division Worksheet / Worksheet
Let’s solve each improper fraction by turning it into a division problem. Remember: an improper fraction like $\frac{a}{b}$ means “a divided by b”. We’ll write the answer as a mixed number (whole number + fraction) if there’s a remainder.
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1. $\frac{40}{3} = 13 \frac{1}{3}$ ← already done for you
→ 40 ÷ 3 = 13 with remainder 1 → so $13 \frac{1}{3}$
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2. $\frac{21}{8}$
→ 21 ÷ 8 = 2 with remainder 5 → because 8 × 2 = 16, and 21 - 16 = 5
→ So, $2 \frac{5}{8}$
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3. $\frac{15}{6}$
→ 15 ÷ 6 = 2 with remainder 3 → because 6 × 2 = 12, and 15 - 12 = 3
→ But we can simplify $\frac{3}{6}$ to $\frac{1}{2}$
→ So, $2 \frac{1}{2}$
*(Note: Sometimes teachers want simplified fractions — this one should be simplified.)*
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4. $\frac{85}{9}$
→ 85 ÷ 9 = 9 with remainder 4 → because 9 × 9 = 81, and 85 - 81 = 4
→ So, $9 \frac{4}{9}$
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5. $\frac{14}{3}$
→ 14 ÷ 3 = 4 with remainder 2 → because 3 × 4 = 12, and 14 - 12 = 2
→ So, $4 \frac{2}{3}$
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6. $\frac{37}{2}$
→ 37 ÷ 2 = 18 with remainder 1 → because 2 × 18 = 36, and 37 - 36 = 1
→ So, $18 \frac{1}{2}$
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7. $\frac{15}{7}$
→ 15 ÷ 7 = 2 with remainder 1 → because 7 × 2 = 14, and 15 - 14 = 1
→ So, $2 \frac{1}{7}$
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8. $\frac{44}{5}$
→ 44 ÷ 5 = 8 with remainder 4 → because 5 × 8 = 40, and 44 - 40 = 4
→ So, $8 \frac{4}{5}$
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Now let’s check the right side of the worksheet — it looks like they’re asking for the same problems but maybe in decimal or just quotient? Wait — looking again, the right side says:
> Look at each improper fraction as a division problem. One has been done for you.
> Example: $\frac{40}{3} = 13 \frac{1}{3}$
And then lists numbers 1–15 with blank boxes. But the left side only goes to #8. Maybe the right side is a different set? Actually, looking closely, the right side seems to have the same fractions but listed vertically with small boxes — perhaps for writing the whole number part only? Or maybe it's a duplicate?
Wait — actually, comparing both sides:
Left side:
1. 40/3 → 13 1/3
2. 21/8
3. 15/6
4. 85/9
5. 14/3
6. 37/2
7. 15/7
8. 44/5
Right side:
1. 40/3 → 13 1/3 (same)
2. 21/8 → box
3. 15/6 → box
...
up to 15. 77/9
Ah! The right side has MORE problems — up to #15. Let me list them all from the right side since that’s probably the full assignment.
From the image (right column):
1. $\frac{40}{3} = 13 \frac{1}{3}$ ← given
2. $\frac{21}{8}$
3. $\frac{15}{6}$
4. $\frac{85}{9}$
5. $\frac{14}{3}$
6. $\frac{37}{2}$
7. $\frac{15}{7}$
8. $\frac{44}{5}$
9. $\frac{77}{9}$
10. $\frac{22}{4}$
11. $\frac{17}{5}$
12. $\frac{55}{7}$
13. $\frac{21}{4}$
14. $\frac{39}{5}$
15. $\frac{77}{9}$ ← wait, #9 and #15 are both 77/9? That might be a typo, but let’s assume it’s correct.
Actually, looking again — #9 is 77/9, #10 is 22/4, #11 is 17/5, #12 is 55/7, #13 is 21/4, #14 is 39/5, #15 is 77/9 — yes, duplicates happen sometimes.
But the user uploaded an image with two columns — left has 8 problems, right has 15. Since the instruction says “solve the problem accurately”, and the image shows both, I think we should do ALL 15 from the right side, since that’s the full worksheet.
Also, note: some fractions can be simplified before dividing — like 15/6 = 5/2, but the worksheet says “look at each improper fraction as a division problem” — so probably divide as-is, then simplify the fractional part if needed.
Let’s go one by one for all 15 on the right side.
---
1. $\frac{40}{3} = 13 \frac{1}{3}$ ← given
2. $\frac{21}{8}$
21 ÷ 8 = 2 R5 → $2 \frac{5}{8}$
3. $\frac{15}{6}$
15 ÷ 6 = 2 R3 → $\frac{3}{6} = \frac{1}{2}$ → $2 \frac{1}{2}$
4. $\frac{85}{9}$
85 ÷ 9 = 9 R4 → $9 \frac{4}{9}$
5. $\frac{14}{3}$
14 ÷ 3 = 4 R2 → $4 \frac{2}{3}$
6. $\frac{37}{2}$
37 ÷ 2 = 18 R1 → $18 \frac{1}{2}$
7. $\frac{15}{7}$
15 ÷ 7 = 2 R1 → $2 \frac{1}{7}$
8. $\frac{44}{5}$
44 ÷ 5 = 8 R4 → $8 \frac{4}{5}$
9. $\frac{77}{9}$
77 ÷ 9 = 8 R5 → because 9×8=72, 77-72=5 → $8 \frac{5}{9}$
10. $\frac{22}{4}$
22 ÷ 4 = 5 R2 → $\frac{2}{4} = \frac{1}{2}$ → $5 \frac{1}{2}$
11. $\frac{17}{5}$
17 ÷ 5 = 3 R2 → $3 \frac{2}{5}$
12. $\frac{55}{7}$
55 ÷ 7 = 7 R6 → because 7×7=49, 55-49=6 → $7 \frac{6}{7}$
13. $\frac{21}{4}$
21 ÷ 4 = 5 R1 → $5 \frac{1}{4}$
14. $\frac{39}{5}$
39 ÷ 5 = 7 R4 → $7 \frac{4}{5}$
15. $\frac{77}{9}$ ← same as #9 → $8 \frac{5}{9}$
---
Double-checking a few:
- #3: 15/6 = 2.5 = 2 1/2 ✔️
- #10: 22/4 = 5.5 = 5 1/2 ✔️
- #12: 55÷7: 7*7=49, 55-49=6 → 7 6/7 ✔️
- #15: same as #9 → 77÷9=8*9=72, 77-72=5 → 8 5/9 ✔️
All look correct.
Final Answer:
1. $13 \frac{1}{3}$
2. $2 \frac{5}{8}$
3. $2 \frac{1}{2}$
4. $9 \frac{4}{9}$
5. $4 \frac{2}{3}$
6. $18 \frac{1}{2}$
7. $2 \frac{1}{7}$
8. $8 \frac{4}{5}$
9. $8 \frac{5}{9}$
10. $5 \frac{1}{2}$
11. $3 \frac{2}{5}$
12. $7 \frac{6}{7}$
13. $5 \frac{1}{4}$
14. $7 \frac{4}{5}$
15. $8 \frac{5}{9}$
---
1. $\frac{40}{3} = 13 \frac{1}{3}$ ← already done for you
→ 40 ÷ 3 = 13 with remainder 1 → so $13 \frac{1}{3}$
---
2. $\frac{21}{8}$
→ 21 ÷ 8 = 2 with remainder 5 → because 8 × 2 = 16, and 21 - 16 = 5
→ So, $2 \frac{5}{8}$
---
3. $\frac{15}{6}$
→ 15 ÷ 6 = 2 with remainder 3 → because 6 × 2 = 12, and 15 - 12 = 3
→ But we can simplify $\frac{3}{6}$ to $\frac{1}{2}$
→ So, $2 \frac{1}{2}$
*(Note: Sometimes teachers want simplified fractions — this one should be simplified.)*
---
4. $\frac{85}{9}$
→ 85 ÷ 9 = 9 with remainder 4 → because 9 × 9 = 81, and 85 - 81 = 4
→ So, $9 \frac{4}{9}$
---
5. $\frac{14}{3}$
→ 14 ÷ 3 = 4 with remainder 2 → because 3 × 4 = 12, and 14 - 12 = 2
→ So, $4 \frac{2}{3}$
---
6. $\frac{37}{2}$
→ 37 ÷ 2 = 18 with remainder 1 → because 2 × 18 = 36, and 37 - 36 = 1
→ So, $18 \frac{1}{2}$
---
7. $\frac{15}{7}$
→ 15 ÷ 7 = 2 with remainder 1 → because 7 × 2 = 14, and 15 - 14 = 1
→ So, $2 \frac{1}{7}$
---
8. $\frac{44}{5}$
→ 44 ÷ 5 = 8 with remainder 4 → because 5 × 8 = 40, and 44 - 40 = 4
→ So, $8 \frac{4}{5}$
---
Now let’s check the right side of the worksheet — it looks like they’re asking for the same problems but maybe in decimal or just quotient? Wait — looking again, the right side says:
> Look at each improper fraction as a division problem. One has been done for you.
> Example: $\frac{40}{3} = 13 \frac{1}{3}$
And then lists numbers 1–15 with blank boxes. But the left side only goes to #8. Maybe the right side is a different set? Actually, looking closely, the right side seems to have the same fractions but listed vertically with small boxes — perhaps for writing the whole number part only? Or maybe it's a duplicate?
Wait — actually, comparing both sides:
Left side:
1. 40/3 → 13 1/3
2. 21/8
3. 15/6
4. 85/9
5. 14/3
6. 37/2
7. 15/7
8. 44/5
Right side:
1. 40/3 → 13 1/3 (same)
2. 21/8 → box
3. 15/6 → box
...
up to 15. 77/9
Ah! The right side has MORE problems — up to #15. Let me list them all from the right side since that’s probably the full assignment.
From the image (right column):
1. $\frac{40}{3} = 13 \frac{1}{3}$ ← given
2. $\frac{21}{8}$
3. $\frac{15}{6}$
4. $\frac{85}{9}$
5. $\frac{14}{3}$
6. $\frac{37}{2}$
7. $\frac{15}{7}$
8. $\frac{44}{5}$
9. $\frac{77}{9}$
10. $\frac{22}{4}$
11. $\frac{17}{5}$
12. $\frac{55}{7}$
13. $\frac{21}{4}$
14. $\frac{39}{5}$
15. $\frac{77}{9}$ ← wait, #9 and #15 are both 77/9? That might be a typo, but let’s assume it’s correct.
Actually, looking again — #9 is 77/9, #10 is 22/4, #11 is 17/5, #12 is 55/7, #13 is 21/4, #14 is 39/5, #15 is 77/9 — yes, duplicates happen sometimes.
But the user uploaded an image with two columns — left has 8 problems, right has 15. Since the instruction says “solve the problem accurately”, and the image shows both, I think we should do ALL 15 from the right side, since that’s the full worksheet.
Also, note: some fractions can be simplified before dividing — like 15/6 = 5/2, but the worksheet says “look at each improper fraction as a division problem” — so probably divide as-is, then simplify the fractional part if needed.
Let’s go one by one for all 15 on the right side.
---
1. $\frac{40}{3} = 13 \frac{1}{3}$ ← given
2. $\frac{21}{8}$
21 ÷ 8 = 2 R5 → $2 \frac{5}{8}$
3. $\frac{15}{6}$
15 ÷ 6 = 2 R3 → $\frac{3}{6} = \frac{1}{2}$ → $2 \frac{1}{2}$
4. $\frac{85}{9}$
85 ÷ 9 = 9 R4 → $9 \frac{4}{9}$
5. $\frac{14}{3}$
14 ÷ 3 = 4 R2 → $4 \frac{2}{3}$
6. $\frac{37}{2}$
37 ÷ 2 = 18 R1 → $18 \frac{1}{2}$
7. $\frac{15}{7}$
15 ÷ 7 = 2 R1 → $2 \frac{1}{7}$
8. $\frac{44}{5}$
44 ÷ 5 = 8 R4 → $8 \frac{4}{5}$
9. $\frac{77}{9}$
77 ÷ 9 = 8 R5 → because 9×8=72, 77-72=5 → $8 \frac{5}{9}$
10. $\frac{22}{4}$
22 ÷ 4 = 5 R2 → $\frac{2}{4} = \frac{1}{2}$ → $5 \frac{1}{2}$
11. $\frac{17}{5}$
17 ÷ 5 = 3 R2 → $3 \frac{2}{5}$
12. $\frac{55}{7}$
55 ÷ 7 = 7 R6 → because 7×7=49, 55-49=6 → $7 \frac{6}{7}$
13. $\frac{21}{4}$
21 ÷ 4 = 5 R1 → $5 \frac{1}{4}$
14. $\frac{39}{5}$
39 ÷ 5 = 7 R4 → $7 \frac{4}{5}$
15. $\frac{77}{9}$ ← same as #9 → $8 \frac{5}{9}$
---
Double-checking a few:
- #3: 15/6 = 2.5 = 2 1/2 ✔️
- #10: 22/4 = 5.5 = 5 1/2 ✔️
- #12: 55÷7: 7*7=49, 55-49=6 → 7 6/7 ✔️
- #15: same as #9 → 77÷9=8*9=72, 77-72=5 → 8 5/9 ✔️
All look correct.
Final Answer:
1. $13 \frac{1}{3}$
2. $2 \frac{5}{8}$
3. $2 \frac{1}{2}$
4. $9 \frac{4}{9}$
5. $4 \frac{2}{3}$
6. $18 \frac{1}{2}$
7. $2 \frac{1}{7}$
8. $8 \frac{4}{5}$
9. $8 \frac{5}{9}$
10. $5 \frac{1}{2}$
11. $3 \frac{2}{5}$
12. $7 \frac{6}{7}$
13. $5 \frac{1}{4}$
14. $7 \frac{4}{5}$
15. $8 \frac{5}{9}$
Parent Tip: Review the logic above to help your child master the concept of fraction division worksheet.
