Math worksheet designed to teach students how to divide fractions by first establishing connections with whole number division and finding common denominators.
Two-column math worksheet featuring 44 division problems ranging from place value concepts to dividing fractions using common denominators.
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Show Answer Key & Explanations
Step-by-step solution for: Eureka Math Grade 6 Module 4 Lesson 2 Division of Fractions Answer ...
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Show Answer Key & Explanations
Step-by-step solution for: Eureka Math Grade 6 Module 4 Lesson 2 Division of Fractions Answer ...
The task is to solve all 44 division problems listed. Each problem involves dividing two numbers — sometimes whole numbers, sometimes fractions (including unit fractions like “12 ones ÷ 2 ones”, “12 halves ÷ 2 halves”, etc.). The pattern shows that many are simple divisions where the units cancel (e.g., “12 ones ÷ 2 ones” = 12 ÷ 2 = 6), or fraction division using the rule:
a/b ÷ c/d = a/b × d/c.
Let’s go one by one and compute each carefully.
---
1. 12 ones ÷ 2 ones
→ 12 ÷ 2 = 6
2. 12 ÷ 2
→ 6
3. 12 tens ÷ 2 tens
→ 12 × 10 = 120; 2 × 10 = 20; 120 ÷ 20 = 6
Or just cancel “tens”: 12 ÷ 2 = 6
4. 120 ÷ 20
→ 120 ÷ 20 = 6
5. 12 hundreds ÷ 2 hundreds
→ 12 ÷ 2 = 6
6. 1,200 ÷ 200
→ 1200 ÷ 200 = 6
7. 12 halves ÷ 2 halves
“halves” means ×½, but since both have same unit, cancel: 12 ÷ 2 = 6
Alternatively: 12 × ½ = 6; 2 × ½ = 1; 6 ÷ 1 = 6 ✔
8. 12/2 ÷ 2/2
12/2 = 6; 2/2 = 1; 6 ÷ 1 = 6
Or use fraction division: (12/2) ÷ (2/2) = (12/2) × (2/2) = 6 × 1 = 6
9. 12 fourths ÷ 3 fourths
Cancel “fourths”: 12 ÷ 3 = 4
Check: 12 × ¼ = 3; 3 × ¼ = ¾; 3 ÷ ¾ = 3 × 4/3 = 4 ✔
10. 12/4 ÷ 3/4
= (12/4) ÷ (3/4) = 3 ÷ (3/4) = 3 × (4/3) = 4
11. 8/8 ÷ 3/8
8/8 = 1; so 1 ÷ (3/8) = 1 × (8/3) = 8/3
Wait — double-check: Actually, it's (8/8) ÷ (3/8) = 1 ÷ (3/8) = 8/3 ✔️
But let’s keep exact fractions unless simplifiable.
12. 2/4 ÷ 1/4
= (2/4) ÷ (1/4) = (1/2) ÷ (1/4) = (1/2) × 4 = 2
Or cancel denominators: 2 ÷ 1 = 2
13. 1/4 ÷ 2/4
= (1/4) ÷ (2/4) = (1/4) × (4/2) = 1/2 → 1/2
14. 4/5 ÷ 2/5
= (4/5) × (5/2) = 4/2 = 2
15. 2/5 ÷ 4/5
= (2/5) × (5/4) = 2/4 = 1/2
16. 3/5 ÷ 4/5
= (3/5) × (5/4) = 3/4 → 3/4
17. 6/8 ÷ 2/8
= (6/8) × (8/2) = 6/2 = 3
18. 6/8 ÷ 4/8
= (6/8) × (8/4) = 6/4 = 3/2
19. 6/8 ÷ 5/8
= (6/8) × (8/5) = 6/5 → 6/5
20. 6/10 ÷ 2/10
= (6/10) × (10/2) = 6/2 = 3
21. 10/10 ÷ 8/10
= 1 ÷ (8/10) = 1 × (10/8) = 10/8 = 5/4
22. 4/10 ÷ 7/10
= (4/10) × (10/7) = 4/7 → 4/7
Now right column:
23. 6/12 ÷ 4/12
= (6/12) × (12/4) = 6/4 = 3/2
24. 6/12 ÷ 2/6 = 6/12 ÷ 6/12? Wait — check:
Problem says:
24. 6/12 ÷ 2/6 = 6/12 ÷ 2/6
Simplify: 6/12 = 1/2; 2/6 = 1/3
So (1/2) ÷ (1/3) = (1/2) × 3 = 3/2
But the image shows:
"6/12 ÷ 2/6 = 6/12 ÷ 6/12" — no, actually it writes:
> 24. 6/12 ÷ 2/6 = 6/12 ÷ 6/12
That seems like a *mistake in the problem statement* — maybe it's showing the student’s attempt? But per instructions, we solve the left expression: 6/12 ÷ 2/6.
So compute:
6/12 = 1/2
2/6 = 1/3
(1/2) ÷ (1/3) = 3/2 → 3/2
25. 8/14 ÷ 7/14
= (8/14) × (14/7) = 8/7 → 8/7
26. 8/14 ÷ 1/2 = 8/14 ÷ 1/2
= (8/14) × 2 = 16/14 = 8/7
Wait — the problem shows:
"8/14 ÷ 1/2 = 8/14 ÷ __" — maybe they want to fill blank? But again, we solve the expression as written: 8/14 ÷ 1/2 = 8/14 × 2 = 16/14 = 8/7.
But looking at pattern, many problems are of form A/B ÷ C/B = A/C. So likely all are meant to be straightforward.
Let me re-express all with consistent method:
If both fractions have same denominator, e.g., a/d ÷ b/d = a/b.
If different denominators, use reciprocal.
Let’s continue carefully:
27. 11/14 ÷ 2/14 = 11/2 = 11/2
28. 11/14 ÷ 1/14 = 11/1 = 11
29. 1/7 ÷ 6/14
Note: 6/14 = 3/7
So 1/7 ÷ 3/7 = 1/3 → 1/3
30. 7/18 ÷ 3/18 = 7/3 → 7/3
31. 7/18 ÷ 1/6
1/6 = 3/18
So 7/18 ÷ 3/18 = 7/3 → 7/3
32. 1/18 ÷ 12/18 = 1/12 → 1/12
Wait — problem says:
"1/18 ÷ 12/18" — yes, so 1 ÷ 12 = 1/12
33. 1/6 ÷ 4/18
4/18 = 2/9
1/6 ÷ 2/9 = (1/6) × (9/2) = 9/12 = 3/4
Alternative: convert to common denominator:
1/6 = 3/18; 4/18 stays → 3/18 ÷ 4/18 = 3/4 ✔
34. 4/12 ÷ 8/6
Simplify: 4/12 = 1/3; 8/6 = 4/3
So (1/3) ÷ (4/3) = (1/3) × (3/4) = 1/4 → 1/4
35. 1/3 ÷ 1/15 = (1/3) × 15 = 5
36. 2/6 ÷ 1/9 = 1/3 ÷ 1/9 = (1/3) × 9 = 3
Also: 2/6 = 1/3, so yes → 3
But problem shows: "2/6 ÷ 1/9 = 18/18"? That seems like student work. We ignore and compute correctly: 3
37. 1/6 ÷ 4/9 = (1/6) × (9/4) = 9/24 = 3/8
38. 2/3 ÷ 3/4 = (2/3) × (4/3) = 8/9 → 8/9
39. 1/3 ÷ 1/5 = (1/3) × 5 = 5/3
40. 1/7 ÷ 1/2 = (1/7) × 2 = 2/7
41. 5/6 ÷ 2/9 = (5/6) × (9/2) = 45/12 = simplify: divide by 3 → 15/4 → 15/4
42. 5/9 ÷ 2/6
2/6 = 1/3
So (5/9) ÷ (1/3) = (5/9) × 3 = 15/9 = 5/3
43. 5/6 ÷ 4/9 = (5/6) × (9/4) = 45/24 = simplify: divide by 3 → 15/8 → 15/8
44. 1/2 ÷ 4/5 = (1/2) × (5/4) = 5/8 → 5/8
Now let’s list all 44 answers clearly:
1. 6
2. 6
3. 6
4. 6
5. 6
6. 6
7. 6
8. 6
9. 4
10. 4
11. 8/3
12. 2
13. 1/2
14. 2
15. 1/2
16. 3/4
17. 3
18. 3/2
19. 6/5
20. 3
21. 5/4
22. 4/7
23. 3/2
24. 3/2
25. 8/7
26. 8/7
27. 11/2
28. 11
29. 1/3
30. 7/3
31. 7/3
32. 1/12
33. 3/4
34. 1/4
35. 5
36. 3
37. 3/8
38. 8/9
39. 5/3
40. 2/7
41. 15/4
42. 5/3
43. 15/8
44. 5/8
Let me double-check a few tricky ones:
- #11: 8/8 ÷ 3/8 = 1 ÷ 3/8 = 8/3 ✔️
- #29: 1/7 ÷ 6/14 = 1/7 ÷ 3/7 = 1/3 ✔️
- #33: 1/6 ÷ 4/18 = 1/6 ÷ 2/9 = (1×9)/(6×2)=9/12=3/4 ✔️
- #36: 2/6 = 1/3; 1/3 ÷ 1/9 = 3 ✔️
- #41: 5/6 ÷ 2/9 = 5/6 × 9/2 = 45/12 = 15/4 ✔️
- #43: 5/6 × 9/4 = 45/24 = 15/8 ✔️
All correct.
Since the user only wants the final answer (and no explanation sections because ExplainAnswer = false), I will output only the list of 44 answers in order, separated by commas, as a single final answer.
Final Answer:
6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 8/3, 2, 1/2, 2, 1/2, 3/4, 3, 3/2, 6/5, 3, 5/4, 4/7, 3/2, 3/2, 8/7, 8/7, 11/2, 11, 1/3, 7/3, 7/3, 1/12, 3/4, 1/4, 5, 3, 3/8, 8/9, 5/3, 2/7, 15/4, 5/3, 15/8, 5/8
a/b ÷ c/d = a/b × d/c.
Let’s go one by one and compute each carefully.
---
1. 12 ones ÷ 2 ones
→ 12 ÷ 2 = 6
2. 12 ÷ 2
→ 6
3. 12 tens ÷ 2 tens
→ 12 × 10 = 120; 2 × 10 = 20; 120 ÷ 20 = 6
Or just cancel “tens”: 12 ÷ 2 = 6
4. 120 ÷ 20
→ 120 ÷ 20 = 6
5. 12 hundreds ÷ 2 hundreds
→ 12 ÷ 2 = 6
6. 1,200 ÷ 200
→ 1200 ÷ 200 = 6
7. 12 halves ÷ 2 halves
“halves” means ×½, but since both have same unit, cancel: 12 ÷ 2 = 6
Alternatively: 12 × ½ = 6; 2 × ½ = 1; 6 ÷ 1 = 6 ✔
8. 12/2 ÷ 2/2
12/2 = 6; 2/2 = 1; 6 ÷ 1 = 6
Or use fraction division: (12/2) ÷ (2/2) = (12/2) × (2/2) = 6 × 1 = 6
9. 12 fourths ÷ 3 fourths
Cancel “fourths”: 12 ÷ 3 = 4
Check: 12 × ¼ = 3; 3 × ¼ = ¾; 3 ÷ ¾ = 3 × 4/3 = 4 ✔
10. 12/4 ÷ 3/4
= (12/4) ÷ (3/4) = 3 ÷ (3/4) = 3 × (4/3) = 4
11. 8/8 ÷ 3/8
8/8 = 1; so 1 ÷ (3/8) = 1 × (8/3) = 8/3
Wait — double-check: Actually, it's (8/8) ÷ (3/8) = 1 ÷ (3/8) = 8/3 ✔️
But let’s keep exact fractions unless simplifiable.
12. 2/4 ÷ 1/4
= (2/4) ÷ (1/4) = (1/2) ÷ (1/4) = (1/2) × 4 = 2
Or cancel denominators: 2 ÷ 1 = 2
13. 1/4 ÷ 2/4
= (1/4) ÷ (2/4) = (1/4) × (4/2) = 1/2 → 1/2
14. 4/5 ÷ 2/5
= (4/5) × (5/2) = 4/2 = 2
15. 2/5 ÷ 4/5
= (2/5) × (5/4) = 2/4 = 1/2
16. 3/5 ÷ 4/5
= (3/5) × (5/4) = 3/4 → 3/4
17. 6/8 ÷ 2/8
= (6/8) × (8/2) = 6/2 = 3
18. 6/8 ÷ 4/8
= (6/8) × (8/4) = 6/4 = 3/2
19. 6/8 ÷ 5/8
= (6/8) × (8/5) = 6/5 → 6/5
20. 6/10 ÷ 2/10
= (6/10) × (10/2) = 6/2 = 3
21. 10/10 ÷ 8/10
= 1 ÷ (8/10) = 1 × (10/8) = 10/8 = 5/4
22. 4/10 ÷ 7/10
= (4/10) × (10/7) = 4/7 → 4/7
Now right column:
23. 6/12 ÷ 4/12
= (6/12) × (12/4) = 6/4 = 3/2
24. 6/12 ÷ 2/6 = 6/12 ÷ 6/12? Wait — check:
Problem says:
24. 6/12 ÷ 2/6 = 6/12 ÷ 2/6
Simplify: 6/12 = 1/2; 2/6 = 1/3
So (1/2) ÷ (1/3) = (1/2) × 3 = 3/2
But the image shows:
"6/12 ÷ 2/6 = 6/12 ÷ 6/12" — no, actually it writes:
> 24. 6/12 ÷ 2/6 = 6/12 ÷ 6/12
That seems like a *mistake in the problem statement* — maybe it's showing the student’s attempt? But per instructions, we solve the left expression: 6/12 ÷ 2/6.
So compute:
6/12 = 1/2
2/6 = 1/3
(1/2) ÷ (1/3) = 3/2 → 3/2
25. 8/14 ÷ 7/14
= (8/14) × (14/7) = 8/7 → 8/7
26. 8/14 ÷ 1/2 = 8/14 ÷ 1/2
= (8/14) × 2 = 16/14 = 8/7
Wait — the problem shows:
"8/14 ÷ 1/2 = 8/14 ÷ __" — maybe they want to fill blank? But again, we solve the expression as written: 8/14 ÷ 1/2 = 8/14 × 2 = 16/14 = 8/7.
But looking at pattern, many problems are of form A/B ÷ C/B = A/C. So likely all are meant to be straightforward.
Let me re-express all with consistent method:
If both fractions have same denominator, e.g., a/d ÷ b/d = a/b.
If different denominators, use reciprocal.
Let’s continue carefully:
27. 11/14 ÷ 2/14 = 11/2 = 11/2
28. 11/14 ÷ 1/14 = 11/1 = 11
29. 1/7 ÷ 6/14
Note: 6/14 = 3/7
So 1/7 ÷ 3/7 = 1/3 → 1/3
30. 7/18 ÷ 3/18 = 7/3 → 7/3
31. 7/18 ÷ 1/6
1/6 = 3/18
So 7/18 ÷ 3/18 = 7/3 → 7/3
32. 1/18 ÷ 12/18 = 1/12 → 1/12
Wait — problem says:
"1/18 ÷ 12/18" — yes, so 1 ÷ 12 = 1/12
33. 1/6 ÷ 4/18
4/18 = 2/9
1/6 ÷ 2/9 = (1/6) × (9/2) = 9/12 = 3/4
Alternative: convert to common denominator:
1/6 = 3/18; 4/18 stays → 3/18 ÷ 4/18 = 3/4 ✔
34. 4/12 ÷ 8/6
Simplify: 4/12 = 1/3; 8/6 = 4/3
So (1/3) ÷ (4/3) = (1/3) × (3/4) = 1/4 → 1/4
35. 1/3 ÷ 1/15 = (1/3) × 15 = 5
36. 2/6 ÷ 1/9 = 1/3 ÷ 1/9 = (1/3) × 9 = 3
Also: 2/6 = 1/3, so yes → 3
But problem shows: "2/6 ÷ 1/9 = 18/18"? That seems like student work. We ignore and compute correctly: 3
37. 1/6 ÷ 4/9 = (1/6) × (9/4) = 9/24 = 3/8
38. 2/3 ÷ 3/4 = (2/3) × (4/3) = 8/9 → 8/9
39. 1/3 ÷ 1/5 = (1/3) × 5 = 5/3
40. 1/7 ÷ 1/2 = (1/7) × 2 = 2/7
41. 5/6 ÷ 2/9 = (5/6) × (9/2) = 45/12 = simplify: divide by 3 → 15/4 → 15/4
42. 5/9 ÷ 2/6
2/6 = 1/3
So (5/9) ÷ (1/3) = (5/9) × 3 = 15/9 = 5/3
43. 5/6 ÷ 4/9 = (5/6) × (9/4) = 45/24 = simplify: divide by 3 → 15/8 → 15/8
44. 1/2 ÷ 4/5 = (1/2) × (5/4) = 5/8 → 5/8
Now let’s list all 44 answers clearly:
1. 6
2. 6
3. 6
4. 6
5. 6
6. 6
7. 6
8. 6
9. 4
10. 4
11. 8/3
12. 2
13. 1/2
14. 2
15. 1/2
16. 3/4
17. 3
18. 3/2
19. 6/5
20. 3
21. 5/4
22. 4/7
23. 3/2
24. 3/2
25. 8/7
26. 8/7
27. 11/2
28. 11
29. 1/3
30. 7/3
31. 7/3
32. 1/12
33. 3/4
34. 1/4
35. 5
36. 3
37. 3/8
38. 8/9
39. 5/3
40. 2/7
41. 15/4
42. 5/3
43. 15/8
44. 5/8
Let me double-check a few tricky ones:
- #11: 8/8 ÷ 3/8 = 1 ÷ 3/8 = 8/3 ✔️
- #29: 1/7 ÷ 6/14 = 1/7 ÷ 3/7 = 1/3 ✔️
- #33: 1/6 ÷ 4/18 = 1/6 ÷ 2/9 = (1×9)/(6×2)=9/12=3/4 ✔️
- #36: 2/6 = 1/3; 1/3 ÷ 1/9 = 3 ✔️
- #41: 5/6 ÷ 2/9 = 5/6 × 9/2 = 45/12 = 15/4 ✔️
- #43: 5/6 × 9/4 = 45/24 = 15/8 ✔️
All correct.
Since the user only wants the final answer (and no explanation sections because ExplainAnswer = false), I will output only the list of 44 answers in order, separated by commas, as a single final answer.
Final Answer:
6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 8/3, 2, 1/2, 2, 1/2, 3/4, 3, 3/2, 6/5, 3, 5/4, 4/7, 3/2, 3/2, 8/7, 8/7, 11/2, 11, 1/3, 7/3, 7/3, 1/12, 3/4, 1/4, 5, 3, 3/8, 8/9, 5/3, 2/7, 15/4, 5/3, 15/8, 5/8
Parent Tip: Review the logic above to help your child master the concept of 6th grade math answer key.