The document explains the concept of division using the examples of 20 ÷ 5 and 17 ÷ 3. It demonstrates how to partition numbers into groups, calculating both the quotient and remainder for each example. The process emphasizes that division can be understood as repeated subtraction.

1. Division as
...Repeated...Repeated Subtraction...Subtraction...

2. 20 ÷ 5 means dividing 20 into 5 parts

3. 20 ÷ 5 means dividing 20 into 5 parts

4. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts

5. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 1

6. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 2

7. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 3

8. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 4

9. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5

10. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 1

11. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 2

12. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 3

13. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 4

14. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5

15. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5

16. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5

17. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5

18. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5 – 1

19. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5 – 2

20. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5 – 3

21. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5 – 4

22. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5 – 5

23. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5 – 5 – 1

24. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5 – 5 – 2

25. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5 – 5 – 3

26. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5 – 5 – 4

27. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
now, we are left with 20 – 5 – 5 – 5 – 5

28. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
Since each box gets 4 blocks, the Quotient is 4
Since after division, no block is left, the Remainder is 0
20 ÷ 5 is the same as 20 – 5 – 5 – 5 – 5 / r0

29. Box 1 Box 2 Box 3 Box 4 Box 5
20 ÷ 5 means dividing 20 into 5 parts
Q = 4
R = 0
Since each box gets 4 blocks, the Quotient is 4
Since after division, no block is left, the Remainder is 0
20 ÷ 5 is the same as 20 – 5 – 5 – 5 – 5 / r0

30. Another Example . . .

31. 17 ÷ 3 means dividing 17 into 3 parts
how many boxes to take?

32. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts

33. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts

34. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts

35. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts

36. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts

37. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts

38. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts

39. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts

40. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 1

41. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 2

42. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 3

43. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 3 – 1

44. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 3 – 2

45. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 3 – 3

46. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 3 – 3 – 1

47. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 3 – 3 – 2

48. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 3 – 3 – 3

49. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 3 – 3 – 3 – 1

50. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 3 – 3 – 3 – 2

51. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 3 – 3 – 3 – 3

52. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 3 – 3 – 3 – 3 – 1

53. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 3 – 3 – 3 – 3 – 2

54. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
now, we are left with 17 – 3 – 3 – 3 – 3 – 3

55. Box 1 Box 2 Box 3
17 ÷ 3 means dividing 17 into 3 parts
1 2
3
3 4
5
4
1 2
5
3
4
2
5
1
now, we are left with 17 – 3 – 3 – 3 – 3 – 3

56. 17 ÷ 3 means dividing 17 into 3 parts
Box 1 Box 2 Box 3
1 2
3
3 4
5
4
1 2
5
3
4
2
5
1
Q = 5 R =
now, we are left with 17 – 3 – 3 – 3 – 3 – 3

57. 17 ÷ 3 means dividing 17 into 3 parts
Box 1 Box 2 Box 3
1 2
3
3 4
5
4
1 2
5
3
4
2
5
1
Q = 5 R =
now, we are left with 17 – 3 – 3 – 3 – 3 – 3

58. 17 ÷ 3 means dividing 17 into 3 parts
Box 1 Box 2 Box 3
1 2
3
3 4
5
4
1 2
5
3
4
2
5
1
Q = 5 R = 2
now, we are left with 17 – 3 – 3 – 3 – 3 – 3