Most of us in India had rote learned the algorithm to divide 2 numbers at primary school level. Unfortunately, a vast majority of students DO NOT understand the concept of division. This is a graphical representation of division 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