1. Multiplication Past Paper Questions.
This demonstrates a Past Paper question using several different methods to find the answer.
Working correctly through any of the following methods will get full marks for the question.
Further practice can be obtained using the relevant activities in the Multiplication section of the Moodle.

2. 469 x 36 Multiply 469 by 36 Traditional Method.
Write the question with the bigger number above the smaller number 36
[3]

3. 469 x 36 4 Multiply 469 by 36 Traditional Method.
First multiply the top row by the units of the second row.
9 x 6 = 54: 4 goes in the 1st column and the 5 is carried over to the next column. 36 5 4
[3]

4. 469 x 36 1 4 Multiply 469 by 36 Traditional Method.
First multiply the top row by the units of the second row.
6 x 6 = 36: add the 5 that has been carried over to make 41.
The 1 goes in the 2nd column and the 4 is carried over to the next column 36 4 5 1 4
[3]

5. 469 x 36 8 1 4 Multiply 469 by 36 Traditional Method.
First multiply the top row by the units of the second row.
6 x 4 = 24: add the 4 that has been carried over to make 28.
The 8 goes in the 3rd column and the 2 is carried over to the next column 36 2 4 5 8 1 4
[3]

6. 469 x 36 2 8 1 4 Multiply 469 by 36 Traditional Method.
First multiply the top row by the units of the second row.
Carry the 2 down
1 mark to get this far. 36 2 4 5 2 8 1 4
[3]

7. 469 x 36 2 8 1 4 Multiply 469 by 36 Traditional Method.
Next multiply the top row by the tens of the second row. Remember to add the 0 to the units column. 36 2 4 5 2 8 1 4
[3]

8. 469 x 36 2 8 1 4 7 Multiply 469 by 36 Traditional Method.
Next multiply the top row by the tens of the second row.
3 x 9 = 27: the 7 goes in the 2nd column and the 2 is carried over to the 3rd column. 36 2 4 5 2 8 1 4 7 2
[3]

9. 469 x 36 2 8 1 4 7 Multiply 469 by 36 Traditional Method.
Next multiply the top row by the tens of the second row.
3 x 6 = 18: add to this the 2 that was carried over and we have 20. The 0 goes in the 3rd column and the 2 is carried over to the 4th column. 36 2 4 5 2 8 1 4 7 2 2
[3]

10. 469 x 36 2 8 1 4 4 7 Multiply 469 by 36 Traditional Method.
Next multiply the top row by the tens of the second row.
3 x 4 = 12: add to this the 2 that was carried over and we have 14. The 4 goes in the 4th column and the 1 is carried over to the 5th column. 36 2 4 5 2 8 1 4 4 7 1 2 2
[3]

11. 469 x 36 2 8 1 4 1 4 7 Multiply 469 by 36 Traditional Method.
Carry the 1 up.
Another mark for getting this far. 36 2 4 5 2 8 1 4 1 4 7 1 2 2
[3]

12. 469 x 36 2 8 1 4 1 4 7 4 Multiply 469 by 36 Traditional Method.
Now add the two rows of numbers together.
4 + 0 = 4 36 2 4 5 2 8 1 4 1 4 7 1 2 2 4
[3]

13. 469 x 36 2 8 1 4 1 4 7 8 4 Multiply 469 by 36 Traditional Method.
Now add the two rows of numbers together.
1 + 7 = 8 36 2 4 5 2 8 1 4 1 4 7 1 2 2 8 4
[3]

14. 469 x 36 2 8 1 4 1 4 7 8 8 4 Multiply 469 by 36 Traditional Method.
Now add the two rows of numbers together.
8 + 0 = 8 36 2 4 5 2 8 1 4 1 4 7 1 2 2 8 8 4
[3]

15. 469 x 36 2 8 1 4 1 4 7 6 8 8 4 Multiply 469 by 36 Traditional Method.
Now add the two rows of numbers together.
2 + 4 = 6 36 2 4 5 2 8 1 4 1 4 7 1 2 2 6 8 8 4
[3]

16. Multiply 469 by 36
Traditional Method.
469 x
Now add the two rows of numbers together.
0 + 1 = 1 36 2 4 5 2 8 1 4 1 4 7 1 2 2 1 6 8 8 4
[3]

17. Multiply 469 by 36
Traditional Method.
469 x
We now have the answer.
Final mark for a correct addition. 36 2 4 5 2 8 1 4 1 4 7 1 2 2 1 6 8 8 4
[3]

18. Multiply 469 by 36 Multiplication Grid. x
Draw the multiplication grid and write the numbers across the top and down the side.
[3]

19. Multiply 469 by 36 Multiplication Grid. x 400 60 9 30 6
Draw the multiplication grid and write the numbers across the top and down the side.
[3]

20. Multiply 469 by 36 Multiplication Grid. x 400 60 9 30 6
Cross multiply each number in the top row by each number up the side.
400 x 30 = (4 x 3 = 12 and there are three 0’s in total)
[3]

21. Multiply 469 by 36 Multiplication Grid. x 400 60 9 30 12000 6
Cross multiply each number in the top row by each number up the side.
400 x 30 = (4 x 3 = 12 and there are three 0’s in total)
[3]

22. Multiply 469 by 36 Multiplication Grid. x 400 60 9 30 12000 1800 270 6
2400
360 54
Do the same for the other cells.
[3]

23. Multiply 469 by 36 Multiplication Grid. x 400 60 9 30 12000 1800 270 6
2400
360 54
Do the same for the other cells.
[3]

24. Multiply 469 by 36 Multiplication Grid. x 400 60 9 30 12000 1800 270 6
2400
360 54
Do the same for the other cells.
[3]

25. Multiply 469 by 36 Multiplication Grid. x 400 60 9 30 12000 1800 270 6
2400
360 54
Do the same for the other cells.
[3]

26. Multiply 469 by 36 Multiplication Grid. x 400 60 9 30 12000 1800 270 6
2400
360 54
Do the same for the other cells.
[3]

27. Multiply 469 by 36 Multiplication Grid. x 400 60 9 30 12000 1800 270
14070 6
2400
360 54
2814
16884
Add up the rows to complete the final column.
[3]

28. Multiply 469 by 36 Multiplication Grid. x 400 60 9 30 12000 1800 270
14070 6
2400
360 54
2814
16884
Add up the rows to complete the final column.
= 14070
[3]

29. Multiply 469 by 36 Multiplication Grid. x 400 60 9 30 12000 1800 270
14070 6
2400
360 54
2814
16884
Add up the rows to complete the final column.
= 2814
[3]

30. Multiply 469 by 36 Multiplication Grid. x 400 60 9 30 12000 1800 270
14070 6
2400
360 54
2814
16884
Add up the final column to get your answer.
= 16884
[3]

31. Multiply 469 by 36 Multiplication Grid. x 400 60 9 30 12000 1800 270
14070 6
2400
360 54
2814
16884
Answer = 16884
[3]

32. Multiply 469 by 36 Chinese Method. x 4 6 9 3
Draw the table and write the numbers across the top and down the side.
Remember to write the digits in the vertical column upwards from the bottom to the top.
[3]

33. Multiply 469 by 36 Chinese Method. x 4 6 9 3
Cross multiply every digit in the horizontal column by every digit in the vertical column.
6 x 4 = 24
[3]

34. Multiply 469 by 36 Chinese Method. x 4 6 9 3 4 2
Cross multiply every digit in the horizontal column by every digit in the vertical column.
6 x 4 = 24 4 2
[3]

35. Multiply 469 by 36 Chinese Method. x 4 6 9 3 4 6 2 3
Cross multiply every digit in the horizontal column by every digit in the vertical column.
6 x 6 = 36 4 6 2 3
[3]

36. Multiply 469 by 36 Chinese Method. x 4 6 9 3 4 6 4 2 3 5
Cross multiply every digit in the horizontal column by every digit in the vertical column.
6 x 9 = 54 4 6 4 2 3 5
[3]

37. Multiply 469 by 36 Chinese Method. x 4 6 9 3 4 6 4 2 3 5 2 1
Cross multiply every digit in the horizontal column by every digit in the vertical column.
3 x 4 = 12 4 6 4 2 3 5 2 1
[3]

38. Multiply 469 by 36 Chinese Method. x 4 6 9 3 4 6 4 2 3 5 2 8 1 1
Cross multiply every digit in the horizontal column by every digit in the vertical column.
3 x 6 = 18 4 6 4 2 3 5 2 8 1 1
[3]

39. Multiply 469 by 36 Chinese Method. x 4 6 9 3 4 6 4 2 3 5 2 8 7 1 1 2
Cross multiply every digit in the horizontal column by every digit in the vertical column.
3 x 9 = 27 4 6 4 2 3 5 2 8 7 1 1 2
[3]

40. Multiply 469 by 36 Chinese Method. x 4 6 9 3 4 6 4 2 3 5 2 8 7 1 1 2
Next add the digits diagonally. 4 6 4 2 3 5 2 8 7 1 1 2
[3]

41. Multiply 469 by 36 Chinese Method. x 4 6 9 3 4 6 4 2 3 5 2 8 7 1 1 2
Next add the digits diagonally.
4 = 4 4 6 4 2 3 5 2 8 7 1 1 2
[3]

42. Multiply 469 by 36 Chinese Method. x 4 6 9 3 8 1 4 6 4 2 3 5 2 8 7 1 1
Next add the digits diagonally.
= 18.
Write 8 next to the last digit and carry the 1 under where the next answer will be. 4 6 4 2 3 5 2 8 7 1 1 2
[3]

43. Multiply 469 by 36 Chinese Method. x 4 6 9 3 8 1 4 6 4 2 3 5 2 8 7 1 1
Next add the digits diagonally.
= 17 plus the remainder from the previous sum.
17+1 = 18
Write 8 under the last digit and carry the 1 under where the next answer will be. 4 6 4 2 3 5 2 8 7 1 1 2
[3]

44. Multiply 469 by 36 Chinese Method. x 4 6 9 3 8 1 4 6 4 2 3 5 2 8 7 1 1
Next add the digits diagonally.
= 5 plus the remainder from the previous sum
5 + 1 = 6.
Write 8 under the last digit and carry the 1 under where the next answer will be. 4 6 4 2 3 5 2 8 7 1 1 2
[3]

45. Multiply 469 by 36 Chinese Method. x 4 6 9 3 8 1 4 6 4 2 3 5 2 8 7 1 1
Next add the digits diagonally.
Finally
1 = 1 and there is no remainder to add. 4 6 4 2 3 5 2 8 7 1 1 2
[3]

46. Multiply 469 by 36 Chinese Method. x 4 6 9 3 8 1 4 6 4 2 3 5 2 8 7 1 1
Read the answer in the direction of the arrows.
(Do not include the remainders).
The answer is 16884 4 6 4 2 3 5 2 8 7 1 1 2
[3]

47. Multiply 469 by 36 Egyptian Method (Double and Half). 1 469
Write down 1 in the left hand column and 469 in the right hand column.
[3]

48. Multiply 469 by 36 Egyptian Method (Double and Half). 1 469
= 938 2
938
Double the number in each column.
1 + 1 = 2
= 938.
Write these answers underneath in the 2nd row.
[3]

49. Multiply 469 by 36 Egyptian Method (Double and Half). 1 469
= 938 2
938
= 1876 4
1876
Double the number in each column again.
2 + 2 = 4
= 1876.
Write these answers underneath in the 3nd row.
[3]

50. Multiply 469 by 36 Egyptian Method (Double and Half). 1 469
= 938 2
938
= 1876 4
1876
= 3752 8
3752
Double the number in each column again.
4 + 4 = 8
= 3752.
Write these answers underneath in the 4th row.
[3]

51. Multiply 469 by 36 Egyptian Method (Double and Half). 1 469
= 938 2
938
= 1876 4
1876
= 3752 8
3752
= 7504 16
7504
= 15008 32
15008
Continue until, when you double the number in the left hand column, you get to a number greater than the one you are going to multiply it by 9 (in this case 36).
[3]

52. Multiply 469 by 36 Egyptian Method (Double and Half). 1 469
= 938 2
938
= 1876 4
1876
= 3752 8
3752
= 7504 16
7504
= 15008 32
15008
Continue until, when you double the number in the left hand column, you get to a number greater than the one you are going to multiply it by 9 (in this case 36).
[3]

53. Multiply 469 by 36 Egyptian Method (Double and Half). 1 469
= 938 2
938
= 1876 4
1876
= 3752 8
3752
= 7504 16
7504
= 15008 32
15008
Now decide how you can make 36 by adding the numbers in the left hand column.
36 =
[3]

54. Multiply 469 by 36 Egyptian Method (Double and Half). 1 469
= 938 2
938
= 1876 4
1876
= 3752 8
3752
= 7504 16
7504
= 15008 32
15008
Now decide how you can make 36 by adding the numbers in the left habd column.
36 =
Highlight these two numbers and the matching numbers in the other column.
[3]

55. Multiply 469 by 36 Egyptian Method (Double and Half). 1 469
= 938 2
938
= 1876 4
1876
= 3752 8
3752
= 7504 16
7504
= 15008 32
15008 36
16884
Now add together the other two highlighted numbers.
= 16884
Answer =
[3]

56. For further practice using any of the explained methods then please see the relevant Excel sheet in the Moodle.