Multiplication The Complement Method
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This document introduces the complement method for multiplication. It begins by explaining that the complement of a number is the number needed to make 10 when added together. It then provides 6 examples of using the complement method to solve multiplication problems step-by-step. The examples show finding the complement of each digit, multiplying those numbers, and then adding or subtracting as needed based on the complement. It concludes by stating that the complement method enriches mathematical skills, though it may not be faster.
Multiplication The Complement Method
- 1. CoffeeMath:Methods, Tips And Tricks Series.Complement Method
- 2. Foreword ( I )The 10 complement of 1is 9 because 1 + 9 = 10 The 10 complement of 2is 8 because 2 + 8 = 10 The 10 complement of 3is 7 because 3 + 7 = 10 The 10 complement of 4is 6 because 4 + 6 = 10 The 10 complement of 5is 5 because 5 + 5 = 10 The 10 complement of 6is 4 because 6 + 4 = 10 The 10 complement of 7is 3 because 7 + 3 = 10 The 10 complement of 8is 2 because 8 + 2 = 10 The 10 complement of 9is 1 because 9 + 1 = 10 We can write in these ways127348956983762154
- 3. Foreword ( II )1. We must able to differentiate place value and digit value567Place value of 7 is ones butdigit value of 7 is 7Example:-Place value of 6 is tens butdigit value of 6 is 60Place value of 5 is hundreds butdigit value of 5 is 5002. We must able to synthesize number to it’s digit valueExample:-567 = 500 + 60 + 73028 = 3000 + 000 + 20 + 8Further:-567 X 8 = ( 500 x 8 ) + (60 x 8 ) + ( 7 x 8 )3028 X 52 = ( 3000 x 52 ) + ( 20 x 52 ) + ( 8 x 52 )
- 4. INTRODUCTIONX78X788 + 2 = 10, the complement of 8 is 2 7 + 3= 10, the complement of 7 is 33256ii) 8 - 3= 5 or 7 - 2 = 5iii) 2 X 3= 6
- 5. Example 1 :9 6X8
- 6. Example 1 :9 6X89 6X8124
- 7. Example 1 :9 6X89 6X81242 X 4 = 082 X 1 = 02028
- 8. Example 1 :9 6X89 6X81242 X 4 = 08 80 22 X 1 = 02028
- 9. Example 1 :9 6X89 6X81242 X 4 = 08 80 22 X 1 = 02+0028+0Append;
- 10. Example 1 :9 6X89 6X81242 X 4 = 08 80 22 X 1 = 02+4+0028+0Append;8 – 4 = +4
- 11. Example 1 :9 6X89 6X81242 X 4 = 08 80 22 X 1 = 02+4+7+0028+0Append;8 – 4 = +48 – 1 = +7
- 12. Example 1 :9 6X89 6X81242 X 4 = 08 80 22 X 1 = 02+4+7+0028++0Append;8 – 4 = +48 – 1 = +7 7 6 8
- 13. Example 2 :9 6X8
- 14. Example 2 :9 6X89 6 7X84123
- 15. Example 2 :9 6X89 6 7X841232X 3 = 060 2 8 62 X 4 = 282 X 1 = 02
- 16. Example 2 :9 6X89 6 7X841232X 3 = 060 2 8 62 X 4 = 28+5+4+0+72 X 1 = 028 – 3 = +58 – 4 = +48 – 1 = +7
- 17. Example 2 :9 6X89 6 7X841232X 3 = 060 2 8 62 X 4 = 28+5+4+0+72 X 1 = 02+8 – 3 = +58 – 4 = +48 – 1 = +77 7 3 6
- 18. Example 3 :3 6X6
- 19. Example 3 :3 6X63 6X6744
- 20. Example 3 :3 6X63 6X6744 62 94X 4 = 164 X 7 = 28
- 21. Example 3 :3 6X63 6X6744 62 94X 4 = 164 X 7 = 28+2-1+06 – 4 = +26 – 7 = -1
- 22. Example 3 :3 6X63 6X6744 62 94X 4 = 164 X 7 = 28+2-1+06 – 4 = +2+6 – 7 = -1 2 1 6
- 23. Example 4 :9 6 1X7
- 24. Example 4 :9 6 1X79 6 1X74913
- 25. Example 4 :9 6 1X79 6 1X749133X 9 = 270 4 4 73 X 4 = 123 X 1 = 03
- 26. Example 4 :9 6 1X79 6 1X749133X 9 = 270 4 4 73 X 4 = 12-2+3+0+63 X 1 = 037 – 9 = -27 – 4 = +37 – 1 = +6
- 27. Example 4 :9 6 1X79 6 1X749133X 9 = 270 4 4 73 X 4 = 12-2+3+0+63 X 1 = 03+7 – 9 = -27 – 4 = +37 – 1 = +66 7 2 7
- 28. Example 5 :9 3 1X6
- 29. Example 5 :9 3 1X69 3 1X67914
- 30. Example 5 :9 3 1X69 3 1X679144X 9 = 360 7 1 64 X 7 = 284 X 1 = 04
- 31. Example 5 :9 3 1X69 3 1X679144X 9 = 360 7 1 64 X 7 = 28-3-1+04 X 1 = 04+56 – 9 = -36 – 7 = -16 – 1 = +5
- 32. Example 5 :9 3 1X69 3 1X679144X 9 = 360 7 1 64 X 7 = 28-3-1+04 X 1 = 04+5+6 – 9 = -36 – 7 = -16 – 1 = +55 5 8 6
- 33. Example 6 :4 3 2X5
- 34. Example 6 :4 3 2X54 3 2X57865
- 35. Example 6 :4 3 2X54 3 2X578655X 8 = 403 3 9 05 X 7 = 355 X 6 = 30
- 36. Example 6 :4 3 2X54 3 2X578655X 8 = 403 3 9 05 X 7 = 35-3-2-1+05 X 6 = 305 – 8 = -35 – 7 = -25 – 6 = -1
- 37. Example 6 :4 3 2X54 3 2X578655X 8 = 403 3 9 05 X 7 = 35-3-2-1+05 X 6 = 30+5 – 8 = -35 – 7 = -25 – 6 = -12 1 6 0
- 38. I never say that this method is faster and safer but I strongly think that this method enrich our field.
- 39. End ShowGOOD LUCK !