CoffeeMath:Methods, Tips And Tricks Series.

Complement Method

The 10 complement of 1 is 9 because 1 + 9 = 10

Foreword ( I )

The 10 complement of 2 is 8 because 2 + 8 = 10 The 10 complement of 3 is 7 because 3 + 7 = 10 The 10 complement of 4 is 6 because 4 + 6 = 10 The 10 complement of 5 is 5 because 5 + 5 = 10 The 10 complement of 6 is 4 because 6 + 4 = 10 The 10 complement of 7 is 3 because 7 + 3 = 10 The 10 complement of 8 is 2 because 8 + 2 = 10 The 10 complement of 9 is 1 because 9 + 1 = 10

We can write in these ways

19

28

73

37

46

82

91

55

64

Foreword ( II )

567

1. We must able to differentiate place value and digit value

2. We must able to synthesize number to it’s digit value

Example:- Place value of 7 is ones but digit value of 7 is 7

Place value of 6 is tens but digit value of 6 is 60

Place value of 5 is hundreds but digit value of 5 is 500

567 = 500 + 60 + 7

Example:-

3028 = 3000 + 000 + 20 + 8

567 X 8 = ( 500 x 8 ) + (60 x 8 ) + ( 7 x 8 )

Further:-

3028 X 52 = ( 3000 x 52 ) + ( 20 x 52 ) + ( 8 x 52 )

X 73

82

X 78

i) 8 + 2 = 10, the complement of 8 is 2 7 + 3 = 10, the complement of 7 is 3

ii) 8 - 3 = 5 or 7 - 2 = 5

iii) 2 X 3 = 65 6

INTRODUCTION

9 6 X 8

Example 1 :

9 6 X 8

9 6 X 81 24

Example 1 :

9 6 X 8

9 6 X 81 24

2 X 1 = 022 X 4 = 08

Example 1 :

028

9 6 X 8

9 6 X 81 24

80 2 2 X 1 = 022 X 4 = 08

Example 1 :

028

9 6 X 8

9 6 X 81 24

80 2 2 X 1 = 022 X 4 = 08

+0

Example 1 :

028+0

Append;

9 6 X 8

+4

9 6 X 81 24

80 2

8 – 4 = +4

2 X 1 = 022 X 4 = 08

+0

Example 1 :

028+0

Append;

9 6 X 8

+4

+7

9 6 X 81 24

80 2

8 – 1 = +7

8 – 4 = +4

2 X 1 = 022 X 4 = 08

+0

Example 1 :

028+0

Append;

9 6 X 8

+4

+7

9 6 X 81 24

80 2

8 – 1 = +7

8 – 4 = +4

2 X 1 = 022 X 4 = 08

7 6 8

+ +0

Example 1 :

028+0

Append;

9 6 X 8

Example 2 :

9 6 X 8

9 6 7 X 84 231

Example 2 :

9 6 X 8

9 6 7 X 84 23

0 2 8 6 2 X 4 = 282X 3 = 06

1

2 X 1 = 02

Example 2 :

9 6 X 8

+5

+4

9 6 7 X 84 23

0 2 8 6

8 – 4 = +48 – 3 = +5

2 X 4 = 282X 3 = 06

+0

1

2 X 1 = 02

8 – 1 = +7

+7

Example 2 :

9 6 X 8

+5

+4

9 6 7 X 84 23

0 2 8 6

8 – 4 = +48 – 3 = +5

2 X 4 = 282X 3 = 06

7 7 3 6

++0

1

2 X 1 = 02

8 – 1 = +7

+7

Example 2 :

3 6 X 6

Example 3 :

3 6 X 6

3 6 X 67 44

Example 3 :

3 6 X 6

3 6 X 67 44

62 94 X 7 = 284X 4 = 16

Example 3 :

3 6 X 6

+2

-1

3 6 X 67 44

62 9

6 – 7 = -1

6 – 4 = +2

4 X 7 = 284X 4 = 16

+0

Example 3 :

3 6 X 6

+2

-1

3 6 X 67 44

62 9

6 – 7 = -1

6 – 4 = +2

4 X 7 = 284X 4 = 16

2 1 6

++0

Example 3 :

Example 4 :

9 6 1 X 7

9 6 1 X 74 391

Example 4 :

9 6 1 X 7

9 6 1 X 74 39

0 4 4 7 3 X 4 = 123X 9 = 27

1

3 X 1 = 03

Example 4 :

9 6 1 X 7

-2

+3

9 6 1 X 74 39

0 4 4 7

7 – 4 = +37 – 9 = -2

3 X 4 = 123X 9 = 27

+0

1

3 X 1 = 03

7 – 1 = +6

+6

Example 4 :

9 6 1 X 7

-2

+3

9 6 1 X 74 39

0 4 4 7

7 – 4 = +37 – 9 = -2

3 X 4 = 123X 9 = 27

+0

1

3 X 1 = 03

7 – 1 = +6

+6

6 7 2 7

Example 4 :

9 6 1 X 7

+

Example 5 :

9 3 1 X 6

9 3 1 X 67 491

Example 5 :

9 3 1 X 6

9 3 1 X 67 49

0 7 1 6 4 X 7 = 284X 9 = 36

1

4 X 1 = 04

Example 5 :

9 3 1 X 6

-3

-1

9 3 1 X 67 49

0 7 1 6

6 – 7 = -16 – 9 = -3

4 X 7 = 284X 9 = 36

+0

1

4 X 1 = 04

6 – 1 = +5

+5

Example 5 :

9 3 1 X 6

-3

-1

9 3 1 X 67 49

0 7 1 6

6 – 7 = -16 – 9 = -3

4 X 7 = 284X 9 = 36

5 5 8 6

+0

1

4 X 1 = 04

6 – 1 = +5

+5

Example 5 :

9 3 1 X 6

+

Example 6 :

4 3 2 X 5

4 3 2 X 57 586

Example 6 :

4 3 2 X 5

4 3 2 X 57 58

3 3 9 0 5 X 7 = 355X 8 = 40

6

5 X 6 = 30

Example 6 :

4 3 2 X 5

-3

-2

4 3 2 X 57 58

3 3 9 0

5 – 7 = -25 – 8 = -3

5 X 7 = 355X 8 = 40

+0

6

5 X 6 = 30

5 – 6 = -1

-1

Example 6 :

4 3 2 X 5

-3

-2

4 3 2 X 57 58

3 3 9 0

5 – 7 = -25 – 8 = -3

5 X 7 = 355X 8 = 40

2 1 6 0

+0

6

5 X 6 = 30

5 – 6 = -1

-1+

Example 6 :

4 3 2 X 5

I never say that this method is faster and safer but I strongly

think that this method enrich our field.

GOOD LUCK !

End Show