Xtra Math:

Methods, Tips And Tricks Series.

By Puwork UtaraMay 2012

Multiplying 2 Numbers

Starting With Same Digit(s)

16

13

10

10

- 6

- 3

1st Examination

Means 13 is 3 more than 10

Means 16 is 6 more than 10

16 - ( - 3 )( ) 10X = 19 X 10 = 190

13 - ( - 6 )( ) 10X = 19 X 10 = 190

( -6 ) ( -3 )X = 18

+ =18190 208#

Step 1 : Determine how much 16 from 10 and how much 13 from 10

Step 2 :

Or

Either

Step 3 :

Step 4 :

We just solved this using reference point method of the base 10

16 X 13 = ___ if reference point is 10

16

13

20

20

+ 4

+ 7 Means 13 is 7 less than 20

Means 16 is 4 less than 20

16 - ( + 7)( ) 20X = 9 X 20 = 180

13 - ( + 4)( ) 20X = 9 X 20 = 190

( + 4 ) ( + 7 )X = 28

+ =28180 208#

Step 1 : Determine how much 16 from 20 and how much 13 from 20

Step 2 :

Or

Either

Step 3 :

Step 4 :

2nd Examination

We just solved this using reference point method of the base 20

16 X 13 = ___ if reference point is 20

16

13

30

30

+ 14

+ 17 Means 13 is 17 less than 30

Means 16 is 14 less than 30

16 - ( + 17)( ) 30X = -1 X 30 = - 30

13 - ( + 14)( ) 30X = -1 X 30 = - 30

( + 14 ) ( +1 7 )X = 28

+ =238- 30 208#

Step 1 : Determine how much 16 from 30 and how much 13 from 30

Step 2 :

Or

Either

Step 3 :

Step 4 :

We just solved this using reference point method of the base 30

3rd Examination16 X 13 = ___ if reference point is 30

16

13

90

90

+ 74

+ 77 Means 13 is 77 less than 90

Means 16 is 74 less than 90

16 - ( + 77)( ) 90X = - 61 X 90 = - 5490

13 - ( + 74)( ) 90X = - 61 X 90 = - 5490

( + 74 ) ( +77 )X = 5698

+ =5698- 5490 208#

Step 1 : Determine how much 16 from 90 and how much 13 from 90

Step 2 :

Or

Either

Step 3 :

Step 4 :

The higher the base number the more difficult to solve the

problem, but we still get the same result.

9th Examination16 X 13 = ___ if reference point is 90

11 to 19 use 10 as the Base Number

So, here are the recommendation of reference point

21 to 29 use 20 as the Base Number

31 to 39 use 30 as the Base Number

41 to 49 use 40 as the Base Number

51 to 59 use 50 as the Base Number

61 to 69 use 60 as the Base Number

71 to 79 use 70 as the Base Number

81 to 89 use 80 as the Base Number

101 – 109 use 100 as the Base Number

91 to 99 use either 90 or 100 as the Base Number

Now!

Adjust your chair to

see the rest of this

slideshow….

23 X 21 = _____

23

21

20

20

- 3

- 1( 21 is 1 more than 20 )

( 23 is 3 more than 20 )

23 - ( - 1 )( ) 20X = 24 X 20 = 480Either

21 - ( - 3 )( ) 20X = 24 X 20 = 480Or

(-3 ) (-1)X = 3And

+ =3Last 480 483#

( Let’s us use 20 as the Base Number )

Either [ (23+1)*20 ] + (-3)(-1) = 483 or [ (21+3)*20 ] + (-3)(-1) = 483

34 X 32 = _____

34

32

30

30

- 4

- 2( 32 is 2 more than 30 )

( 34 is 4 more than 30 )

34 - ( - 2 )( ) 30X = 36 X 30 = 1080Either

32 - ( - 4 )( ) 30X = 36 X 30 = 1080Or

(-4 ) (-2)X = 8And

+ =8Last 1080 1088#

( Let’s us use 30 as the Base Number )

Either [ (34+2)*30 ] + (-4)(-2) = 1080 or [ (32+4)*30 ] + (-4)(-2) = 1080

43 X 45 = _____

43

45

30

30

- 3

- 5( 45 is 5 more than 40 )

( 43 is 3 more than 40 )

43 - ( - 5 )( ) 40X = 48 X 40 = 1920Either

45 - ( - 3 )( ) 40X = 48 X 40 = 1920Or

(- 3 ) ( -5 )X = 15And

+ =15Last 1920 1935#

( Let’s us use 40 as the Base Number )

Either [ (43+5)*40 ] + (-3)(-5) = 1935 or [ (45+3)*40 ] + (-3)(-5) = 1935

53 X 55 = _____

53

55

50

50

- 3

- 5( 55 is 5 more than 50 )

( 53 is 3 more than 50 )

53 - ( - 5 )( ) 50X = 58 X 50 = 2900Either

55 - ( - 3 )( ) 50X = 58 X 50 = 2900Or

(- 3 ) ( -5 )X = 15And

+ =15Last 2900 2915#

( Let’s us use 50 as the Base Number )

Either [ (53+5)*50 ] + (-3)(-5) = 2915 or [ (55+3)*50 ] + (-3)(-5) = 2915

62 X 67 = _____

62

67

60

60

- 2

- 7( 67 is 7 more than 60 )

( 62 is 2 more than 60 )

62 - ( - 7 )( ) 60X = 69 X 60 = 4140Either

67 - ( - 2 )( ) 60X = 69 X 60 = 4140Or

(- 2 ) ( - 7 )X = 14And

+ =14Last 4140 4154#

( Let’s us use 60 as the Base Number )

Either [ (62+7)*60 ] + (-2)(-7) = 4154 or [ (67+2)*60 ] + (-2)(-7) = 4154

73 X 76 = _____

73

76

70

70

- 3

- 6( 76 is 6 more than 70 )

( 73 is 3 more than 70 )

73 - ( - 6 )( ) 70X = 79 X 70 = 5530Either

76 - ( - 3 )( ) 70X = 79 X 70 = 5530Or

(- 3 ) ( - 6 )X = 18And

+ =18Last 5530 5548#

( Let’s us use 70 as the Base Number )

Either [ (73+6)*70 ] + (-3)(-6) = 5548 or [ (76 + 3)*70 ] + (-3)(-6) = 5548

83 X 84 = _____

83

84

80

80

- 3

- 4( 84 is 4 more than 80 )

( 83 is 3 more than 80 )

83 - ( - 4 )( ) 80X = 87 X 80 = 6960Either

84 - ( - 3 )( ) 80X = 87 X 80 = 6960Or

(- 3 ) ( - 4 )X = 12And

+ =12Last 6960 6972#

( Let’s us use 80 as the Base Number )

Either [ (98+5)*90 ] + (-8)(-5) = 9310 or [ (95+8)*90 ] + (-8)(-5) = 9310

98 X 95 = _____

98

95

90

90

- 8

- 5( 95 is 5 more than 90 )

( 98 is 8 more than 90 )

98 - ( - 5 )( ) 90X = 103 X 90 = 9270Either

95 - ( - 8 )( ) 90X = 103 X 90 = 9270Or

(- 8 ) ( - 5 )X = 40And

+ =12Last 9270 9310#

( Let’s us use 90 as the Base Number )

Either [ (98+5)*90 ] + (-8)(-5) = 9310 or [ (95+8)*90 ] + (-8)(-5) = 9310

98 X 95 = _____

98

95

100

100

+ 2

+ 5( 95 is 5 less than 100 )

( 98 is 2 less than 100 )

98 - ( + 5 )( ) 100X = 93 X 100 = 9300Either

95 - ( + 2 )( ) 100X = 93 X 100 = 9300Or

(- 2 ) ( - 5 )X = 10And

+ =10Last 9300 9310#

( Let’s us use 100 as the Base Number )

Either [ (98-5)*100 ] + (-5)(-2) = 9310 or [ (95-2)*100 ] + (-5)(-3) = 9310

103 X 105 = _____

103

105

100

100

- 3

- 5( 105 is 5 more than 100 )

( 103 is 3 more than 100 )

103 - ( - 5 )( ) 100X = 108 X 100 = 10800Either

105 - ( - 3 )( ) 100X = 108 X 100 = 10800Or

(- 3 ) ( - 5 )X = 15And

+ =15Last 10800 10815#

( Let’s us use 100 as the Base Number )

Either [ (103+5)*100 ] + (-5)(-3) = 10815 or [ (105+3)*100 ] + (-5)(-3) = 10815

How to deal with

234 x 232 = ____

The reference point is 230

234

232

230

230

- 4

- 2( 105 is 5 more than 230 )

( 234 is 4 more than 230 )

234 - ( - 2 )( ) 230X = 236 X 230 = 54280Either

232 - ( - 4 )( ) 230X = 236 X 230 = 54280Or

(- 4 ) ( - 2 )X = 08And

+ =08Last 54280 54288#

234 x 232 = __________

The method and concept is same but it’s very tough for the beginners.

GOOD LUCK !

End Show