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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