1. Xtra Math:
Methods,
Tips And Tricks
Series.
By
Puwork Utara
May 2012

2. Multiplying
2 Numbers
Starting With
Same Digit(s)

3. 1st Examination 16 X 13 = ___ if reference point is 10
Step 1 : Determine how much 16 from 10 and how much 13 from 10
-6 Means 16 is 6 more than 10
16 10
13 - 3 Means 13 is 3 more than 10
10
Step 2 :
Either ( 16 - (-3) ) X 10 = 19 X 10 = 190
Or (-6) =
( 13 - ) X 10 19 X 10 = 190
Step 3 : ( -6 ) X ( -3 ) = 18
Step 4 : 190 + 18 = 208
#
We just solved this using reference point method of the base 10

4. 2nd Examination 16 X 13 = ___ if reference point is 20
Step 1 : Determine how much 16 from 20 and how much 13 from 20
+4 Means 16 is 4 less than 20
16 20
13 +7 Means 13 is 7 less than 20
20
Step 2 :
Either ( 16 - ( + 7) ) X 20 = 9 X 20 = 180
Or ( + 4) =
( 13 - ) X 20 9 X 20 = 190
Step 3 : (+4) X ( + 7 ) = 28
Step 4 : 180 + 28 = 208
#
We just solved this using reference point method of the base 20

5. 3rd Examination 16 X 13 = ___ if reference point is 30
Step 1 : Determine how much 16 from 30 and how much 13 from 30
+ 14 Means 16 is 14 less than 30
16 30
13 + 17 Means 13 is 17 less than 30
30
Step 2 :
Either ( 16 - ) X 30
( + 17) = -1 X 30 = - 30
Or
( 13 - ( + 14) ) X 30 = -1 X 30 = - 30
Step 3 : ( + 14 ) X ( +1 7 ) = 28
Step 4 : - 30 + 238 = 208
#
We just solved this using reference point method of the base 30

6. 9th Examination 16 X 13 = ___ if reference point is 90
Step 1 : Determine how much 16 from 90 and how much 13 from 90
+ 74 Means 16 is 74 less than 90
16 90
13 + 77 Means 13 is 77 less than 90
90
Step 2 :
Either ( 16 - ) X 90
( + 77) = - 61 X 90 = - 5490
Or
( 13 - ( + 74) ) X 90 = - 61 X 90 = - 5490
Step 3 : ( + 74 ) X ( +77 ) = 5698
Step 4 : - 5490 + 5698 = 208
#
The higher the base number the more difficult to solve the
problem, but we still get the same result.

7. So, here are the recommendation of reference point
11 to 19 use 10 as the Base Number
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
91 to 99 use either 90 or 100 as the Base Number
101 – 109 use 100 as the Base Number

8. Now!
Adjust your chair to
see the rest of this
slideshow….

9. ( Let’s us use 20 as the Base Number )
23 X 21 = _____
-3
23 20 ( 23 is 3 more than 20 )
-1
21 20 ( 21 is 1 more than 20 )
Either ( 23 - ( - 1 )) X 20 = 24 X 20 = 480
Or ( 21 - ( - 3 )) X 20 = 24 X 20 = 480
And (-3 ) X (-1) = 3
Last 480 + 3 = 483
#
Either [ (23+1)*20 ] + (-3)(-1) = 483 or [ (21+3)*20 ] + (-3)(-1) = 483

10. ( Let’s us use 30 as the Base Number )
34 X 32 = _____
-4
34 30 ( 34 is 4 more than 30 )
-2
32 30 ( 32 is 2 more than 30 )
Either ( 34 - ( - 2 )) X 30 = 36 X 30 = 1080
Or ( 32 - ( - 4 )) X 30 = 36 X 30 = 1080
And (-4 ) X (-2) = 8
Last 1080 + 8 = 1088
#
Either [ (34+2)*30 ] + (-4)(-2) = 1080 or [ (32+4)*30 ] + (-4)(-2) = 1080

11. ( Let’s us use 40 as the Base Number )
43 X 45 = _____
-3
43 30 ( 43 is 3 more than 40 )
-5
45 30 ( 45 is 5 more than 40 )
Either ( 43 - ( - 5 )) X 40 = 48 X 40 = 1920
Or ( 45 - ( - 3 )) X 40 = 48 X 40 = 1920
And (- 3 ) X ( -5 ) = 15
Last 1920 + 15 = 1935
#
Either [ (43+5)*40 ] + (-3)(-5) = 1935 or [ (45+3)*40 ] + (-3)(-5) = 1935

12. ( Let’s us use 50 as the Base Number )
53 X 55 = _____
-3
53 50 ( 53 is 3 more than 50 )
-5
55 50 ( 55 is 5 more than 50 )
Either ( 53 - ( - 5 )) X 50 = 58 X 50 = 2900
Or ( 55 - ( - 3 )) X 50 = 58 X 50 = 2900
And (- 3 ) X ( -5 ) = 15
Last 2900 + 15 = 2915
#
Either [ (53+5)*50 ] + (-3)(-5) = 2915 or [ (55+3)*50 ] + (-3)(-5) = 2915

13. ( Let’s us use 60 as the Base Number )
62 X 67 = _____
-2
62 60 ( 62 is 2 more than 60 )
-7
67 60 ( 67 is 7 more than 60 )
Either ( 62 - ( - 7 )) X 60 = 69 X 60 = 4140
Or ( 67 - ( - 2 )) X 60 = 69 X 60 = 4140
And (- 2 ) X ( - 7 ) = 14
Last 4140 + 14 = 4154
#
Either [ (62+7)*60 ] + (-2)(-7) = 4154 or [ (67+2)*60 ] + (-2)(-7) = 4154

14. ( Let’s us use 70 as the Base Number )
73 X 76 = _____
-3
73 70 ( 73 is 3 more than 70 )
-6
76 70 ( 76 is 6 more than 70 )
Either ( 73 - ( - 6 )) X 70 = 79 X 70 = 5530
Or ( 76 - ( - 3 )) X 70 = 79 X 70 = 5530
And (- 3 ) X ( - 6 ) = 18
Last 5530 + 18 = 5548
#
Either [ (73+6)*70 ] + (-3)(-6) = 5548 or [ (76 + 3)*70 ] + (-3)(-6) = 5548

15. ( Let’s us use 80 as the Base Number )
83 X 84 = _____
-3
83 80 ( 83 is 3 more than 80 )
-4
84 80 ( 84 is 4 more than 80 )
Either ( 83 - ( - 4 )) X 80 = 87 X 80 = 6960
Or ( 84 - ( - 3 )) X 80 = 87 X 80 = 6960
And (- 3 ) X ( - 4 ) = 12
Last 6960 + 12 = 6972
#
Either [ (98+5)*90 ] + (-8)(-5) = 9310 or [ (95+8)*90 ] + (-8)(-5) = 9310

16. ( Let’s us use 90 as the Base Number )
98 X 95 = _____
-8
98 90 ( 98 is 8 more than 90 )
-5
95 90 ( 95 is 5 more than 90 )
Either ( 98 - ( - 5 )) X 90 = 103 X 90 = 9270
Or ( 95 - ( - 8 )) X 90 = 103 X 90 = 9270
And (- 8 ) X ( - 5 ) = 40
Last 9270 + 12 = 9310
#
Either [ (98+5)*90 ] + (-8)(-5) = 9310 or [ (95+8)*90 ] + (-8)(-5) = 9310

17. ( Let’s us use 100 as the Base Number )
98 X 95 = _____
+2
98 100 ( 98 is 2 less than 100 )
+5
95 100 ( 95 is 5 less than 100 )
Either ( 98 - ( + 5 ) X 100 = 93 X 100 = 9300
Or ( 95 - ( + 2 ) X 100 = 93 X 100 = 9300
And (- 2 ) X ( - 5 ) = 10
Last 9300 + 10 = 9310
#
Either [ (98-5)*100 ] + (-5)(-2) = 9310 or [ (95-2)*100 ] + (-5)(-3) = 9310

18. ( Let’s us use 100 as the Base Number )
103 X 105 = _____
-3
103 100 ( 103 is 3 more than 100 )
-5
105 100 ( 105 is 5 more than 100 )
Either ( 103 - ( - 5 )) X 100 = 108 X 100 = 10800
Or ( 105 - ( - 3 )) X 100 = 108 X 100 = 10800
And (- 3 ) X ( - 5 ) = 15
Last 10800 + 15 = 10815
#
Either [ (103+5)*100 ] + (-5)(-3) = 10815 or [ (105+3)*100 ] + (-5)(-3) = 10815

19. How to deal with
234 x 232 = ____

20. 234 x 232 = __________
The reference point is 230
-4
234 230 ( 234 is 4 more than 230 )
-2
232 230 ( 105 is 5 more than 230 )
Either ( 234 - ( - 2 )) X 230 = 236 X 230 = 54280
Or ( 232 - ( - 4 )) X 230 = 236 X 230 = 54280
And (- 4 ) X ( - 2 ) = 08
Last 54280 + 08 = 54288
#
The method and concept is same but it’s very tough for the beginners.

21. End Show
GOOD LUCK !