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Lesson6 |
Multiplying Close Numbers
Here we learn how to calculate close numbers multiplication like 96x92, 43x49 ,88x98
Multiply 88 by 98.
Both 88 and 98
are close to 100.
88 is 12 below 100 and 98 is 2
below 100.
As before
the 86 comes from
(or 98 - 12 = 86: you can
subtract
either way, you will
always get
the same answer).
And the 24 in the answer is
just 12 x 2: you multiply
vertically.
So 88 x 98 = 8624
93 x96 =??
9 3 + 7
9 6 + 4
89 28
our required answer is 8928 .Here our base is 100. Now we consider
some other base
Ex:- 53 / + 3
57 / + 7
60 / +21
Here base is shifted to 50 .so we multiply 60 by 50 and add 21 60x30
+21
× 50
Therefore, the answer is 3021.
3000 / +21
See one more example
54 / +4
48 / -2
52 / -8
x50
Here our base is 50
2600
/-8 2600-8 =2592
Therefore the answer is 2592
Again see one more example
48 /-2
45 /-5
43 /+10
x 50
Base is 50
2150 +10 = 2160
We can do this
example taking base 40
48 / +8
45/ + 5
53 / +40
x40
2120 +40 =2160 Why we take base 50 instead
of 40 ? Reason is simple calculation of 50 is easy compare to 40.
Let us consider
another example for practice.
Ex:- 82 / + 2 Shifted base = 80
76 / - 4
78 / (-8)
× 80
6240 / (-8) ie 6240
- 8
Answer is 6232
Advantages : -
(1) The computation time is reduced drastically.
(2) This method is particularly useful when the numbers under consideration
are close to base.
(3) Very useful in finding the squares.
Disadvantage : -
The disadvantage of this method is that the numbers under
consideration should be very close to each other. If there is a large duration
in the numbers from each other then it is very difficult to fix the base for
ex:- 32 × 78 etc.
Practice Test
96x 98 97 x 88 91X93 96 x 93 89x92
52 X49 73x82 45x48 69x72 78x79
45x42 72x75 48 x52 95x88 82x75