Sunday, March 29, 2009

SIM - MULTIPLICATION - 4

In this post, we will learn to multiply two numbers whose ending digit is 5 and the sum of the other digits of both numbers is an odd number. For example,
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1) 25 * 75 (Both the numbers end in 5 and the sum of the other digits of the numbers is an odd number, that is, (2 + 7) = 9)
2) 45 * 95 (Ends in 5 & (4 + 9) = 13)
3) 85 * 115 (Ends in 5 & (8 + 11) = 19)
4) 135 * 165 (Ends in 5 & (13 + 16) = 29)
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Let us consider the first example and see the steps for the actual multiplication.
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1) 25 * 75
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a) The answer has two parts LHS and RHS.
b) The answer looks like LHS/RHS.
c) The value of RHS is always 75. That is, RHS = 75.
d) To arrive at the value of the LHS, first we need to multiply the other digits of the numbers besides the ending digit 5. That is, in this case, it is 2 * 7 = 14.
e) Next, we have to halve the sum of those two numbers and take the integer part of the answer. That is, (2+7)/2 = 9/2 = 4.5 = 4.
f) Add the numbers obtained in step (d) & (e). That is, 14 + 4 = 18.
g) The final answer is LHS/RHS = 18/75 = 1875.
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Solved Examples
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2) 45 * 95
= ((4*9)+((4+9)/2))/75
= (36+(13/2))/75
= (36+6)/75
= 42/75
= 4275
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3) 85 * 115
= ((8*11)+((8+11)/2))/75
= (88+(19/2))/75
= (88+9)/75
= 97/75
= 9775
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4) 135 * 165
= ((13*16)+((13+16)/2))/75
= (208+(29/2))/75
= (208+14)/75
= 222/75
= 22275

1 comment:

  1. Nice method...Really useful..Looking forward to more methods..
    Thanks

    Aravindan

    ReplyDelete

 
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