MULTIPLICATION WITH 99999
With less than 5 seconds
In the whole number series 9 is a most interesting number ,and so multiplication by 9 is also very interesting in it self .
If a number is to be multiplied by another number consisting of only 9's or a series of 9's the answer can be arrived in very easy and amazing way.
The formulae used for these calculation are :
1.By one less than the one before
2.All from nine and last from ten
When two number are multiplied any one of them is the multiplicand and the other is the multiplier .
Ex. 23× 99, here we consider 23 is a multiplicand and the other number ,i.e 99 as multiplier.
In this topic ,whenever we are talking about a number having 9's we will consider that number as a multiplier.
We have categorized the multiplication by 9's in three types according to the number of 9's present in the multiplier.
TYPE 1 : MULTIPLICANT DIGIT = MULTIPLIER DIGIT
When the number of digit in the multiplicand ( number to be multiplied ), are equal to the numbers of 9's in the multiplier.
The answer compose in two parts ; LHS & RHS
For LHS, we apply the Formulae
: by one less than the one before ,
i.e. subtract one from the multiplicand.
Fo r RHS,we write the compliment of the multiplicand, by using the
formulae. :”all from nine and last from ten”
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Example 1. 46 × 99
46 is a two digit number and 99 has also a two 9's in it.
for LHS. subtract 1 from 46 i.s. 46-1=45
for RHS. write the compliment of 46 i.e. 54
so answer is 4554
46 × 99 = 4554
389 is a three digit number and 999 has also a three 9's in it.
for LHS. subtract 1 from 389 i.s. 389-1=388
for RHS. write the compliment of 389 i.e. 611
so answer is 388611
389 × 999 = 388611.
Example 3. 942678 × 999999
942678 is a six digit number and 999999 has also a six 9's in it.
for LHS. subtract 1 from 942678 i.s. 942678-1=942677
for RHS. write the compliment of 942678 i.e. 057322
so answer is 942677057322
942678 × 999999 = 942677057322
Isn't it amazing to find the answer of such a big calculation a simple subtraction.
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