Multiplying any number by 25, 125, 625.

Multiplying any number by

25, 125 and 625.

Multiply by 25

a) 62 x 25

Just put two zeros on 62 to get 6200 and divide it by 4

as 6200 / 4    =  1550

Hence 62 x 25 = 1550

b) 98 x 25

Just put two zeros on 98 to get 9800 and then divide it by 4

as 9800 / 4   =  2450

Multiply by 125

a) 62 x 125

Just put three zeros on 62 to get 62000 then divide it by 8

as 62 x 125   =  62000 / 8   =  7750

b) 98 x 125

Just put three zeros on 98 then divide it by 8

as 98 x 125  =  98000 / 8    =   12250

Multiply by 625.

a) 62 x 625

Just put four zeros on 62 to get 620000 then divide it by 8.

As  62 x 625  = 620000 / 16  = 38750

Special Cases of Multiplication II

Multiplication by 11

a) Multiplication by 11 of any two digit number, whose sum of the digits is less than 10

i) 63 x 11 = 693

In such multiplication we do not carry out any multiplication but simly put the sum of the digits of multiplicand between it digits.

Hence, the unit’s place digit is 3  and ten’s place digit is 6  we put 9 ( 6 + 3 ) in between 6 and 3 to get 693

ii) 72 x 11 = 7 (ten’s place digit) 9 ( 7 + 2 ) 2 (ten’s place digit) = 792

b) Multiplication by 11 of any two

digit number, total of whose digits is

more than 10.

If the sum of the digits of multiplicand is more than 10 then put unit’s place digit of multiplicand as unit’s place digit of product and add the ten’s place dgit to the multiplicand and put this sum to the left of unit’s place digit of the multiplicand to get the final product.

i) 89 x 11 =

The sum of 8 and 9 is 17 so write 7 next to unit’s place digit i.e 9. latter carry on 1 and add it to the ten’s place digit i.e 8 + 1 = 9, put it next to 7.

89 x 11 = 979

ii) 78 x 11 = (7 + 1) 1 is carried on after adding 7 + 8 = 15 / 5 ( 7 + 8 = 15) / 9 ( units place digit.

Special Cases of Multiplication.

Multiplication of any even number

with 51

a) Multiplication of any even number with 51

i) 48 x 51 = 24   48    = 2448

In this technique the multiplicand is put on right hand side to form right hand position of the product and lift to it is placed half of the multiplicand.

In the above case the multiplicand is 48 so it is placed to the right hand side and its half is 48/2 = 24 so it is placed at the left hand side to get,

2448

ii) 32 x 51 = = 16    32    = 1632

Here the multiplicand is 32, so it is placed to the right hand side and half of 32 is 32/2 = 16, so 16 is placed to the left and side to get 1632 as the product.

iii) 124 x 51 = 6324

In this the technique is bit changed. Since the multiplicand is three digit number we just take a number formed by unit place digit and tens place digit. and the hundreds place digit we carry on.

In the above case the multiplicand is 124, so we write 24 to the right hand side and carry 1. Then we take half of 124 i.e. 62 and add carried number to it i.e. 1 to get 63 this number we place to the left hand side.

In the above case   124 x 51 = 63 (half of 124 + carried 1 from 124) 24 ( from 124)  = 6324

b) Multiplication of any Odd number

with 51

i) Whe we multiply any odd number with 51 then the multiplicand forms the unit’s and ten’s place digits of the product. Half of the multiplicand consists of a whole number and 0.5 e.g. 19/2 = 9.5. the whole number part of the left hand side and the part 0.5 is taken as 50 and added to 19 ( 19 + 50 ) to get 69. This becomes the right hand side.

so  19 x 51  = 9 ( 19/2 = 9.5) 69 ( 19 + 50) =  969

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