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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