Question

Multiply the following numbers by formula Nikhilam:
(i) $98\times 99$
(ii) $51\times 52$

Answer 1

(i)

$1$. Both numbers are of base $100$.

$2$. $98$ is $2$ less than $100$ and $99$ is $1$ less than $100$.

$3$. $\left(-2\right)\times \left(-1\right)=2$ (since base is 100 we take $02$).

$4$. $98-1$ OR $99-2=97$

$5$. FINAL ANSWER=9702.

(ii)

$1$. Both numbers are of base $100$.

$2$. $51$ is $49$ less than $100$ and $52$ is $48$ less than $100$.

$3$. $\left(-49\right)\times \left(-48\right)=2352$ (since base is $100$ we take $52$ and $23$ to the following).

$4$. $51-48$ OR $52-48=3$ (we add $23$ to $3$ we get $26$)

$5$. FINAL ANSWER=$2652$.