Question

Evaluate the following products without actual multiplication.
$50\frac{1}{2}\times 49\frac{1}{2}$

Answer 1

$50\frac{1}{2}\times 49\frac{1}{2}$

=$(50+\frac{1}{2})(50-\frac{1}{2})$

We know suitable idenitities $(x+y)(x-y)=x^2-y^2$

$\therefore (50+\frac{1}{2})(50-\frac{1}{2})$

=$(50{)}^2-{\left(\frac{1}{2}\right)}^2$

=$2500-\frac{1}{4}$

=$\frac{10000-1}{4}=\frac{9999}{4}=2499\frac{3}{4}$