Question

While mulitplying $256\times 196$ by box method, find the missing numbers in the below box.

• A. A $=1,200$; B $=540$ and C $=36$
• B. A $=1,200$; B $=4,500$ and C $=300$
• C. A $=1,200$; B $=4,500$ and C $=36$
• D. None of the above

Answer 1

The correct option is C A $=1,200$; B $=4,500$ and C $=36$

To multiply two numbers using the box method, we must first express them in expanded form.

$\therefore$ Numbers in expanded form are:
$256=200+50+6$ and
$196=100+90+6$

Now, $256\times 196=(200+50+6)\times (100+90+6)$
Since, both the numbers are of three digits, we need $3\times 3$ box as depicted in figure below,


now, multiplying numbers on left of box by numbers on top of box one by one as shown in below figure,


Therefore, comparing this box with the given box,
A $=1,200$; B $=4,500$ and C $=36$.

$\therefore$ (c) is the correct option.