Question

What is the number that equals $512\times 4$?
(Apply lattice method of multiplication)

• A. $2,048$
• B. $2,084$
• C. $2,148$
• D. $7,168$

Answer 1

The correct option is A $2,048$

To find: $512\times 4$

Applying lattice method of multiplication:

Since the numbers of multiplication are of $3$ digits and $1$, so take a rectangle of 3 by 1

Step 1:
Place the face value of each digits of 512 on top and 4 on the right of the rectangle as in the figure below,

Step 2:
Now, three diagonals of each smaller rectangles is drawn as shown in figure below,


Step 3:
Now, multiply the numbers on top with the number on right of the rectangle one by one and place the digits of products on both sides of the diagonals of respective rectangles.

Multiply $2$ on top and $4$ on right of rectangle, $2\times 4=8$, here we get $8$ as the product and write it as $08$, now place $0$ on above the diagonal and $8$ below the diagonal as shown in below figure,


similarly we will put digits of other products as depicted in below figure,
Step 4:
Now adding the digits along the diagonals as shown in below figure,

Step 5:
Finally, add the digits on the left and the bottom in order to get the product of $53\times 4$ i.e $53\times 4=2,048$

Therefore, (a) is the correct option.