To multiply large numbers, stack the first number on top of the second. Then multiply each digit of the bottom number, from right to left, by the top number. In other words, first multiply the top number by the ones digit of the bottom number. Then write down a 0 as a placeholder and multiply the top number by the tens digit of the bottom number.

Continue the process, adding placeholders and multiplying the top number by the next digit in the bottom number.

When the result is a two-digit number, write down the ones digit and carry the tens digit to the next column. After multiplying the next two digits, add the number you carried over.

Add the products to obtain the final answer.

## Sample question

1. Multiply 742 x 136.

100,912. Stack the first number on top of the second, by aligning the ones places:

Now multiply 6 by every number in 742, starting from the right. Because 2 x 6 = 12, a two-digit number, you write down the 2 and carry the 1 to the tens column. In the next column, you multiply 4 x 6 = 24, and add the 1 you carried over, giving you a total of 25.

Write down the 5, and carry the 2 to the hundreds column. Multiply 7 x 6 = 42, and add the 2 you carried over, giving you 44:

Next, write down a 0 in the ones place in the next row. Multiply 3 by every number in 742, starting from the right and carrying when necessary:

Write down two 0s as placeholders for the ones and tens place in the next row. Repeat the process with 1:

To finish, add up the products:

So 742 x 136 = 100,912.

## Practice questions

1. Multiply 75 x 42.

2. What’s 136 x 84?

3. Solve 1,728 x 405.

4. Multiply 8,912 x 767.

Following are the answers to the practice questions:

1. 3,150

2. 11,424

3. 699,840

4. 6,835,504