It’s normal to feel daunted by long multiplication, especially when working with large numbers. However, lengthy multiplication is easily mastered if approached methodically. Follow the instructions in Step 1 below to get ready to crush your upcoming arithmetic tests.
Performing the Usual Extended Multiplication
1. Put the larger number above the smaller one.
Suppose you need products 756 and 32. Write 756 on top of 32, aligning the ones and tens columns so that the 6 in 756 sits directly above the 2 in 32, the 5 in 756 sits directly above the 3 in 32, and so on.
This can help you picture the lengthy multiplication procedure more clearly.
- Multiply the 2 in 32 by every 756 digits, then multiply the 3 in 32 by every 756. Yet, let’s not jump the gun.
- The larger number is the one with more significant digits (numbers).
2. To do this, multiply the digits in one place of the bottom and top numbers, respectively.
To get a total, multiply the 6 in 756 by the 2 from 32.
If you multiply 6 by 2, you get 12. Put 2 under “units” and “carry 1 over 5” to represent a decimal.
Numbers in the one’s place are recorded, and tens place numbers are carried to the left of the product they multiplied.
Specifically, a 2 will be seen underneath the 6 and the 2.
3. If you want to multiply the bottom number by the top number in tens, multiply the one’s digits.
Multiplying 2 by 5 yields 10.
When you get to 11, add the one you brought down from the space above the five to the ten already there, and then add another to the space adjacent to the two at the bottom.
4. The extra 1 in the tens place must be added to the 7 already there.
Using the hundreds place, multiply the digits in the bottom number by the tens in the top.
To get 14, add together 2 and 7. Then, add the extra 1 to 14 to make 15. Since there are no more digits to multiply on this column, you can safely ignore the “carry the tens over” instruction. Put 15 on the bottom line.
5. Below the first product, in one column, draw a zero.
Now that you know you need to multiply the number in the tens place, 32, by each digit in 756 before you can proceed, draw a zero below the 2 in 1512 so that you are already in the tens place. To continue, you’d have to write two zeroes if you wanted to multiply a number in the hundreds place by the top number, and so on.
6. Add the digits in the tens position of the bottom number to the digits in the one’s position of the first number.
Now, 18 is the result of multiplying 3. Put the 8 on the line once more, and this time bring the 1 over the 5.
7. You may get the product by multiplying the tens digits of the two numbers together.
Add up 3 and 5 and see what you get. This brings the total to 15, but you need to add the carrying 1 to make it 16. The 6 should be written on the line, and the 1 should be carried over the 7.
8. Add the tens digit of the bottom number to the hundreds digit of the top number.
The result of multiplying 3 by 7 is 21. Therefore, multiplying by 7 yields 21. Now you have a total of 22 after adding in the extra 1. As there are no more multiplicands on this line, the 2 in 22 can be written next to the 6 without being carried.
9. The products’ leading digits are added.
You need only add together the numbers 1512 and 22680 now. Let’s begin with the obvious: 2 + 0 = 2. In the column labeled “ones,” record the answer.
10. Compute the sum of the tens place values of both numbers.
It’s easy to see that 9 may be calculated by adding 1 to 8. To the left of the number 2, write a 9.
11. The last hundred digits of each product are added together.
If you add the digits of your phone number, you get 11. Enter 1 in the one’s place and 1 in the tens place over 1 to the left of the first product.
12. Thousands-place digit addition of both numbers.
Add the 1 you carried over to the sum of 1 and 2 and get 4. Put it in writing.
13. Multiply each integer by 10 thousand.
The tens-of-thousands spot is empty in the first number, whereas, in the second, it contains the number 2.
In this case, please record the calculation of 2 as the sum of 0 and 2. This brings you to the correct answer of 24,192.
14. Use a calculator to double-check your calculation.
You can enter the problem into a calculator to check your answers and ensure you haven’t made any mistakes. Multiplying 756 by 32 should give you 24,192.
Now you can stop!