How to Perform Long Multiplication

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Long multiplication is a fundamental mathematical operation used to solve complex multiplication problems involving multiple-digit numbers. This technique is essential to master, as it enables us to accurately and efficiently find the product of numbers that cannot be easily calculated mentally or using a calculator. By following a specific step-by-step process, long multiplication allows us to break down an extensive multiplication problem into smaller, more manageable parts, ultimately arriving at the correct result. In this article, we will explore the detailed procedure of how to perform long multiplication successfully, providing clear instructions along the way. Whether you are a student looking to improve your math skills or an individual seeking to refresh your understanding of long multiplication, this guide will equip you with the necessary knowledge to conquer even the most complex multiplication challenges with ease.

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Long multiplication can seem intimidating, especially when multiplying rather large numbers. However, if you follow the steps step by step, you should be able to do the long multiplication in no time at all. Get ready to master the math by starting with Step 1 below.

Table of Contents

Steps

Perform Standard Long Multiplication

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Write the big number above the small number. Let’s say you’re going to multiply 756 by 32. Write 756 above 32, so that the units and tens row of numbers line up, the 6 of 756 is above the 2 of 32 and con. The 5 of 756 is above the 3 of 32, and so on. This will make it easier to see during long multiplications.

• It’s essential to start by multiplying 2 in 32 for each number of 756, then multiply by 3 in 32 for each number of 756. But don’t go too fast.

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Multiply the units number of the bottom number by the units number of the top number. Multiply 2 in 32 by 6 in 756. The product of 6 and 2 is 12. Write the number of units of 2 as 2 in the product, and write 1 on top of 5. Basically, you would write down any digit. in the units, and if there is a tens digit, write it to the top left of the number above you just multiplied. You’ve got the number 2 written directly under the number 6 and number 2.

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Multiply the units number of the lower number by the tens digit of the top number. Now multiply 2 by 5 and you get 10. Add the 1 you remembered above 5 to 11, then write 1 next to the 2 in the bottom row. Remember to add 1 to the tens above the number 7.

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Multiply the units number of the bottom number by the hundreds of the top number. Multiply 2 by 7 to get 14. Add the remembered 1 to 14 to 15. No need to remember this time, because you have no more numbers to multiply in the row. Just write 15 in the last row.

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Write 0 in the units row column below the first result. Now you’ll be multiplying the tens digit of 32, which is 3, by every digit of 756, so add a 0 below the 2 in 1512 before you start so you can multiply straight by tens. If you continue to multiply the hundreds digit by the number above, you need to add two zeros, and so on.

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Multiply the tens digit of the bottom number by the units digit of the top number. Multiply 3 by 6 to get 18. Again write 8 in the result and remember 1 above the 5.

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Multiply the tens digit of the number below by the tens digit of the number above. Multiply 3 by 5 to get 15, but you have to add 1 to remember, so the result is 16. Write 6 in the answer, and remember 1 on top of 7.

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Multiply the tens digit of the bottom number by the hundreds digit of the top number. Multiply 3 by 7 and you get 21. Add 1 and you get 22. You don’t have to remember 2 in 22, because there’s no more to multiply, so just write it down next to 6.

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Add together the units digits of the results. Now, simply add 1512 to 22680. First, add 2 plus 0 to get 2. Write the result in the units column.

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Add the tens digit of the results together. Add 1 to 8 to get 9. Write 9 to the left of 2.

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Add the hundreds digits of the results together. The sum of 5 and 6 is 11. Write 1 in the result and remember one to the left of the upper result.

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Add the thousands digits of the results together. Work 1 with 2 gets 3 and then add 1 memorized to get 4. Write it in the result.

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Add the tens of thousands digits of the results together. The first result is nothing in the tens of thousands, and the second is 2. So 0 plus 2 equals 2, write it in the result. We got 24,192 and that’s your final result.

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Check the results by computer. If you want to double check your results, enter the problem into the calculator to see if you got it right. The result should be 756 times 32 equals 24,192. And that’s it!

Turn off

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Write calculations. For example, you are multiplying 325 by 12. Write down the calculation. One number is next to the other, not below.

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Divide small numbers into tens and units. Leave 325 as it is and divide 12 into 10 and 2. The 1 is in the tens place so you have to add a 0 behind it to keep it in place, and since 2 is in the units order, you just need to write 2 out.

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Multiply the large number by the number in the tens. Now multiply 325 by 10. All you have to do is add 0 to the end of that number, you get 3250.

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Multiply the large number by the number in the units row. Now just multiply 325 by 2. Just look at it with your eyes and you get 650, because 300 times 2 equals 600 and 25 times 2 equals 50. 600 plus 50 gives 650.

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Add the two results. Now we just need to add 3250 to 650. You can do it using the old-fashioned addition method. Write 3250 on top of 650 and do all the rest, you get 3900. Actually this is similar to doing standard long multiplication, but breaking a number into tens and single rows. It allows you to do a little bit of math in your head to avoid having to multiply and remember too much. Either way will produce the same results, depending on which way you do it faster.

Advice

• Practice with numbers small and easy numbers first.
• Make sure you have written the numbers in the correct columns.
• Don’t forget to watch out for the tens, or things will get messy.
• Always add zeros at the end of tens, at hundreds add TWO zeros and so on. Check your work and then check it with a calculator – but don’t cheat.
• For numbers with more than two digits, follow these steps: first multiply the number above by the units row, then add 0 after it and multiply by the tens, add two zeros and then multiply by the row hundred, then add three zeros and multiply by thousands, and so on. Finally, we add the results together.

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X

wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 88 people, some of whom are anonymous, have edited and improved the article over time.

This article has been viewed 52,257 times.

Long multiplication can seem intimidating, especially when multiplying rather large numbers. However, if you follow the steps step by step, you should be able to do the long multiplication in no time at all. Get ready to master the math by starting with Step 1 below.

In conclusion, performing long multiplication is a useful skill to have as it allows for accurate and efficient calculation of large numbers. By following the steps outlined in this guide, one can easily perform long multiplication by breaking down the numbers, multiplying each digit, and adding the results together. Additionally, the use of grids and visual aids can further simplify the process and reduce the likelihood of errors. With practice and familiarity, individuals can become proficient in long multiplication, making complex calculations much more manageable. Through this technique, individuals can confidently solve mathematical problems and have a deeper understanding of numerical operations.

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