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Long Multiplication

Last updated date: 23rd Feb 2024
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What is Long Multiplication?

You might wonder what is long multiplication. To answer your question, it is a way of finding the product of huge numbers. Now you might think it must be a difficult task, do not worry we will provide the easiest explanation for you to understand the topic easily.

A strategy used to solve multiplication issues for large numbers is long multiplication. Long multiplication is the type of multiplication that is widely taught in the world to elementary school students.

Long Multiplication Calculator

Multiplication is done with a multiplicand and multiplier to approximate the variable by the long multiplication method of positive or negative integer numbers or decimal numbers. For the Standard Algorithm, the task is shown by the solution. With their least significant digits aligned, the numbers to be multiplied are positioned vertically over each other. If you know the multiplication table by heart, one thing that will really help you increase your speed.

Long Multiplication Method

  1. Arrange the numbers on top of each other and line up the columns with the location values. Usually, the number with the most digits is put on top as the multiplicand.

  2. Multiply the multiplier, starting with the one digit of the bottom number, by the last digit of the top number.

  3. Write the solution below the equivalent line.

  4. If the answer is greater than nine, write the answer in one position and hold the tens of digits.

  5. Always move right to left. Multiply the digits in the top number from the bottom number to the next digit to the left. Attach it to the result if you were holding a digit and write the answer below the equals line. Do so if you need to hold it again.

  6. Moving to the tens digit in the bottom number when you have multiplied the one digit by every digit in the top number.

  7. Multiply as before, but write down your replies in a new row this time, moving one digit to the left.

  8. Draw another answer line below your last row of answer numbers when you finish multiplying.

  9. To add the number columns from right to left, use long addition, carrying as you usually do for a long addition.

Long Multiplication Steps

Step 1: With the greater number on top, arrange the numbers. Align numbers by columns of the place value.

Step 2: Multiply each digit of the bottom by the digits with the top number.

Step 3: Switch one spot to the left. Multiply tens place digits in the bottom number by every digit in the top number.

Step 4: Using long addition, add numbers in column format.

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Long Multiplication Examples

1. 5249 x 61


Here, 5249 is the multiplicand and 61 is the multiplier.

Therefore on multiplying, we get 320189.

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2. 5156 x 61


Here, 5156 is the multiplicand and 61 is the multiplier.

Therefore on multiplying, we get 314516.

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3. 9802 x 46


Here, 9802 is the multiplicand and 46 is the multiplier.

Therefore on multiplying, we get 450892.

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4. 3920 x 45


Here, 3920 is the multiplicand and 45 is the multiplier.

Therefore on multiplying, we get 176400.

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5. 505 x 117


Here, 505 is the multiplicand and 117 is the multiplier.

Therefore on multiplying, we get 59085.

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Long multiplication is a method of finding the product of two bigger numbers. It can include a product of a three-digit number with a two-digit number, three-digit number with a three-digit number or a four-digit number. The operations are done in column format. It can be extended to two arbitrarily big numbers or to the number of decimal digits.

To multiply such huge numbers, it is important to learn the method of long multiplication. Although there are several ways to multiply big numbers, few of which are:

  • Grid Method

  • Long multiplication

  • Lattice multiplication

  • Binary or peasant multiplication

  • Shift and add

  • Quarter square

  • Lower bounds

However, the other methods are a little complicated which will be covered in the higher classes.

FAQs on Long Multiplication

1. What are the Three Multiplication Sections?

Answer: The three parts of multiplication are multiplicand, multiplier, and product.

2. Define Multiplicand, Multiplier, and Product.


Multiplicand: Multiplicand is the number that is being multiplied.

Multiplier: Multiplier is the number that multiplies the multiplicand.

Product: Product is the answer that we get after multiplying the multiplicand and the multiplier.

3. Is Long Multiplication in Decimals Different?

Answer : 

  • Count the total number of decimal places that both the multiplicand and the multiplier include.

  • Ignore the decimals and align the numbers on top of each other as if they were integer numbers.

  • Using long multiplications to multiply the numbers.

  • Insert the product with a decimal point so that it has the same number of decimal places equal to the sum of the first step.