How to Do Long Multiplication Step by Step with Solved Examples
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
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.
Multiply the multiplier, starting with the one digit of the bottom number, by the last digit of the top number.
Write the solution below the equivalent line.
If the answer is greater than nine, write the answer in one position and hold the tens of digits.
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.
Moving to the tens digit in the bottom number when you have multiplied the one digit by every digit in the top number.
Multiply as before, but write down your replies in a new row this time, moving one digit to the left.
Draw another answer line below your last row of answer numbers when you finish multiplying.
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
Solution:
Here, 5249 is the multiplicand and 61 is the multiplier.
Therefore on multiplying, we get 320189.
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2. 5156 x 61
Solution:
Here, 5156 is the multiplicand and 61 is the multiplier.
Therefore on multiplying, we get 314516.
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3. 9802 x 46
Solution:
Here, 9802 is the multiplicand and 46 is the multiplier.
Therefore on multiplying, we get 450892.
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4. 3920 x 45
Solution:
Here, 3920 is the multiplicand and 45 is the multiplier.
Therefore on multiplying, we get 176400.
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5. 505 x 117
Solution:
Here, 505 is the multiplicand and 117 is the multiplier.
Therefore on multiplying, we get 59085.
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Conclusion
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 Method for Large Numbers
1. What is long multiplication in maths?
Long multiplication is a written method used to multiply large numbers by breaking the calculation into smaller, manageable steps. It is also called the standard algorithm for multiplication.
- You multiply each digit of one number by each digit of the other.
- Partial products are written in rows according to place value.
- The partial products are added to get the final result.
2. How do you do long multiplication step by step?
To do long multiplication, multiply each digit in the bottom number by the top number and then add the partial products. For example, multiply 23 × 14:
- Step 1: Multiply 23 × 4 = 92.
- Step 2: Multiply 23 × 10 = 230.
- Step 3: Add the partial products: 92 + 230 = 322.
3. What is the long multiplication method for 2-digit numbers?
The long multiplication method for 2-digit numbers involves multiplying each digit separately and adding the results. For example, 34 × 12:
- 34 × 2 = 68
- 34 × 10 = 340
- Add: 68 + 340 = 408
4. Why do we add a zero in long multiplication?
We add a zero in long multiplication to show that we are multiplying by a tens (or higher place value) digit. For example, when multiplying 46 × 23:
- 46 × 3 = 138
- 46 × 20 = 920 (notice the zero because 20 = 2 tens)
5. What is an example of long multiplication?
An example of long multiplication is calculating 125 × 36 using partial products.
- 125 × 6 = 750
- 125 × 30 = 3750
- Add: 750 + 3750 = 4500
6. What is the difference between long multiplication and short multiplication?
The difference is that long multiplication writes out all partial products, while short multiplication is a compact mental or written method.
- Long multiplication: Used for 2-digit or larger numbers and shows each step clearly.
- Short multiplication: Typically used for multiplying a large number by a single digit.
7. How do you multiply 3-digit numbers using long multiplication?
To multiply 3-digit numbers using long multiplication, multiply each digit step by step and add all partial products. For example, 123 × 45:
- 123 × 5 = 615
- 123 × 40 = 4920
- Add: 615 + 4920 = 5535
8. What are common mistakes in long multiplication?
Common mistakes in long multiplication usually involve place value errors and incorrect addition of partial products.
- Forgetting to add the zero when multiplying by tens.
- Misaligning digits in columns.
- Making errors in basic multiplication facts.
- Adding partial products incorrectly.
9. Can you use long multiplication with decimals?
Yes, long multiplication can be used with decimals by multiplying as whole numbers first and then placing the decimal point correctly. For example, 2.3 × 1.4:
- Ignore decimals: 23 × 14 = 322
- Total decimal places = 2
- Place decimal: 3.22
10. How do you check your answer in long multiplication?
You can check your long multiplication answer by using the inverse operation or estimation.
- Division check: Divide the product by one factor to see if you get the other factor.
- Estimation: Round numbers and multiply mentally to see if your answer is reasonable.
