Step-by-Step Long Multiplication Method with Solved Problems
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 Made Simple
1. What are the basic steps of the long multiplication method?
The long multiplication method involves a few simple steps to multiply numbers with two or more digits. Here is a basic overview:
Align Numbers: Write the numbers one below the other, aligning them by place value (ones under ones, tens under tens, etc.).
Multiply by Ones Digit: Multiply the entire top number (the multiplicand) by the ones digit of the bottom number (the multiplier).
Add Placeholder: Place a zero as a placeholder in the ones column of the next line.
Multiply by Tens Digit: Multiply the entire top number by the tens digit of the bottom number and write the result next to the placeholder zero.
Add Partial Products: Add the results from the previous steps (the partial products) together to get your final answer.
2. What are the key parts of a multiplication problem?
Every multiplication problem has three main parts. For example, in the equation 125 x 5 = 625:
Multiplicand: This is the number that is being multiplied. In this case, it is 125.
Multiplier: This is the number that you are multiplying by. Here, it is 5.
Product: This is the final answer you get after performing the multiplication. Here, the product is 625.
3. How do you do long multiplication with 3-digit numbers?
When multiplying by a 3-digit number, you follow the same logic as with a 2-digit number but add one extra step. After you multiply by the ones and tens digits, you add a third partial product for the hundreds digit. To do this, you place two placeholder zeros (one in the ones column and one in the tens column) before you multiply the top number by the hundreds digit of the multiplier. Finally, you add all three partial products to get the final answer.
4. How is long multiplication with decimals handled?
Multiplying decimals using the long multiplication method is straightforward. First, ignore the decimal points and multiply the numbers as if they were whole numbers. Once you have the product, count the total number of decimal places in both the original numbers you multiplied. Finally, place the decimal point in your answer so that it has the same number of decimal places you just counted.
5. Why do we add a zero as a 'placeholder' in long multiplication?
Adding a zero as a placeholder is crucial because of place value. When you move to the second line of a long multiplication problem, you are no longer multiplying by a ones digit; you are multiplying by a tens digit. For example, in 42 x 23, after multiplying by 3, you then multiply by 2. However, that '2' actually represents 20. The placeholder zero ensures that your second partial product is correctly shifted to the left, reflecting that you are multiplying by a value in the tens place, not the ones place.
6. What is the difference between long multiplication and short multiplication?
The main difference lies in the multiplier. Short multiplication is a faster method used when the multiplier is a single-digit number (e.g., 145 x 7). Long multiplication is a systematic, step-by-step method required when the multiplier has two or more digits (e.g., 145 x 27). It breaks the problem down into a series of simpler multiplications, creating 'partial products' that are then added together.
7. Where can long multiplication be used in real life?
Long multiplication is very useful in many everyday situations. For example, you might use it to:
Calculate the total cost of buying multiple items, like 15 notebooks that each cost ₹45.
Figure out the total number of seats in an auditorium that has 35 rows with 28 seats in each row.
Calculate the area of a large rectangular garden or room by multiplying its length and width.
8. What is a common mistake students make in long multiplication and how can it be avoided?
One of the most common mistakes is the misalignment of partial products. Students often forget to place the placeholder zero or line up the numbers correctly according to their place value. To avoid this, always start by placing the placeholder zero on the second line and make sure your columns (ones, tens, hundreds) are neatly aligned before you add the partial products together. Another common error is forgetting to add the 'carried-over' number from a previous calculation.
