Column Method – Definition With Examples

What is the column method?

When we arrange the numbers or shapes or objects one above the other, we refer to it as column method. In other words, the column method is a mathematical way of performing a calculation where the numbers to be added or subtracted or multiplied are set out above one another in columns.

For example:

Column Method Addition

We use the column method for three basic operations i.e.addition, subtraction and multiplication. 

Addition and Subtraction Column Method

Column method of addition and subtraction is the method in which the numbers are ‘carried’ and ‘borrowed’. It is set out like this: The calculation during addition and subtraction is done by ‘carrying’ and ‘borrowing’ numbers from column to column.

Column Method Addition

The column method of addition is also known as columnar addition. Column addition is a formal method of adding two or more numbers. 

For example: 

Columnar Addition

What is Column Subtraction?

The column subtraction is a way of finding the difference between two or more numbers by arranging them one above the other .

Column method Subtraction:

Column Method Subtraction

Why is Place Value Important in the Column Method?

The column method is the quickest way to add and subtract, but place value plays an important role in the column method. 

Let’s look at the example below and use column addition.

  • First, the numbers are lined up one above the other. 
  • Secondly, we add the ones and write the answer. 

For example: Adding $9$ and $5$ gives an answer of $14$, but we write only the ones under the line – in this case, it’s the digit $4$.

  • The third step is to regroup the tens under the tens column. In $14$, the digit $1$ is the value of the tens. 
  • Add the digits at the tens place. In our example, $8 + 1 = 9$, but we add 1 from  under the line. So the answer for the tens is $9$.
Column Method of Addition
  • When two numbers of different digits are added we can place them correctly using place value. For example: the decimal number $0.1$ and a number $28$. 
Column Method Addition for Decimal Numbers

The Expanded Column Method

The expanded method is the breaking down each of the numbers in your sum into the smaller, more manageable numbers that they are made up of. We basically break down the numbers in the expanded form. 

For example, the number $782$ can be broken down into: $700 + 80 + 2$

The expanded method is an addition sum is carried out in the following way: 

Suppose, we have to add $47 + 134$

Firstly, we will expand $47 and 134$.

$47 = 40 and 7 and 134 = 100, 30 and 4$

Now we sort the numbers into hundreds, tens, and ones and add them in their groups. 

  • We will add the digits at ones place. 

In this example, we add $7 + 4 = 11$. We keep 1 at the ones place and take another $1$ to the tens place. 

  • We will add the digits at tens place.

In this example, we add $30 + 40 + 10 = 80$

  • We will add the digits at the hundreds place.

In this example, we add $100 + 0 = 200$

Now, we add all of our digits together, we get $100 + 80 + 1 = 181$

Another example is given below: 

Expanded Column Method

Let us take an example of an expanded column method of subtraction. 

Expanded Column Method of Subtraction

The Column Method for Subtraction without Borrowing

Sometimes we don’t have to borrow the digits from a column in subtraction. 

For example: $76 – 42$

The first step is to sort your numbers into tens and ones:

Tens $→ 7 and 6$

Ones $→ 4 and 2$

Sort Numbers into tens and ones

We should always place the biggest numbers in the top row of the columns.

Now you can subtract the numbers in each column: 

Subtract using column method

The answer to the sum is $76 – 42$ is $34$.

The Column Method for Addition without Borrowing

We use the column method for addition without borrowing or carrying any values between columns. 

For example: $282 + 615$

On expanding, we get 

Hundreds $→ 200$ and $600$

Tens $→ 80$ and $10$

Ones$→ 2$ and $5$

Now, put the values into their columns:

Place numbers to add in columns

Next, we add up all of your values within their groups.

Column Method to Add Numbers

Therefore, the answer to the sum $262 + 615$ is $897$.

The Column Method of Multiplication

We also use the column method to multiply two numbers which involves writing one number underneath the other in a similar way to column addition and subtraction.

When we multiply two numbers using the column method multiplication, we use the following steps: 

Suppose we are multiplying $96$ and $36$. 

Step I: We multiply the multiplicand $(96)$ by the ones digit of multiplier $(6)$ i.e.,

Multiply Multiplicand by the ones digit of multiplier

Step II: The next step is to multiply the multiplicand $(96)$ by the tens digit of multiplier $(3)$ i.e.,

Multiply Multiplicand by the tens digit of multiplier

Step III: The next step is to add the partial products i.e.,

Partial product $1 (576 ones) +$ Partial product $2 (288 tens)$

$576 × 1 + 288 × 10$ 

$576 + 2880 = 3456$

It actually means: 

Column Method multiplication

Now we shall apply the same method for multiplying a $3-$digit number by a $2-$digit number. 

Example:

Column Method for multiplication

Let’s take another example. Find the product of $145$ times $12$ using the column method.

Step I:

Multiply ones digit of both Multiplicand and multiplier

Step II:-

Multiply tens digit of Multiplicand by the multiplier

Step III:

Multiply hundreds digit of Multiplicand by the multiplier

Step IV:

Multiply Multiplicand by the  tens digit of the multiplier

Step V:

Multiply 3-digit and 2-digit number by column method

Step VI:

Use column method to multiply numbers

Solved Examples

1. Find the error in the following. 

Find error in column method addition

Answer: The error is that the tens and hundreds columns aren’t correctly added. The carryover digits weren’t added. The correct sum will be:

Add 4-digit numbers using column method addition

2. Find the value of ‘A’ in the following.

Use column method subtraction to find the value of A

Solution: $300 – $A$  = 200$

$So, $A$ = 100$

3. The cost of 1 necklace is Rs $342$. What will be the cost of $23$ necklaces? If Sharon has Rs $8000$, how much money will be left after paying for the necklaces?

Answer: Cost of 1 necklace $=$ Rs $342$

Cost of $23$ necklaces $= 342 ✕ 23 =$ Rs $7866$

Cost of $23$ necklaces $= 6000 + 900 + 800 + 120 + 40 + 6 =$ Rs $7866$

Amount left $= 8000 – 7866$

Column method subtraction for 4-digit numbers

Amount left $=$ Rs $134$

Practice Problems

Column Method - Definition With Examples

Attend this quiz & Test your knowledge.

1If we use the column method to multiply 543 and 16, then what will come in one's place?

7
8
6
None of these
CorrectIncorrect
Correct answer is: 8
$6\times3 = 18$, so at ones place, we will get $8$.

2What will replace A in the following?

Column Method – Definition With Examples
4
5
3
2
CorrectIncorrect
Correct answer is: 4
$4500 − 1352 = 3148$
So, at tens place, we get 4.
Column Method – Definition With Examples

3Add: 2785 and 1948

4533
4674
4733
4534
CorrectIncorrect
Correct answer is: 4733
$2785 + 1948 = 4733$
Column Method – Definition With Examples

Frequently Asked Questions

The column method is the method of arranging the numbers one above the other and adding, subtracting or multiplying in the columns. On the other hand, the horizontal method is the way of arranging the numbers in a horizontal line then the terms are arranged to collect all the groups of like terms.

The other name for column method of addition is columnar addition or vertical method of addition.

The column method division is a simple way of the traditional long division method. The lines are drawn in order to separate the digits of the divisor. Each place-value column is solved from left to right.