Subtraction

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

Subtraction is an operation used to find the difference between numbers. When you have a group of objects and you take away a few objects from it, the group becomes smaller. For example, you bought 9 cupcakes for your birthday party and your friends ate 7 cupcakes. Now you are left with 2 cupcakes. This can be written in the form of a subtraction expression: 9 - 7 = 2 and is read as "nine minus seven equals two". When we subtract 7 from 9, (9 - 7) we get 2. Here, we performed the subtraction operation on two numbers 9 and 7 to get the difference of 2. 

Subtraction Symbol

In mathematics, we have different symbols. The subtraction symbol is one of the important math symbols that we use while performing subtraction. In the above section, we read about subtracting two numbers 9 and 7. If we observe this subtraction: (9 - 7 = 2), the symbol (-) connects the two numbers and completes the given expression. This symbol is also known as the minus sign.

When we subtract two numbers, we use some terms which are used in the subtraction expression:

• Minuend: The number from which the other number is subtracted. 
• Subtrahend: The number which is to be subtracted from the minuend.
• Difference: The final result after subtracting the subtrahend from the minuend.

The subtraction formula is written as: Minuend - Subtrahend = Difference

Let us understand the subtraction formula or the mathematical equation of subtraction with an example.

Here, 9 is the minuend, 7 is the subtrahend, and 2 is the difference.

While solving subtraction problems, one-digit numbers can be subtracted in a simple way, but for larger numbers, we split the numbers into columns using their respective place values, like Ones, Tens, Hundreds, Thousands, and so on. While solving such problems we may encounter some cases with borrowing and some without borrowing. Subtraction with borrowing is also known as subtraction with regrouping. When the minuend is smaller than the subtrahend, we use the regrouping method. While regrouping, we borrow 1 number from the preceding column to make the minuend bigger than the subtrahend. Let us understand this with the help of a few examples.

Subtraction Without Regrouping

Example: Subtract 25632 from 48756.

Note: In subtraction, we always subtract the smaller number from the larger number to get the correct answer.

Solution: Follow the given steps and try to relate them with the following figure.

Step 1: Start with the digit at ones place. (6 - 2 = 4)
Step 2: Move to the tens place. (5 - 3 = 2)
Step 3: Now subtract the digits at hundreds place. (7 - 6 = 1)
Step 4: Now subtract the digits at thousands place. (8 - 5 = 3)
Step 5: Finally, subtract the digits at ten thousands place. (4 - 2 = 2)
Step 6: Therefore, the difference between the two given numbers is: 48756 - 25632 = 23124.

Subtraction With Regrouping

Example: Subtract 3678 from 8162.

Solution: Follow the given steps and try to relate them with the following figure.
We need to solve: 8162 - 3678
Step 1: Start subtracting the digits at ones place. We can see that 8 is greater than 2. So, we will borrow 1 from the tens column which will make it 12. Now, 12 - 8 = 4 ones.
Step 2: After giving 1 to the ones column in the previous step, 6 becomes 5. Now, let us subtract the digits at the tens place (5 - 7). Here, 7 is greater than 5, so we will borrow 1 from the hundreds column. This will make it 15. So,15 - 7 = 8 tens.
Step 3: In step 2 we had given 1 to the tens column, so we are left with 0 at the hundreds place. To subtract the digits on the hundreds place, i.e., (0 - 6) we will borrow 1 from the thousands column. This will make it 10. So, 10 - 6 = 4 hundreds.
Step 4: Now, let us subtract the digits at the thousands place. After giving 1 to the hundreds column, we have 7. So, 7 - 3 = 4
Step 5: Therefore, the difference between the two given numbers is: 8162 - 3678 = 4484

A number line is a visual aid which helps us understand subtraction because it allows us to jump backward and forward on each number. To understand how this works, let us explore subtraction using a number line. Let us subtract 4 from 9 using a number line. We will start by marking the number 9 on the number line. When we subtract using a number line, we count by moving one number at a time towards the left-hand side. Since we are subtracting 4 from 9, we will move 4 times to the left. The number on which you land after 4 backward jumps, is the answer. Thus, 9 - 4 = 5.

The concept of subtraction is often used in our day-to-day activities. Let us understand how to solve real life subtraction word problems with the help of an interesting example.

Example: A soccer match had a total of 4535 spectators. After the first innings, 2332 spectators left the stadium. Find the number of remaining spectators.

Solution:
Given:
The total number of spectators present in the first innings = 4535; The number of spectators who left the stadium after the first innings = 2332
Here, 4535 is the minuend and 2332 is the subtrahend.

 Th H T O
  4  5  3  5 
 -2  3  3  2 
  2  2  0  3 

Therefore, the number of remaining spectators = 2203.

Important Notes on Subtraction:

Here are a few important notes that you can follow while performing subtraction in your everyday life.

• Any subtraction problem can be transformed into an addition problem and vice-versa.
• Subtracting 0 from any number gives the number itself as the difference.
• When 1 is subtracted from any number, the difference equals the predecessor of the number.
• Words like "Minus", "Less", "Difference", "Decrease", "Take Away" and "Deduct" indicate that you need to subtract one number from another.

Topics Related to Subtraction

Check out these interesting articles to know about subtraction and its related topics.

• Binary Subtraction
• Subtraction Calculator
• Addition and Subtraction of Fractions
• Subtraction of Complex Numbers
• Subtraction of Fractions

Where do we Use subtraction?

Subtraction is used in our day-to-day life. For example, if we want to know how much money we spent on the items that we bought, or, how much money is left with us, or, if we want to calculate the time left in finishing a task, we use subtraction.

What are the Types of Subtraction?

The types of subtraction mean the various methods used in subtraction. For example, subtraction with and without regrouping, subtraction using number charts, subtraction using number line, the subtraction of small numbers using your fingers, and so on.

What are Subtraction Strategies?

Subtraction strategies are different ways in which subtraction can be learned. For example, using a number line, with the help of a Place Value Chart, separating the Tens and Ones and then subtracting them separately, and many others.

Give Some Subtraction Examples.

There can be various real life examples of subtraction. For example, if you have 5 apples and your friend ate 3 apples. Using subtraction, we can find out the number of remaining apples: 5 - 3 = 2. So, 2 apples are left with you. Similarly, if there are 16 students in a class, out of which 9 are girls, then we can find out the number of boys in the class by subtracting 9 from 16. (16 - 9 = 7). So, we know that there are 7 boys in the class.

What are the Three Parts of Subtraction?

The 3 parts of subtraction are named as follows:

• Minuend: The number from which we subtract the other number is known as the minuend.
• Subtrahend: The number which is subtracted from the minuend is known as the subtrahend.
• Difference: The final result obtained after performing subtraction is known as the difference.