Subtraction: Definition, Formula, Examples

Subtraction is the process of finding the difference between any two numbers. If we are given two numbers a and b then subtraction of a and b gives the difference between a and b, i.e. subtraction of 8 and 5 gives result as 3. Let’s learn more about the methods, examples, and applications of subtraction in detail in this article.

Subtraction in Maths

Subtraction in mathematics is an operation that is used to find the difference between two numbers. This means the subtraction operation tells us how much a quantity is smaller than another quantity.

For example, Subtracting 8 from 11, the result is 3 i.e.,

11 – 8 = 3

We can also say that Subtraction is the inverse process of addition. By subtracting we find by how much a number is smaller than another number.

Subtraction Definition

Subtraction is defined as inverse process of addition and between two number it represents the difference between those numbers.

For Example, if the height of Ravi increase from 160 cm to 172 cm, then what is the increase in height? The height increase in height is calculated by subtracting two heights 172 – 160 = 12. Thus, we say that the height is increased by 12 cm.

Subtraction Symbol

Various symbols are used in mathematics for representing various operations. For subtraction operation in mathematics we use minus (–) symbol.

For example, Subtracting 3 from 5 is written as, 5 – 3 and is calculated as,

5 – 3 = 2

In above example, (–) represent the subtraction operation.

Subtraction Parts

There are various parts of subtraction that include,

• Minuend
• Subtraction Symbol
• Subtrahend
• Difference

Let’s learn about the same in detail.

Minuend

In subtraction, the numbers from which the other number is subtracted is called the Minuend.

For example, in 8 – 7, 8 is Minuend.

Subtraction Symbol

In subtraction, the symbol that represents the subtraction is the minus sign (–).

For example, in 8 – 7, (-) represent subtraction symbol.

Subtrahend

In subtraction, the number that is to be subtracted from the first number is called the Subtrahend.

For example, in 8 – 7, 7 is subtrahend.

Difference

In subtraction, the difference is the result of the subtraction operation.

For example, in 8 – 7 = 1. The difference is 1.

Subtraction Formula

Subtraction formula is the basic formula of mathematics that gives the difference of two or more numbers. The subtraction formula is,

Minuend – Subtrahend = Difference

Let’s understand the Subtraction Formula using the following example.

For example, find the difference of 9 and 5.

Solution:

9 – 5 = 4

The same is explained in the following illustration.

Subtraction Table

Subtraction Table is a table that contains the difference of first ten natural numbers. The table added below show the subtraction table.

The subtraction table is used to find the subtraction of two numbers quickly.

Subtraction Methods

We have various methods for finding the sum of two numbers or solving addition. They are

• Using Fingers
• Using Number Lines
• By Regrouping Or Vertical Method

Let’s learn the same in detail.

Subtraction on Fingers

Using fingers one can easily calculated the subtraction of two numbers. To find the difference of two number we first count first number in our fingers and then close the fingers equal to number that we have to subtract. The fingers remaining is the required result of the subtraction problem.

This explained by the image added below,

Subtraction on the Number Line

Finding the result of subtraction operation is very easy using the number line.

We know that, a number line is a line that represents numbers (Integers). If we have to find the difference of two numbers using number lines then we should the following steps.

Let us suppose we have to find the difference of 7 and 3

Step 1: Mark 7 on a number line.

Step 2: Now to find the difference of 7 and 3 we count 3 numbers backwards (in left direction)

Step 3: Mark the final position(here 3). Thus, we get the difference of 7 and 3 to be 4.

These steps can be explained using the following illustration.

Subtraction By Regrouping

Subtracting numbers by regrouping is used to subtract numbers after arranging them in vertical number. We use subtraction by regrouping for mostly 2 and 3 digits numbers. It is also called the Vertical Subtraction method.

In this method we write the number in H T O (Hundreds Tens Ones) format and then subtract one with one, ten with ten and hundred with hundred and so on.

Here if we are in a situation that we our unable to subtract as the number written below is greater then we take carry from the next number in the upper number and the subtraction operation is carried on.

For example, if we have to find the difference of 89 and 74 then the same is calculated as,

Subtraction Properties

As we know that subtraction is one of the fundamental operation of the mathematics. There are various properties associated with it. Some of the important properties of the subtraction are,

• Closure Property of Subtraction
• Commutative Property of Subtraction
• Associative Property of Subtraction
• Identity Property of Subtraction

Closure Property of Subtraction

Closure Property of Subtraction states that,

“Subtraction of two real numbers is always a real number.”

Commutative Property of Subtraction

Commutative property does not hold true for subtraction as for any two real numbers a and b, i.e.,

a – b ≠ b – a.

Associative Property of Subtraction

Associative property does not hold true for subtraction as for any three real numbers a, b and c, i.e.,

(a – b) – c ≠ a – (b – c)

Identity Property of Subtraction

Identity property hold true for subtraction as in real number we have a number such that subtracting that number from the original number result in original number itself.

a – 0 = a

Subtraction of Fractions

Fractions can be easily subtracted. For subtracting fraction first we have to check whether the given fraction is Like Fraction of Unlike Fraction. Then the subtraction of the fraction is carried out accordingly.

Subtracting Like Fraction

In case of the like fraction we simply subtract the numerator of the fraction keeping their denominator the same.

For example, subtract 5/9 from 7/9

7/9 – 5/9

= (7 – 5)/9

= 2/9

Subtracting Unlike Fraction

In case of the unlike fraction we first convert the unlike fraction into like fraction by taking the LCM of their denominators and then subtract them according to like fractions. For examples subtract 2/3 from 3/4

3/4 – 2/3

= (3/4)×(3/3) – (2/3)×(4/4)

= 9/12 – 8/12

= (9 – 8)/12

= 1/12

Subtraction of Integers

Integers are numbers that contain both positive numbers and negative numbers. We can be easily subtracted integers by following various cases as discussed below,

Subtraction between Two Positive Numbers

In this case we simply perform the subtraction operation. This is explained by the example added below,

Example: Subtract 3 from 5

Solution:

5 – 3 = 2

Also, this can be easily explained as suppose we are given 5 liters of water and 3 liters of water is take out from it them the result is 2 litres of water.

Subtraction between Two Negative Numbers

In this case we use the rules of integer subtraction for finding the difference,

Example: Subtract (-6) from (-8)

Solution:

(-8) – (-6)

= -8 + 6

= -2

Subtraction between a Positive and a Negative Number

This operation can be achieve similar to the above operation. This is explained by the example,

Example: Subtract 6 from (-8)

Solution:

(-8) – (6)

= -8 – 6

= -(8 + 6)

= -14

Subtraction of Decimals

Decimals are the numbers where whole part and fractional part is separated by a decimal point. For example, 2.34 is a decimal number where 2 is the whole part, 34 is the fractional part, and both of these parts are separated by “.”.

To subtract any two decimal number we can align the decimal of both number and subtract fractional part first, and then whole part.

Let’s consider an example to learn the Subtraction of Decimals.

Example: Subtract 1.78 from 3.45.

Thus, subtracting 1.78 from 3.45 results in 1.

Subtraction Real-life Applications

These are some of the real-life applications of subtraction:

• Measuring Distances: Subtraction is used in measuring distances. For instance, if you want to find the length of a room, you measure from one end to the other and then subtract the starting point’s measurement.

• Timekeeping: When calculating the duration between two events, you subtract the start time from the end time. For instance, if an event starts at 3:30 PM and ends at 5:15 PM, the duration is 5:15 PM – 3:30 PM = 1 hour and 45 minutes.

• Inventory Management: Businesses use subtraction to track inventory levels. When items are sold, the quantity is subtracted from the total stock to keep track of available items.

• Budgeting: When managing finances, you might subtract expenses from your income to determine your savings or how much money you have left after paying bills.

• Temperature Change: To find the change in temperature, subtract the initial temperature from the final temperature. For example, if the temperature was 80°F in the morning and dropped to 65°F in the evening, the change is 65°F – 80°F = -15°F.

Subtraction Word Problems

Here are some solved word problems on Subtraction.

Problem 1: If a boy spends 230 rupees for movie ticket out of 500 rupees. How much money is left with him.

Solution:

Total money the boy has = 500 rupees

Money spent on movie ticket = 230 rupees

Money left with the boy = 500 – 230 = 270 rupees.

Problem 2: If Kabir has 100 pens and he distribute 55 pens in his class, then how much pens are left with him.

Solution:

Total pen Kabir has = 100 pens

Pens distributed by him in the class = 55 pens

Pens left with him = 100 – 55 = 45 pens

Subtraction Example Problems

Here are some solved problems on subtraction methods.

Example 1: Subtract 76 from 98

Solution:

98 – 76 = 24

Example 2: If a man buys 26 apples from the market and out of which 8 apples are rotten, how many good apple he has?

Solution:

Total Apple brought by the man = 25 Apples

Rotten Apples = 8 Apples

Good Apples = Total Apple – Rotten Apple = 25 – 8 = 17 Apples

Example 3: By how much is 1234 less than 2345?

Solution:

2345 – 1234 = 1111

Thus, 1234 is 1111 less than 2345.

Subtraction Practice Problems

We have given a few exercise problems on subtraction here for your practice.

P1: Calculate the following differences:

• 25 – 8 = ?
• 42 – 15 = ?
• 84 – 29 = ?
• 135 – 68 = ?
• 452 – 237 = ?
• 2768 – 1420 = ?
• 6352 – 4819 = ?

P2: Sarah had 15 candies, and she gave 6 candies to her friend Sophie. How many candies does she have now?

P3: A bookstore had 38 books on the shelf. If 12 books were sold and 3 were rented out, how many books are still on the shelf?

P4: A garden had 120 flowers. The gardener picked 56 flowers to make bouquets and sold 31 flowers to individuals. How many flowers are still in the garden?

Subtraction Short Notes

Some important observations on Subtraction are as follows :

1. Definition: Subtraction is a basic arithmetic operation in mathematics.
2. Symbol: Denoted by “-“.
3. Purpose: It finds the difference between two numbers.
4. Example: In (7-3), 7 is the minuend, 3 is the subtrahend, and the result is 4.
5. Complement: Subtraction is the inverse operation of addition (i.e., [Tex]a-b = a + (-b) [/Tex].
6. Negative Results: Subtraction can result in negative numbers when the minuend is smaller than the subtrahend.

Subtraction in Maths- FAQs

What is Subtraction in Maths?

Among the four fundamental mathematical operations, Subtraction is one of them. In subtraction we find the difference between the two numbers.

What are Four Arithmetical Operation?

The four Arithmetical Operations are,

• Addition
• Subtraction
• Multiplication
• Division

How to Subtract Fraction?

To subtract fraction follow the following step

Step 1: Check weather the given fractions are like fractions or unlike fractions.

Step 2: For like fraction directly subtract their numerator by simply taking their denominator the same.

Step 3: For unlike fraction first convert the unlike fraction to like fraction by taking the LCM of their denominator and then subtract the same.

What is Zero Property of Subtraction?

According to zero property of subtraction, if we subtract zero from a number then result is the number itself, i.e. a – 0 = a

What are 3 Parts of Subtraction?

Three parts of the subtraction are Minuend, Subtraction Symbol, and Subtrahend, other then this there is one more component related to it i.e. difference which is the result of the subtraction.

What is Symbol for Subtraction?

The symbol for subtraction is Minus Sign i.e., “-“.

Does Associative Property hold true for Subtraction?

No associative property, does not holds true for subtraction. As, a – (b – c) ≠ (a – b) – c