# Subtraction – Introduction, Definition, Parts, Methods, Examples

Subtraction concepts and worksheets are here. Know the different formulae, definitions, and methods involved in subtraction. Know the representation, parts, and properties of subtraction. Solve various problems involved in subtraction and refer to definitions and examples. Check the below sections to know the various information of subtraction like Signs, properties, definition, subtraction method in special situations, number bonds, etc.

## Subtraction – Definition

Subtraction is the oldest and the important basic arithmetic operation used in day-to-day life. Subtraction is as important as addition is. The word “subtraction” is derived by using two words “sub” which means below or under and “tract” which means carry away or pull. Hence, the final definition of subtraction means to carry the below or lower part.

It’s been 6000 years that subtraction is known to mathematicians. The subtraction symbol was first used by the German mathematician as barrel markings. Later on, from the 1500s its usage started as an operation symbol. Then, in 1557, the famous Mathematician and Physician used in Whetstone of Witte and thus it became common.

### Subtraction Symbol

Subtraction is represented with the symbol hyphen(-). There are 4 parts in subtraction: the difference, an equal sign, the minuend, the subtrahend. Subtraction is useful to understand the parts because it enables the beginners to grasp all the principles and also develop strategies to solve subtraction problems.

#### The Difference

“Difference” is the term used to determine the result or the answer of the equation or operation. For suppose, 8-4 = 4. Therefore, the difference in the case is 4.

#### The Equal Sign

The equal sign indicates that 2 sides of the equation are equal or equivalent. The equal sign is denoted with the symbol “=” and it is inserted between the values which are to be subtracted.

#### The Subtrahend

The subtrahend is the number that is taken away from the starting value or money. For suppose, 8-4 =4, the subtrahend is 4. The subtraction sentence will have multiple subtrahends which depend on the equation complexity.

#### The Minuend

The minuend is the number from which other numbers are taken away. It is the starting value of the subtraction equation. For suppose, 8-4 =4, the minuend is 8.

### Important Points on Subtraction

• The order of numbers or values is important in subtraction. The smaller number is always subtracted from the bigger number. Else it gives a negative value Example: 25 – 5 = 20
• On subtracting the value zero from the given number, it results in the same number. Example: 25 – 0 = 25
• On subtracting the value one from the given number, it results in the preceding number. Example: 25 – 1 = 24
• On subtracting the same number itself from the number, the difference obtained is always zero. Example: 25 – 25 = 0

### Properties of Subtraction

Identity Property

The property of identity states that if zero is added or subtracted to the number, the resultant value will be the number itself.

Example:

5 + 0 = 5

6 – 0 = 6

Commutative Property

If a and b are the two whole numbers then a-b is not equal to b-a, i.e., {a-b ≠ b-a}

Example:

25 – 5 = 20 and 5 – 25 ≠ 20

Closure Property

If a & b are whole numbers, then a-b is a whole number, if a > b or a = b. If a < b, then a-b is not a whole number.

Example:

5 and 4 are whole numbers, then 5 -4 is also a whole number

Since 5 is greater than 4

Associative Property

If a,b,c are whole numbers and c≠0. then (a-b)-c ≠ a – (b – c)

Property of 1

If the value one is subtracted from the given number, it gives the preceding value of the given number

Example:

643 – 1 = 642

Inverse Operations

Subtraction and Addition are opposite operations of each other. In the addition property the value of the resultant increases and in the subtraction property the value of the resultant decreases.

Example: 8 + 4 – 4 = 8

Adding and subtracting the same value indicates the cancellation of two values. Hence, while solving a large group of numbers, notice all the same value numbers and cancel those terms to make the simplification easy.

### Method to Solve Subtraction Problems

1. First of all, know the greater and smaller numbers, write the greater number above the smaller number.
2. Start subtraction from the rightmost digit and then compare the upper and lower digits.
3. In the comparision, if you find that the lower digit is small than the upper digit, subtract the lower value from the upper value and write the answer below.
4. If there is a case that the upper digit is small than the lower digit, then borrow 1 from the next number. Now as the digit has become greater, you can easily subtract the lower value from the higher value and write the answer below.
5. Repeat the procedure in the same way until you run out of all the digits.

### Subtraction Examples

Problem 1:

Tara has 65 shirts. Patan has 42 shirts. How many less shirts does Patan have than Tara?

Solution:

As given in the question,

No of shirts Tara has = 65 shirts

No of shirts Patan has = 42 shirts

To find the less shirts Patan have than Tara, we apply subtraction law

Therefore, no of shirts = 65 – 42

= 23

Thus, Patan has 23 less shirts than Tara has

Problem 2:

A sweet shop has 78 sweets. It sold only 43 sweets. How many sweets are left to be sold?

Solution:

As given in the question,

No of sweets, the sweet shop has = 78

No of sweets sold = 43

To find the no of sweets left, we apply the subtraction law

Therefore, no of sweets left out = 78 – 43

= 35

Thus, No of sweets left = 35

Problem 3:

The total strength of the class is 50. Out of which 24 are girls. Find the total number of boys present in the class?

Solution:

As given in the question,

Total strength of the class = 50

No of girls = 24

To find the total boys present in the class, we apply subtraction law

Therefore, no of boys in the class = 50 – 24

= 26

Thus, the total boys present in the class = 26

Problem 4:

Akshu bought 562 chocolates on her birthday. He distributed 326 chocolates among her friends. How many chocolates are left with her?

Solution:

As given in the question,

No of chocolates Akshu bought = 562

No of chocolates she distributed among her friends = 326

To find the remaining chocolates, we apply the subtraction law

Therefore, to find the remaining chocolates = 562 – 326

= 236

Thus, the number of remaining chocolates = 236

Problem 5:

There are 7 ant raincoats and 4 cockroach raincoats. How many less cockroach raincoats are there than ant raincoats?

Solution:

As given in the question,

No of ant raincoats = 7

No of cockroach raincoats = 4

To find the number of less cockroach raincoats, we apply subtraction law

Therefore, the number of less cockroach raincoats = 7 – 4

= 3

Thus, the number of less cockroach raincoats = 3

Problem 6:

There are 30 green umbrellas and 10 pink umbrellas. What is the difference between the number of green and the pink umbrella?

Solution:

As given in the question,

No of green umbrellas = 30

No of pink umbrellas = 10

To find the difference between the number of green and pink umbrellas. we apply subtraction law

Therefore, to the difference between the number of green and pink umbrellas = 30 – 10

= 20

Thus, the difference between the number of green and pink umbrellas = 20

Problem 7:

Wilson has 7 apples and he ate 4 apples. How many apples are left with him?

Solution:

As given in the equation,

No of apples Wilson has = 7

No of apples he ate = 4

To find the number of apples, we apply the subtraction law

Therefore, number of apples = 7 – 4

= 3

Thus, the number of apples = 3

Problem 8:

Guna has 25 books and Mona has 12 books out of them. How many books are left with Guna?

Solution:

As given in the question,

No of books Guna has = 25

No of books Mona has = 12

To find the number of books left with Guna, we apply subtraction law

Therefore, number of books = 25 – 12

= 13

Thus, the number of books = 13

Problem 9:

Mani bought 36 candles for Diwali, He lit 20 candles. How many candles are left with him?

Solution:

As given in the question,

No of candles Mani bought = 36

No of candles he lit = 20

To find the number of candles left, we apply the law of subtraction

Therefore, number of candles left = 36 – 20

= 16

Thus, the number of candles = 16

Problem 10:

Tom bought 30 eggs from the shop, out of which 12 eggs were broken. How many eggs are left with him?

Solution:

As given in the question,

No of eggs = 30

No of broken eggs = 12

To find the number of eggs left him, we apply subtraction law

Therefore, number of eggs left = 30 – 12 = 22

Thus, the number of eggs left = 22