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# Subtraction – Explanation & Examples

Like addition, subtraction is also one of the oldest and the most basic arithmetic operations. **The word subtraction is derived from the two words**, ‘**sub**’ and ‘**tract**,’ which mean under or below and to pull or carry away, respectively. Therefore, subtraction means to carry away the lower part.

Subtraction is known to mathematicians for more than 6000 years. German Mathematicians first used the symbol of subtraction as markings on barrels. It is then used as an operational symbol in the 1500s. Later in 1557, it became common when Robert Recorde, a famous Physician and Mathematician, used it in the Whetstone of Witte.

## Subtraction Definition

In the 1200s, the method of subtraction was called borrowing or decomposition. After 1600, the mathematicians introduced the term subtraction and defined it as a mathematical operation where an amount is taken away from the total amount. It is also the difference between the two amounts.

**Subtraction is denoted by a hyphen (-).**

For example, in the subtraction sentence 20 – 5= 15, 5 is taken away from 20, leaving 15. The subtraction sentence has four main parts: the subtrahend, the minuend, an equal sign, and the difference.

Understanding parts of a subtraction sentence is useful because it enables the learners to grasp key subtraction principles and develop strategies to tackle subtraction problems.

## Parts of Subtraction

### The Minuend

The minuend in the subtraction sentence is the starting amount from which other amounts are taken away. For example, in a subtraction sentence: 12 – 8 = 4, the minuend is 12.

### The Subtrahend

This the number being taken away from the starting amount. In the subtraction sentence: 12 – 8 = 12, the subtrahend is 8. A subtraction sentence can have multiple subtrahends, depending on the complexity of the equation.

### The Equals Sign

The equals sign being the third part of any subtraction sentence indicates that the two sides of the equation are equivalent. The equals sign is denoted by ‘**=**’ and is inserted between values being subtracted.

### The Difference

In a subtraction sentence, the difference is the answer or result of the operation. For instance, 12 – 8 = 4; the difference, in this case, is 4.

## Properties of Subtraction

**Identity Property**

The identity property states that any number minus or plus zero is the number itself. For example,

4 – 0 = 4.

For this case, it is advisable to remind learners when subtracting large groups of numbers that the number zero does not affect other numbers in the equation.

**Inverse Operations**

Addition and subtraction are normally opposites of each other. For example,

12 + 5 – 5 = 12.

Adding and subtracting the same amount is the same as canceling the two amounts. For this reason, students are encouraged to identify numbers that cancel each out, especially when dealing with the addition and subtraction of large groups of numbers.

**Commutative Property**

The commutative property states that the change of numbers in a mathematical equation does not affect the final answer. The commutative property does not apply to subtraction because 5 – 2 is not the same as 2 – 5.

**Associative Property**

The associative property is applied to equations that use brackets, braces, and parentheses to group numbers together. In other words, you can move the parentheses around different groups without changing the final answer.

This property is also not applicable to subtraction because: (3 – 4) – 2 is not equivalent to 3 – (4 – 2). This shows that you cannot move the brackets around when working on a subtraction equation.

*Example 1*

Sam has 99 cupcakes. If he gave 32 to Nina and 49 to Julie, how many cupcakes left with him?

__Solution__

Total number of cupcakes = 99

Nina takes = 32

Julie takes = 49

Number of cupcakes left = 99 – 32 – 49 = 18

*Example 2*

In 2012, a company had a staff of 1000 employees. Due to the recession, the company terminates its 230 employees in 2015 and 220 employees in 2017. If the company does not hire any new employees in this period, determine the number of employees by the end of 2017.

__Solution__

Total employees in 2012 = 1000

Company terminates its 230 employees in 2015,

Employees left = 1000 – 230 = 770

Company terminates 220 employees in 2017,

Employees left = 770 – 220 = 550

*Example 3*

James, Mike, and Curran have bank accounts in Central Bank. Mike has $500 more than James, and Curran has $300 less than James. If Mike has $1200 in his account, how much does Curran have?

__Solution__

Mike = James + $500

Curran = James – $300

James = Curran + $300

Mike = Curran + $300 + $500

Curran = Mike – $300 – $500

Curran = Mike – $800

Curran = $1200 – $800

Curran = $400

*Practice Questions*

- Out of 568 children of a village, 354 go to school. How many children don’t go to school?
- A person had $5680. If he spent $3456 of the total amount, how much money is he left with?
- By how much is 3689 less than 6789?
- Melvin earns a monthly salary of $6777. Suppose she saves $577 monthly. Calculate her monthly expenditure?
- The cost of a phone is $290, and that of a watch is $78 less than of phone. How much does the watch cost?
- A hardware store had 20000 bags of cement. If 3,450 bags were sold, how many bags are left in the hardware?
- A woman wants to buy a dress that costs $205, but she has only $156. How much more money does she need to purchase the dress?
- A man started a journey of 5067 km car. Out of the total journey, he covered 3589 by train and the rest 20km by motorbike. How many km did he cover by car?
- The difference between the two numbers is 4509. If the smaller number is 68888, Calculate the value of the larger number?
- There are 600 students in grade 4 class of a school. Out of the total, 200 students have the age of between 9 to 11 years, and the rest have the age of between 12 to 13 years. Calculate the number of students with the age difference of 12 to 13 years?

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