Mathematical operations

Introduction:

Arithmetic operations are a fundamental part of mathematics. The use of these operations began in prehistoric times, is present in much ancient Greek work, and is evident in the work of Leonardo da Vinci. In this article, we look at the mathematical operations that are used to perform calculations and discuss their advantages and disadvantages. Sometimes when a student starts to learn math they need to know what mathematical operations are or how they are used. This article will help students understand the different types of mathematical operations that can be used alongside each other for solving problems as well as how they were discovered over time through history. It also talks about what makes some arithmetic operations better than others when being implemented into a problem-solving process by presenting examples with pros and cons for each type of operation.

What are Arithmetic Operations?

Arithmetic Operations are the basic mathematical operations of addition, subtraction, multiplication, and division. Like all the other branches of mathematics, also arithmetic operations are divided into Fundamental Arithmetic operations and Advanced Arithmetic Operations.

Advanced Arithmetic Operations are carried out on a large set of numbers, and so also considered to be difficult.

Types of Basic Arithmetic Operations:

Basic Arithmetic Operations includes only the four operations that we have just discussed. We will be learning all the four basic arithmetic operations here, so let us first get familiar with each of these basic arithmetic operations separately.

1) Addition

We can add two numbers only. If a and b are positive then you can add them to get the sum of their values, If a and b are negative then you cannot add them. Example: To add 5 and 7, take one plus the other 7+5=12

2) Subtraction

Here, we can subtract any number from another number. For example, suppose we want to subtract 10 from 15, we will have 5 left. We can subtract 10 from 5 to get -5 and so we have -15

Example:

To subtract 9 from 18, we will have 16 left. So 18–9=9 so subtraction operation gives us the remainder of division i.e. 9.

3) Multiplication

Multiplication of any two numbers means adding them together and then multiplying the result with the third number. For example, to multiply 5 and 50 we will have to add 5×50=500 and multiply 500 with 3 to get 1,000.

Example: To multiply 7×6, we will have 24 left so, 24×6=216

4) Division

The division is another basic mathematical operation, that involves the division of all the numbers by a given number. If a and b are positive, then you can divide both of them for getting remainder. Examples: To divide 7 by 2 (i.e., 7 ÷ 2), we will get 3 as remainder i.e. 7 × 3 = 21.

To divide 35 by 2: 35 ÷ 2 = 17 and so we have 17 left, which is the remainder of the division.

Example: To divide 10 by 2 will give 5 as remainder. Multiplication by two is the same as subtraction by two and dividing by two gives the remainder of the division

These four arithmetic operations that we discussed above are called the “Basic Arithmetic Operations” because they are used in all the next higher mathematical operations and can be performed easily on numbers up to a certain extent.  We call these operations “basic” because they involve basic concepts such as adding, subtracting, multiplying, and dividing numbers. Mathematical operation questions are very common to every kind of student and therefore are a must for solving an exam.

Basic Arithmetic Properties

The basic arithmetic properties can be classified into:

1) Associative Property of Addition and Multiplication

When the numbers involved in addition or multiplication are the same, then the order in which they are added or multiplied does not matter. For example 3+2×2=6. In other words, adding two pairs of numbers is equal to adding first one pair and then adding another pair. Similarly, multiplying two pairs of numbers is equal to first multiplying one pair and then multiplying another pair.

2) Commutative property: The order of operations does not matter in subtraction and addition. For example: –(–5)+1=5+1. The order of operations also does not matter in multiplication and division. For example: 5×2=10 ÷ 2 = 5 ÷ 2 = 10

3) Distributive property: Distributive Property of multiplication over addition.

1. a) The sum of a number and the product of the same number and another number is equal to the sum of that other number and the product of that number with itself. For example: (3+2×3) + (3×3)=7+9=16
2. b) The sum of two numbers is equal to the product of one plus the first, one minus the second, one multiplied by itself and divided by 2, that is one squared, times the second. For example: (1+8)+(1-8)=17

4) Zero property: Multiplication by zero gives zero.

Conclusion:

In this article, we have explained all the basic arithmetic operations which can be used to perform any mathematical operation on a pair of numbers.  Next time you see questions with mathematical operations on them, you will not face any difficulty in solving them.  Remember, whatever time you practice something on paper, it becomes easier for you to solve it next time in an exam. So practice these operations whenever you have time and remember to go back to this article whenever you need.