CSEET QT - Arithmetic Operations

Arithmetic Operations Definition

Arithmetic operations are a set of four basic operations to be performed to add, subtract, multiply or divide two or more quantities. They include the study of numbers including order of operations which are useful in all the other parts of mathematics such as algebra, data handling, and geometry. We cannot solve the problem without using the rules of arithmetic operations. The arithmetic operations include four basic rules that are addition, subtraction, multiplication, and division. There is a particular symbol used for each of the four arithmetic operations which are given in the image below.

Four Basic Arithmetic Operations

Here we are discussing the four basic rules of arithmetic operations for all real numbers.

· Addition (sum; ‘+’)

· Subtraction (difference; ‘-’)

· Multiplication (product; ‘×’ )

· Division (÷)

Addition

The addition is a basic mathematical skill of finding or calculating the total of two or more numbers, or we can say in simple words adding things together. It is denoted by the symbol ‘+’. When we add two or more numbers it results in a single term. The order of numbers does not matter in the addition.

For example: 67 + 85 = 152

Subtraction

The subtraction arithmetic operation shows the difference between two numbers. It is denoted by the symbol ‘-‘. Subtraction is mostly used to find out what is left when things are taken away or in other words, taking one number away from another number.

For example: 70 - 59 = 21

Multiplication

The repeated addition is known as multiplication. It is represented by the symbol ‘×’. Multiplication as an arithmetic operation helps us to find out the total when a number is repeating itself a number of times. For example, 2 times 3 is 6. Mathematically, we can write it as 2 × 3 = 6. Multiplicand and multiplier are the terms used in the multiplication process. The product is the term we use for the result of the multiplication of multiplicand and the multiplier.

For example: 10 × 31 = 310

In the above example, “10” is the multiplier, “31” is the multiplicand, and the result “310” is known as the product.

Division

The division is an act of dividing something into equal parts or groups. It is one of the four basic arithmetic operations which gives a fair result of equal sharing. The division is an inverse of multiplication. For example, 2 groups of 3 pencils each make 6 pencils (2 × 3) in multiplication, and in the case of division 6 pencils divided into 2 equal groups give 3 pencils in each group. It is represented by the symbol ‘÷ ’. So, here we can write it as 6 ÷ 2 = 3.

Arithmetic Operations with Whole Numbers

With whole numbers, we can easily perform the four basic arithmetic operations. Whole numbers are a set of numbers that starts from 0 and go on up to infinity. Such numbers do not have any fractional or decimal parts. The addition of two or more whole numbers always leads to an increase in the final sum. For example, if we add three numbers 4, 5, and 6, we will get 4 + 5 + 6 = 9 + 6 = 15. So, here 15 is greater than all the three addends. The addition of any number with 0 always results in the same number, and if we add 1 to any whole number, we get its consecutive number or successor.

In the case of whole numbers, we always subtract a smaller quantity from a larger quantity to get a difference that is less than the minuend. Subtraction of 0 from any number always results in the same number, and deducting 1 from a number gives its predecessor. Multiplication of two or more whole numbers can be done by using multiplication tables. The product is always greater than both the numbers except in the case of multiplication with 1 and 0. A number multiplied to 0 always results in 0 and multiplication with 1 gives us the same number as the product.

The division of two whole numbers may or may not result in whole numbers. If the quotient is a whole number, it means that the dividend is a multiple of the divisor. If it is not, then it will result in a decimal number as the quotient.

Arithmetic Operations with Rational Numbers

Arithmetic operations with rational numbers are the same as that of whole numbers. The only difference is that rational numbers are in the form of p/q, where p and q are integers and q is not equal to 0. While adding or subtracting two rational numbers, we have to take the LCM of the denominators.