Arithmetic: Definition and Examples

Arithmetic: Arithmetic is the fundamental area of Mathematics that studies numbers, especially the properties of operation such as addition, subtraction, multiplication and division. Arithmetic includes operations such as addition, subtraction, multiplication, and division as well as more complex computations such as percentages, logarithms, exponentiation, and square roots. Arithmetic is an integral part of number theory along with Algebra and Geometry. The term arithmetic was introduced in the 20th century. 

It’s been used to perform routine calculations since ancient times. These include measurements, labeling, and other computations to achieve precise results. The name derives from the Greek word “arithmos” which means “numbers”. Arithmetic is taught early so that students get a grasp of the basics of Mathematics and can later solve problems accurately. You can check NCERT Solutions for Class 10 Maths Chapter 1 for a better understanding of the concept. We have provided detailed information on arithmetic in this article. Read on to find out about its definition, arithmetic operations and examples.

What is Arithmetic?

Arithmetic is a branch of mathematics that deals with numbers and the operations such as addition, subtraction, multiplication, and division. The word arithmetic was derived from the Greek word “arithmos” meaning numbers.

According to the fundamental theorem of arithmetic, any integer greater than 1 has a unique prime factorization excluding the orders of the factors. This theory was provided by Carl Friedrich Gauss in 1801. There are four arithmetic operations such as addition, subtraction, multiplication, and division.

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Arithmetic Operations

The basic arithmetic operations are as follows:

Addition

Addition is the basic operation of arithmetic. It combines two or more numbers to form a single number. The addition is denoted as (+). We can say that adding more than two numbers is called summation. Addition is commutative and associative.

For example, 5+5= 10 or 7+3= 10

Subtraction

The difference between two numbers is called subtraction. It is the inverse operation to the addition i.e., the minuend minus the subtrahend. We can say that the difference is positive when the minuend is greater than the subtrahend whereas, the difference is negative when the minuend is less than the subtrahend. The difference will be zero if the minuend and subtrahend are equal. The Subtraction is denoted as (-). It is neither commutative and associative.

For example, 5-2 = 3

Multiplication

Multiplication combines two or more values to form a product. The original number is called a multiplier and multiplicand. Multiplication is commutative and associative. It plays important role in the distributive property over addition and subtraction. Multiplying by 1 results in the same number.

It is denoted by . or x. We can express the product as a. b or a x b. In the case of computer programming language, it is expressed with asterisk a*b.

For example, 7 x 7 = 49

Division

The division is an inverse operation to multiplication. It has a quotient of two numbers i.e., dividend divided by a divisor. If the dividend is larger than the divisor, the quotient will be greater than 1 for positive numbers. On the other hand, the quotient will be less than or equal to 1 for any negative numbers. The division is neither commutative nor associative. It is denoted by / or ÷.

For example, 3 ÷ 5= 0.6

Examples of Arithmetic

Some of the arithmetic questions and solutions are given below. These arithmetic practice problems will help you a lot in understanding the concept.

Example 1: Express each number as a product of its prime factors:

(i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

Solution:

(i) 140 = 2 × 2 × 5 × 7 = 22 × 5 × 7

(ii) 156 = 2 × 2 × 3 × 13 = 22 × 3 × 13

(iii) 3825 = 3 × 3 × 5 × 5 × 17 = 32 × 52 × 17

(iv) 5005 = 5 × 7 × 11 × 13

(v) 7429 = 17 × 19 × 23

Example 2: Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

(i) 26 and 91

Solution: Given, 26 and 91

26 = 2 × 13

91 = 7 × 13

13 is the largest number which divides both 26 and 91. So, HCF = 13.

LCM = 2 × 7 × 13 = 182

Product of the two numbers = 26 × 91 = 2366

HCF × LCM = 13 × 182 = 2366

Hence, product of two numbers = HCF × LCM

FAQs on Arithmetic

The frequently asked questions on arithmetic are given below:

Practice Class 10 Maths and Science Questions

We hope this detailed article on Arithmetic helps you. Make the best use of them and crack your CBSE Class 10 Board Exam with good scores and choose the career you want for your future.

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