What are the four branches of arithmetic?

Arithmetic probably has the longest history during the time. It is a method of calculation that is been in use from ancient times for normal calculations like measurements, labeling, and all sorts of day-to-day calculations to obtain definite values. The term got originated from the Greek word “arithmos” which simply means numbers.

Arithmetic is the elementary branch of mathematics that specifically deals with the study of numbers and properties of traditional operations like addition, subtraction, multiplication, and division.

Besides the traditional operations of addition, subtraction, multiplication, and division arithmetic also include advanced computing of percentage, logarithm, exponentiation and square roots, etc. Arithmetic is a branch of mathematics concern with numerals and their traditional operations.

Basic Operations of Arithmetic

Arithmetic has four basic operations that are used to perform calculations as per the statement:

• Addition
• Subtraction
• Multiplication
• Division

Addition

The process of taking two or more numbers and adding them together is termed as Addition, or you can say it is the total sum of all the numbers. Addition of Whole Numbers results in a number greater than the added numbers. The procedure of adding more than two values is called summation and also involves methods to add n number of values.

3 + 3 = 6

It is represented by symbol ( + )

The identity element of addition is 0, which clearly means that adding 0 to any value gives the same result. The inverse element of addition is the opposite of any value, which means that adding the opposite of any digit to the digit itself gives the additive identity.

 For example, 

The opposite of 5 is -5, therefore 5 + (-5) = 0.

Subtraction

The process in which we remove objects from the original group are termed as Subtraction. In the operation of subtraction, the numerical value of the original number becomes less. 

Subtraction can also be labelled as the inverse of addition. It also computes the difference between two values, i.e., the minuend minus the subtrahend. 

If the minuend is greater than the subtrahend then the difference is positive. If the minuend is less than the subtrahend then the result is negative, and 0 if the numbers are equal.

10 – 5 = 5

It is represented by symbol ( – )

Division

Its the process of  breaking a large object or group into smaller parts or groups. The division is the inverse of multiplication. It also computes the quotient of two numbers and the dividend that is divided by the divisor. The quotient is more than 1 if the dividend is greater than divisor for any well-defined positive number or else it is smaller than 1.

• The number or the larger group of numbers that gets divided is known as the Dividend
• The number which divides the dividend is known as the Divisor
• The number that obtained on dividing the dividend by a Divisor is termed as the Quotient
• The number which left after dividing is called Remainder.

26 ÷ 6 = 4 Is Quotient; 2 Is Remainder

It is represented by symbol ( ÷ )

Multiplication

Multiplication is the process of adding the same number to itself a certain number of times. Multiplication also combined two values like addition and subtraction into a single value or the product. These two original values are known as the multiplicand and the multiplier, or called as factors.

The product of a and b is expressed as a·b or a × b and when we multiply two numbers, the result is called a Product.

5 × 6 = 30

It is represented by symbol ( × )

Sample Questions

Question 1: The sum of two numbers is 40, and their difference is 30. Find the numbers.

Solution: 

Let assume the numbers be x and y. Now, as per the given situation,

x + y = 40……………………(i)

and x – y = 30…………………….(ii)

We can write, x = 40-y, from equation (i),

Therefore, putting the value of x in equation (ii), we get 

40 – y – y = 30

40 -2y = 30

2y = 40-30 

2y = 10

y = 10/2

y = 5

and x = 40 – y  (from above equation)

= 40-5 

x  = 35

Therefore, the two numbers are 35 and 5.

Question 2:  Solve 30+5(27÷3)-9

Solution:

30 + 5(27 ÷ 3) – 9

= 30 + 5 (9) – 9

= 30 + 45 – 9

= 66