Arithmetic is a branch of mathematics that deals with numerals, number system, and their operations from ancient times. The term was originally derived from the Greek word “arithmos” which simply means numbers. It is preferred to get a definite single value. The traditional methods of arithmetic operations are constituent of addition, difference, multiplication, and division. These operations are being carried out for the purpose of human social and economical development for centuries.
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 calculating methods for percentage, logarithm, exponentiation and square roots, etc.
Basic Operations in Arithmetic
The four basic operations of arithmetic are discussed below:
Addition or also known as summation is an operation to combine two or more values or numbers into a single value. The process of adding n numbers of value is called summation.
While adding 0 to any value gives the same result. Hence, 0 is known as the identity element of addition. For example: if we add 0 with 1 the result will still be 1.
0 + 1 = 1
Whereas, when we add the opposite value of the same number is said to be an inverse element. The result of the addition of inverse elements is an identity element that is 0. For example, if we add 1 with its opposite value -1, then the result would be
1 + (-1) = 0
Subtraction is the inverse of addition. It is the arithmetic operation that determines the difference between two values (i.e. minuend minus the subtrahend) is subtraction. In the cases, where the minuend is greater than the subtrahend, the difference is positive.
5 – 2 = 3
While, if the subtrahend is greater than minuend the difference between them will be negative.
2 – 5 = -3
The operation which combines two values to give a single product of them is called multiplication. The two values involved in the operation of multiplication are known as multiplicand and multiplier.
The product of two values is supposedly p and q is expressed in p.q or p × q form.
The division is the inverse of multiplication. It is the operation that computes the quotient of two values. The two values involved in it are known as dividends by the divisor. If the quotient is more than 1, if the dividend is greater than the divisor the result would be a positive number.
9/3 = 3
What is Multiplicative Inverse?
If the multiplication of two rational numbers gives 1 as result, then these two rational numbers are termed as the multiplicative inverse of each other. In other terms, we can say that the reciprocal of numbers is the multiplicative inverse of each other. For the calculation of multiplicative inverse of rational number usually, numerator and denominator got exchanged along with the sign and for the calculation of multiplicative inverse of a number, divide 1 by the number.
How to Find Multiplicative Inverse?
Suppose a rational number is ‘a/b’ where b is not equal to zero, and we have to find out the multiplicative inverse of that number.
Step 1: Exchange the numerator and denominator along with their sign i.e. ‘a’ is changed by ‘b’ and ‘b’ is changed by ‘a’. So the multiplicative inverse is ‘b/a’.
Step 2: For multiplicative inverse of a number ‘a’, divide 1 by that number along with their sign.
The multiplicative inverse of ‘a’ = 1/a.
What is the multiplicative inverse of 7?
Compare (7) with a/b.
a = 7, b = 1
Now change the numerator with denominator and denominator with numerator i.e. (b/a)
Multiplicative inverse = 1/7
The multiplicative inverse of 7 is 1/7
Question 1: Find the multiplicative inverse of (-2/7).
Compare (-2/7) with (a/b).
We got, a = -2 and b = 7
Exchange numerator and denominator with their sign.
Multiplicative inverse = (7/-2)
The multiplicative inverse of (-2/7) is (7/-2).
Question 2: By which number should (-3) be multiplied to get answer 1?
Basically, we have to find out the multiplicative inverse of (-3). Because when we multiply a number with its multiplicative inverse, we got the answer 1.
For the calculation of multiplicative inverse of (-3), divide 1 by (-3).
So, the multiplicative inverse of (-3) is (1/-3).