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What is Multiplicative inverse of (2/−3)?

  • Last Updated : 17 Aug, 2021

For the representation of different quantities in mathematics we use numbers like 20 apples, 10 bananas, etc.  But for the calculation of these numbers, we need mathematical operations. Following are different types of main mathematical operations:

  • Addition: It is represented by ‘+’ sign. It is used for the summation of different quantities or groups of numbers.
  • Subtraction: It is represented by ‘-‘ sign. It is used when some numbers or quantities are taken out from a group of numbers or quantities.
  • Multiplication: It is represented by ‘×’ sign. It is an extended form of addition. It is used when the same type of quantities or group of numbers is added.
  • Division: It is represented by ‘÷’ sign. It is used when the same type of item gets distributed equally to different positions.

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. 

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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 (2/-3)?

Solution: 

Compare (2/-3) with a/b. 

a = 2, b = -3

Now change the numerator with denominator and denominator with numerator along with their sign.

i.e. (b/a)



Multiplicative inverse = (-3/2)

The multiplicative inverse of (2/-3) is (-3/2).

Similar Questions

Question 1: Find the multiplicative inverse of (-3/7).

Solution:

Compare (-3/7) with (a/b).

We got, a = -3 and b = 7

Exchange numerator and denominator with their sign.

Multiplicative inverse = (7/-3)

The multiplicative inverse of (-3/7) is (7/-3).

Question 2: By which number should (-5) be multiplied to get answer 1?

Solution: 

Basically, we have to find out the multiplicative inverse of (-5). Because when we multiply a number with its multiplicative inverse, we got the answer 1.

For the calculation of multiplicative inverse of (-5), divide 1 by (-5).

So, the multiplicative inverse of (-5) is (1/-5).

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