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Multiplicative Inverse

Rational Numbers II - Concepts

Identity Property

Commutative Property

Multiplicative Inverse

Division of Rational Numbers

Multiplication of Rational Numbers

Rational Numbers between Two Rational Numbers

Properties of Rational Numbers

Simplification of Rational Numbers

Class - 8th IMO Subjects

Concept Explanation

Multiplicative Inverse

Multiplicative Inverse:

For every non-zero rational number $large frac{a}{b}$ there exists a rational number $large frac{c}{d}$ such that $large frac{a}{b}times frac{c}{d}=1=frac{c}{d}times frac{a}{b}$

The rational number $large frac{c}{d}$ is called the multiplication inverse or reciprocal of a denoted be $large left ( frac{a}{b} right )^{-1}$

For any non-zero rational number $large frac{a}{b}$ , we have

$large frac{a}{b}times frac{b}{a}=frac{atimes b}{btimes a}=frac{ab}{ba}=frac{ab}{ab}=1$ and $large frac{b}{a}times frac{a}{b}=frac{btimes a}{atimes b}=frac{ba}{ab}=frac{ab}{ab}=1$

$large therefore ;frac{a}{b}times frac{b}{a}=1=frac{b}{a}times frac{a}{b}$

It follows from this result that the multiplication inverse or reciprocal of $large frac{a}{b}$ is $large frac{b}{a}$ .

That is, $large left ( frac{a}{b} right )^{-1}=frac{b}{a}$

It also follows from the result (i) that the multiplicative inverse of $large frac{b}{a}$ is $large frac{a}{b}$ .

That is, $large left ( frac{b}{a} right )^{-1}=frac{a}{b}$ . But, $large frac{b}{a}=left ( frac{a}{b} right )^{-1}$

$large therefore ;;left { left ( frac{a}{b} right )^{-1} right }^{-1}=frac{a}{b}$

In other words, the reciprocal of the reciprocal of a rational number is the number itself. Thus, we have

The reciprocal of $large frac{5}{12}$ is $large frac{12}{5}$ i.e., $large left ( frac{5}{12} right )^{-1}=frac{12}{5}$

The reciprocal of $large frac{-3}{7}$ is $large frac{7}{-3}$ i.e., $large left ( frac{-3}{7} right )^{-1}=frac{7}{-3}$

The reciprocal of -5 is $large frac{1}{-5}$ , since $large -5times frac{1}{-5}=frac{-5}{1}times frac{1}{-5}=frac{-5times 1}{-5times 1}=1$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Find the multiplicative inverse of : - 1
A. -1	B. Doest Not exist	C. 1	D. -2
Right Option : A
View Explanation

Question : 2

Reciprocal of $2frac {1}{3}$ is ___________________
A. $frac {7}{3}$	B. $-frac {7}{3}$	C. $-frac {3}{7}$	D. $frac {3}{7}$
Right Option : D
View Explanation

Question : 3

7 x (1/7) = 1 is explained by which property?
A. Multiplicative inverse	B. Additive inverse	C. Additive identity	D. Multiplicative identity
Right Option : A
View Explanation

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Chapters

Exponents and Power II

Prerequiste

Visualising Soild Shapes

Ratio and Proportion

Introduction to Trigonometry

Constructions

Quadrilaterals II

Quadrilaterals I

Linear Equations in One Variable II

Linear Equations in One Variable I

Cube and Cube Roots

Square and Square Root II

Square and Square Root I

Rational Numbers II

Rational Numbers I

Mensuration I

Exponents and Power I

Direct and Inverse Variation II

Direct and Inverse Variation I

Algebraic Expressions

Comparing Quantities III

Comparing Quantities II

Comparing Quantities I

Playing With Numbers

Introduction to Graphs

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Multiplicative Inverse

Multiplicative Inverse

Students / Parents Reviews [10]

Om Umang

Ayan Ghosh

Cheshta

Eshan Arora

Barkha Arora

Shreya Shrivastava

Hiya Gupta

Shivam Rana

Aman Kumar Shrivastava

Manish Kumar