Multiplicative Inverse


 
 
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

Reciprocal of  frac {6}{3}  is  __________________

Right Option : C
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Explanation
Question : 2

7 x (1/7) = 1  is explained by which property?

Right Option : A
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Explanation
Question : 3

Find the multiplicative inverse of : - 1

Right Option : A
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Explanation
 
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