If y is the reciprocal of rational number x, then the multiplicative inverse of y will be _________.

x

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y

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\frac{x}{y}

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\frac{y}{x}

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Solution

The correct option is A $x$
If $y$ is the reciprocal of rational number $x$ , $\frac{1}{x} = y$ .
By cross-multiplying, we will get
$\frac{1}{y} = x$

Now, multiplicative inverse of $y$ is $y^{- 1}$ .
Here, $y^{- 1} = \frac{1}{y} = \frac{1}{\frac{1}{x}} = x$
$∴$ Multiplicative inverse of $y$ is $x$ .

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Question 11
If x + 0 = 0 + x = x, which is rational number, then 0 is called:
(a) identity for addition of rational numbers.
(b) additive inverse of x.
(c) multiplicative inverse of x.
(d) reciprocal of x.

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If y is the reciprocal of rational number x, then the multiplicative inverse of y will be _________.

The correct option is A xIf y is the reciprocal of rational number x, 1x=y. By cross-multiplying, we will get 1y=x Now, multiplicative inverse of y is y−1. Here, y−1=1y=11x=x ∴ Multiplicative inverse of y is x.