Let a be a non-zero rational number. Is (1)/(a) rational or irrational? Choose 1 answer: (A) Rational (B) Irrational (c) It can be either rational or irrational

Evaluate rational number definition: Evaluate the definition of a rational number. A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where p is the numerator and q is the denominator, with the denominator q not equal to zero.Consider given rational number: Consider the given non-zero rational number a. Since a is rational, it can be expressed as a = p/q, where p and q are integers and q is not equal to zero.Evaluate reciprocal of a: Evaluate the reciprocal of a. The reciprocal of a is 1/a. If a is p/q, then 1/a is q/p.Determine if reciprocal is rational: Determine if the reciprocal is rational. Since both p and q are integers, and a is non-zero (which means p is not zero), the reciprocal q/p is also the quotient of two integers with a non-zero denominator. Therefore, 1/a is also a rational number.

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Let
a be a non-zero rational number. Is
(1)/(a) rational or irrational?
Choose 1 answer:
(A) Rational
(B) Irrational
(c) It can be either rational or irrational

Let $a$ be a non-zero rational number. Is $\frac{1}{a}$ rational or irrational? $\newline$ Choose $1$ answer: $\newline$ (A) Rational $\newline$ (B) Irrational $\newline$ (C) It can be either rational or irrational

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Math Problems

Algebra 2

Classify rational and irrational numbers

Full solution

Q. Let

a

be a non-zero rational number. Is

\frac{1}{a}

rational or irrational?

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

\newline

Evaluate rational number definition: Evaluate the definition of a rational number. $\newline$ A rational number is a number that can be expressed as the quotient or fraction $\frac{p}{q}$ of two integers, where $p$ is the numerator and $q$ is the denominator, with the denominator $q$ not equal to zero.
Consider given rational number: Consider the given non-zero rational number $a$ . $\newline$ Since $a$ is rational, it can be expressed as $a = \frac{p}{q}$ , where $p$ and $q$ are integers and $q$ is not equal to zero.
Evaluate reciprocal of $a$ : Evaluate the reciprocal of $a$ . $\newline$ The reciprocal of $a$ is $\frac{1}{a}$ . If $a$ is $\frac{p}{q}$ , then $\frac{1}{a}$ is $\frac{q}{p}$ .
Determine if reciprocal is rational: Determine if the reciprocal is rational. $\newline$ Since both $p$ and $q$ are integers, and $a$ is non-zero (which means $p$ is not zero), the reciprocal $\frac{q}{p}$ is also the quotient of two integers with a non-zero denominator. Therefore, $\frac{1}{a}$ is also a rational number.