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Let
a and
b be rational numbers, and let
b be non-zero. Is
(a)/(b) rational or irrational?
Choose 1 answer:
(A) Rational
(B) Irrational
(C) It can be either rational or irrational

Let $a$ and $b$ be rational numbers, and let $b$ be non-zero. Is $\frac{a}{b}$ 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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Properties of operations on rational and irrational numbers

Full solution

Q. Let

a

and

b

be rational numbers, and let

b

be non-zero. Is

\frac{a}{b}

rational or irrational?

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

\newline

(C) It can be either rational or irrational

Identify properties of rational numbers: Identify the properties of rational numbers. $\newline$ 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 that is not zero.
Apply definition to $a$ and $b$ : Apply the definition of rational numbers to $a$ and $b$ . $\newline$ Since $a$ and $b$ are both rational, we can write them as $a = \frac{p}{q}$ and $b = \frac{m}{n}$ , where $p$ , $q$ , $m$ , and $n$ are integers, and $q$ and $n$ are not zero.
Determine division of rational numbers: Determine the nature of the division of two rational numbers. $\newline$ When we divide $a$ by $b$ , we get $\frac{a}{b} = \frac{p/q}{m/n}$ . This can be rewritten as $\frac{p}{q} \times \frac{n}{m} = \frac{p \times n}{q \times m}$ , which is the multiplication of two rational numbers.
Check if product of rational numbers is rational: Check if the result of multiplying two rational numbers is rational. $\newline$ The product of two rational numbers is rational because the product of two integers is an integer, and the product of two non-zero integers is a non-zero integer. Therefore, $(p \times n) / (q \times m)$ is a rational number since $p \times n$ and $q \times m$ are integers, and $q \times m$ is not zero.

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