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

Question

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

Bytelearn · Accepted Answer

Identify properties of rational numbers: Identify the properties of rational numbers. 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 that is not zero.Apply definition to a and b: Apply the definition of rational numbers to a and b. Since a and b are both rational, we can write them as a = p/q and b = 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. When we divide a by b, we get (a)/(b) = (p/q) / (m/n). This can be rewritten as (p/q) * (n/m) = (p*n) / (q*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. 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*n) / (q*m) is a rational number since p*n and q*m are integers, and q*m is not zero.

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

Full solution

More problems from Properties of operations on rational and irrational numbers

Related topics

Let aaa and bbb be rational numbers, and let bbb be non-zero. Is ab\frac{a}{b}ba​ rational or irrational?\newlineChoose 111 answer:\newline(A) Rational\newline(B) Irrational\newline(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