Let a and b be rational numbers. Is a*b rational or irrational? Choose 1 answer: (A) Rational (B) Irrational (c) It can be either rational or irrational

Definition of Rational Numbers: Evaluate the definition of rational numbers. Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. This means that any rational number can be written in the form p/q, where p and q are integers and q is not equal to zero.Product of Two Rational Numbers: Consider the product of two rational numbers a and b. Let a = p/q and b = r/s, where p, q, r, and s are integers and q and s are not zero. The product of a and b is (p/q) * (r/s).Calculation of Product: Calculate the product of two rational numbers. (p/q) * (r/s) = (p*r) / (q*s) Since the product of two integers is an integer, p*r is an integer, and q*s is also an integer. Moreover, q*s is not zero because neither q nor s is zero.Determining Rationality of the Product: Determine if the product is rational or irrational. The product (p*r) / (q*s) is in the form of an integer divided by a non-zero integer, which fits the definition of a rational number. Therefore, the product of two rational numbers is rational.

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Let
a and
b be rational numbers. 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. Is $a \times b$ 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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Math Problems

Algebra 2

Classify rational and irrational numbers

Full solution

Q. Let

a

and

b

be rational numbers. Is

a \times b

rational or irrational?

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

\newline

Definition of Rational Numbers: Evaluate the definition of rational numbers. $\newline$ Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. This means that any rational number can be written in the form $\frac{p}{q}$ , where $p$ and $q$ are integers and $q$ is not equal to zero.
Product of Two Rational Numbers: Consider the product of two rational numbers $a$ and $b$ . $\newline$ Let $a = \frac{p}{q}$ and $b = \frac{r}{s}$ , where $p, q, r,$ and $s$ are integers and $q$ and $s$ are not zero. The product of $a$ and $b$ is $b$ $0$ .
Calculation of Product: Calculate the product of two rational numbers. $\newline$ $(\frac{p}{q}) \times (\frac{r}{s}) = \frac{p \times r}{q \times s}$ $\newline$ Since the product of two integers is an integer, $p \times r$ is an integer, and $q \times s$ is also an integer. Moreover, $q \times s$ is not zero because neither $q$ nor $s$ is zero.
Determining Rationality of the Product: Determine if the product is rational or irrational. $\newline$ The product $(p \cdot r) / (q \cdot s)$ is in the form of an integer divided by a non-zero integer, which fits the definition of a rational number. Therefore, the product of two rational numbers is rational.