Back to The Real Number System — Problem 3 · Task Set 30

HSN.RN Tutor Intake — Rational Exponents and Real Number Properties

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Grade 9·12 problems·~13 min·Common Core Math - HS Number and Quantity·domain·rn

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Concepts

Let $r = p/q$ and $s = m/n$ be any two rational numbers
( $p, q, m, n$ integers, $q \neq 0$ , $n \neq 0$ ). Which statement
correctly explains why $r + s$ is rational?

$r + s = (pn + mq)/(qn)$ . Since $pn + mq$ is an integer and
$qn$ is a nonzero integer, the sum is rational.

$r + s$ must be rational because both terms are positive.

$r + s$ equals a whole number whenever $p = m$ and $q = n$ .

We can verify with examples: $1/2 + 1/3 = 5/6$ , which is
rational, so the sum of any two rationals is rational.