Question

Keishas teacher gives her the following information: • m,n,p, and q are all integers and p =/ 0 and q =/ 0 • A= m/q and B = n/pAnswer: A+B = mp + nq / pq, so the sum of a rational number and an irrational number is an irrational number A•B = mp + nq / pq, so the product of two rational number is a rational number A + B = mp + nq / pq, so the sum of two rational number is a rational number. A•B = mp + nq / pq , so the product of two irrational number is an irrational number

Answer 1

Let A and B be the following fractions:

$\begin{gathered} A=\frac{m}{q} \\ B=\frac{n}{p} \\ p,q\ne0 \end{gathered}$

if we add A and B, we get:

$A+B=\frac{m}{q}+\frac{n}{p}=\frac{mp+nq}{pq}$

therefore, the sum of two rational numbers is a rational number