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Because a is rational, there exist integers m and n such that a=m/n.

Because b is rational, there exist integers p and q such that b=p/q.

Consider a+b. a+b=(m/n)+(p/q)=(mq/nq)+(pn/mq)=(mq+pn)/(nq).

(mq+pn) is an integer because the product of two integers is an integer, and the sum of two integers is an integer. nq is an integer since the product of two integers is an integer. Because a+b equals the quotient of two integers, a+b is rational.

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Q: Prove that if a and b are rational numbers then a plus b is a rational number?
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