SOLUTION: Prove that the sum of any pair of rational numbers is a rational number.

Question 566235: Prove that the sum of any pair of rational numbers is a rational number.
Found 2 solutions by jim_thompson5910, richard1234:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let p = a/b and q = c/d be two rational numbers, where a, b, c, d are integers.

Now add them:

p + q

a/b + c/d

(ad)/(bd)+(bc)/(bd)

(ad+bc)/(bd)

So p + q = (ad+bc)/(bd), which is a rational number (the numerator and denominator are both integers since integer addition and multiplication are both closed operations)

So this proves that the sum of any pair of rational numbers is a rational number.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Let and be two rational numbers, where a,b,c,d are integers. Then,

Since integers are closed under addition and multiplication, the numerator and denominator will both be integers. Hence, the sum of two rational numbers is a rational number. We can also say that rational numbers are closed under addition.
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