Math CentralQuandaries & Queries


Question from Fathia, a parent:

Could please help me with this question?

Prove that if a and b are rational numbers then a + b is a rational number.

Thank you,

Hi Fathia,

The definition of a rational number is any number that can be expressed as the ratio of two integers that have no common factors (i.e. a fraction in lowest terms) and the denominator is not zero.

Thus, if a is a rational number, there must exist some w and x which are integers, where x is not equal to zero and in which a = w/x. Furthermore, w and x have no common factors (besides +/-1 of course) and
x ≠ 0.

Use this starting point to determine what this says about b. Then use w, x and the variables you use for describing the value of b to make observations and reasoned conclusions about the sum of the two fractions.

Hope this helps,
Stephen La Rocque.

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