sum or product of two rational numbers is
rational
always a rational number.
When two rational numbers are multiplied, the result is always a rational number. This is because the product of two rational numbers can always be expressed as a ratio of two integers. For example, if we have the rational numbers 1/2 and 3/4, their product is (1/2) x (3/4) = 3/8, which can be expressed as a ratio of two integers (3 and 8).
When two rational numbers are added or subtracted, the result may or may not be a rational number. This is because the sum or difference of two rational numbers may result in an irrational number. For example, if we add the rational numbers 1/2 and 1/3, the result is (1/2) + (1/3) = 5/6, which is a rational number. However, if we subtract the rational numbers 1/2 and 1/√2, the result is (1/2) – (1/√2) = (1/2) – (√2/2), which is an irrational number.
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