sum or product of two rational numbers is
rational
also a rational number.
To understand why this is true, we first need to define what a rational number is. A rational number is any number that can be expressed as a fraction, where the numerator and denominator are integers (whole numbers). For example, 3/4, -7/2, and 0.6 (which can also be written as 3/5) are all rational numbers.
Now, suppose we have two rational numbers, a/b and c/d, where a, b, c, and d are all integers (and b and d are non-zero). To find their sum, we need to add them together:
a/b + c/d = (ad + bc) / bd
Notice that the numerator (ad + bc) and denominator (bd) are both integers, since a, b, c, and d are all integers. Therefore, the sum of two rational numbers is also a rational number.
To find the product of two rational numbers, we need to multiply them together:
(a/b) * (c/d) = ac / bd
Again, the numerator (ac) and denominator (bd) are both integers, so the product of two rational numbers is also a rational number.
In conclusion, we can say that whenever we add or multiply two rational numbers, the result is always a rational number.
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