Why the Sum or Product of Rational Numbers is Always Rational: Explained

sum or product of two rational numbers is

The sum or product of two rational numbers is always a rational number

The sum or product of two rational numbers is always a rational number.

To understand why, let’s first review what rational numbers are. Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. For example, 1/2, 3/4, and -5/6 are all rational numbers.

Now, when we add or subtract two rational numbers, we simply combine the numerators while keeping the same denominator. For example, if we add 1/2 and 3/4, we get (1+3)/(2) which equals to 4/2 or 2. Since both the numerator and denominator are integers, the result is a rational number.

Similarly, when we multiply two rational numbers, we multiply the numerators together and the denominators together. For example, if we multiply 1/2 and 3/4, we get (1*3)/(2*4) which is equal to 3/8. Again, the result is a rational number since both the numerator and denominator are integers.

It is important to note that the only operation between two rational numbers that may result in an irrational number is division. When we divide a rational number by another rational number, the result may or may not be rational. For example, if we divide 1/2 by 3/4, we get (1/2)/(3/4) which is equal to (1/2)*(4/3) or 4/6. In this case, the result is still rational. However, if we divide 1/2 by 1/3, we get (1/2)/(1/3) which is equal to (1/2)*(3/1) or 3/2. In this case, the result is an irrational number.

In summary, the sum or product of two rational numbers is always a rational number. However, division between two rational numbers may result in a rational or an irrational number.

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