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 this is the case, let’s first define what a rational number is. A rational number is any number that can be expressed as the ratio of two integers, where the denominator is not zero. For example, 2/3, -5/7, and 1/2 are all rational numbers.
When we add or multiply two rational numbers, we are essentially performing operations on the fractions.
For addition:
Let’s say we have two rational numbers, a/b and c/d, where a, b, c, and d are integers and b and d are not zero. We can find their sum by cross-multiplying and then adding the numerators:
(a/b) + (c/d) = (ad + bc) / bd
Since both the numerator (ad + bc) and the denominator (bd) are integers, the sum of two rational numbers is also a rational number.
For example, if we add 2/3 and 1/4:
(2/3) + (1/4) = (2*4 + 1*3) / (3*4) = (8 + 3) / 12 = 11/12
In this case, the sum of 2/3 and 1/4 is 11/12, which is a rational number.
For multiplication:
Let’s say we have two rational numbers, a/b and c/d, where a, b, c, and d are integers and b and d are not zero. We can find their product by multiplying the numerators and denominators:
(a/b) * (c/d) = (ac) / (bd)
Again, since both the numerator (ac) and the denominator (bd) are integers, the product of two rational numbers is also a rational number.
For example, if we multiply 2/3 and 1/4:
(2/3) * (1/4) = (2*1) / (3*4) = 2/12 = 1/6
In this case, the product of 2/3 and 1/4 is 1/6, which is a rational number.
Therefore, no matter whether we add or multiply two rational numbers, the result will always be a rational number.
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