How does a closer property prove that the sum of rational number is a rational when the number is rational
To prove that the sum of two rational numbers is rational, we can use the property of closure under addition for rational numbers.
Let's say we have two rational numbers, a/b and c/d, where a, b, c, and d are integers and b ≠ 0 and d ≠ 0.
The sum of these two rational numbers can be expressed as:
(a/b) + (c/d) = (ad + bc) / (bd)
Here, ad + bc is an integer (since adding two integers results in an integer), and bd ≠ 0 because neither b nor d is zero.
Therefore, we can conclude that the sum of the rational numbers (a/b) and (c/d) is rational, as it can be expressed as the ratio of two integers. This demonstrates the closure property of rational numbers under addition.