Let q = a / b and r = c / d be two rational numbers written in lowest terms. Let s = q + r and s = e / f be written in lowest terms. Assume that is not 0. Prove or disprove the following two statements. A.) If b and d are odd, then f is odd. B.) If b and d are even, then f is even.

Question

contestada

Respuesta :

rafikiedu08 rafikiedu08 · Answer 1 · 2022-09-13T14:51:04+02:00

Both the statements are true.

q = a/b and r = c/d.
s = q + r
s = a/b + c/d
s = (ad + bc)/bd
e/f = (ad + bc)/bd
e = ad + bc and f = bd
a) If b and d are odd, we know that the product of two odd numbers is always odd, so f = b*d is odd.
We can prove this because b*d = b*(d-1+1)
b*(d-1+1) = b*(d-1) + b
Since d is odd, d-1 is even, and therefore b*(d-1) is even. Since b is odd and the sum of an odd number and an even number is always odd, the above product is odd.
b) If b and d are even, we know that the product of two even numbers is even, and therefore f = b*d is even.

To learn more about numbers, visit :

https://brainly.com/question/17429689

#SPJ9