Question

Докажите,что если r1 и r2 - рациональные числа(r не равно 0),то r1/r2 - рациональное число. Помогите,пожалуйста

Answer 1

Из определения рационального  числа:
r1=p1/q1
r2=p2/q2
p1 и p2-  целые числа
q1 и q2 -натуральные  числа.
r1/r2=p1*q2/p2*q1
В  числителе  целое число  ,а  в знаменателе  натуральное  (в  противном случае знак минус ,если в знаменателе он есть  ,всегда можно  переместить  в числитель и ничего  не изменится.)
То  есть  r1/r2-рациональное  число

Answer 2

Proof that if r1 and r2 are rational numbers (r is not equal to 0), then r1/r2 is a rational number

To prove that if r1 and r2 are rational numbers (r is not equal to 0), then r1/r2 is a rational number, we can use the definition of rational numbers and basic arithmetic operations.

Let's assume that r1 and r2 are rational numbers. By definition, a rational number can be expressed as the quotient of two integers. Let's say r1 = a/b and r2 = c/d, where a, b, c, and d are integers and b and d are not equal to 0.

Now, let's calculate r1/r2:

r1/r2 = (a/b) / (c/d)

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:

r1/r2 = (a/b) * (d/c)

Multiplying fractions is done by multiplying the numerators and denominators separately:

r1/r2 = (a * d) / (b * c)

Since a, b, c, and d are integers, the product of a * d and b * c is also an integer. Therefore, r1/r2 can be expressed as the quotient of two integers, making it a rational number.

Thus, we have proved that if r1 and r2 are rational numbers (r is not equal to 0), then r1/r2 is a rational number.