Question

The numerator of a rational number is 17 more than its denominator.The numerator of its absolute is 7 more than its denominator.Find the rational number.

Answer 1

Let the absolute value of rational number be x/y. 

Then the rational number will be -x/y, -x/-y, or x/-y. 

Considering -x/y, 

$- x = y + 17$
$x = y + 7$
$- x = - (y + 7) = - y - 7$

$y + 17 = - y - 7$
$= 2y = - 17 - 7 = - 24$
$y = - 24 / 2 = - 12$
$x = - 12 + 7 = - (12 - 7) = -5$

∴ -x/y = -(-5)/-12 = 5/-12

But 5/-12 would not be the answer because in its absolute value 5/12, the numerator 5 is not 7 more than the denominator 12. Here numerator is 7 less than denominator. 

Considering -x/-y, 

$- x = - y + 17 = 17 - y$
$x = y + 7$
$- x = - (y + 7) = - y - 7$

$17 - y = - y - 7$
$= y - y = - 17 - 7$
$= - 24 = 0$

Here we get a wrong equation. So we can't find the answer through -x/-y as the rational number. 

Considering x/-y, 

$x = - y + 17 = 17 - y$
$x = y + 7$

$17 - y = y + 7$
$= 17 - 7 = y + y$
$= 2 y = 10$
$y = 10 / 2 = 5$
$x = 5 + 7 = 12$

∴ Rational number x/-y = 12/-5 (12 = -5 + 17)
and absolute value x/y = 12/5 (12 = 5 + 7). 

So the answer is 12/-5. 

Hope this answer will be helpful. 

Answer 2

Step-by-step explanation:

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