The denominator of a rational number is smaller than its numerator by 4.If the denominator is decrease by 5 and the numerator is increased by 6, the number obtained is 5/2. Find the rational number. Give answer quickly with explanation.
Answers
Answer:
The numerator and denominator of the rational number are 19 and 15 respectively.
Step-by-step explanation:
Let the numerator of the rational number be x
Hence, the denominator will be x-4
By condition,
x+6/x-4-5 = 5/2
=> x+6/x-9 = 5/2
=> 2(x+6) = 5(x-9)
=> 2x+12 = 5x-45
=> 2x-5x = - 45-12
=> - 3x = - 57
=> 3x = 57 => x = 57/3 = 19
Therefore, Numerator = x = 19 (ans).
Denominator = x-4 = 19-4 = 15 (ans).
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Answer:
19/15
Step-by-step explanation:
let numerator be x
then, denominator = x-4
when denominator decreased by 5, it becomes x-4-5 = x-9
when numerator increased by 6, it becomes x+6
x+6 / x-9 = 5/2
(x+6)2 = (x-9)5
2x+12 = 5x-45
2x-5x = -45-12
-3x = -57
x = -57/-3
x = 19
numerator = 19
denominator = 19-4
= 15
number = 19/15