The numerator of a fraction is 3 less than the denominator. If denominator is added to the numerator and the numerator is subtracted from the denominator, we get 11/3. Find the fraction.
Answers
Answer:
The fraction is 4/7.
Step-by-step explanation:
Given :
The numerator of a fraction is 3 less than the denominator. If denominator is added to the numerator and the numerator is subtracted from the denominator, we get 11/3.
To find :
the fraction
Solution :
Let the numerator of the fraction be x and denominator of the fraction be y.
Then, the fraction = x/y
• The numerator of the fraction is 3 less than the denominator.
x = y - 3
• Denominator is added to the numerator,
new numerator = x + y
= y - 3 + y
= 2y - 3
• Numerator is subtracted from the denominator.
new denominator = y - x
= y - y - 3
= 3
• The new fraction obtained = (2y-3)/3
According to the question,
(2y-3)/3 = 11/3
2y - 3 = 11
2y = 11 + 3
2y = 14
y = 14/2
y = 7
Then,
x = 7 - 3 = 4
Therefore the fraction is 4/7.