In a fraction the numerator and denominator differ by 1 & numerator is less than denominator. If 1 is added to the numerator and 4 is added to denominator the fraction becomes 1/2. Find the fraction.
Answers
Step-by-step explanation:
Given :-
In a fraction the numerator and denominator differ by 1 & numerator is less than denominator. If 1 is added to the numerator and 4 is added to denominator the fraction becomes 1/2.
To find :-
Find the fraction ?
Solution :-
Let the numerator of a fraction be X
Then the denominator = X+1
Since Numerator < Denominator
Then the original fraction = X/(X+1)
If 1 is added to the numerator then it
becomes X+1
If 4 is added to the denominator then it becomes X+1+4 = X+5
The new fraction = (X+1)/(X+5)
According to the given problem
The new fraction = 1/2
=> (X+1)/(X+5) = 1/2
On applying cross multiplication then
=> 2(X+1) = 1(X+5)
=> 2X+2 = X+5
=> 2X-X = 5-2
=> X = 3
The value of X = 3
Therefore, Numerator = 3
The Denominator = X+1 = 3+1 = 4
Therefore, Fraction = 3/4
Answer:-
The original fraction for the given problem is 3/4
Check:-
The fraction = 3/4
the numerator and denominator differ by 1
and
numerator is less than denominator.
If 1 is added to the numerator and 4 is added to denominator the fraction becomes
=> (3+1)/(4+4)
=> 4/8
=> 1/2.
Verified the given relations in the given problem.