the sum of numerator and denominator of a fraction is 3 less than twice the denominator. If each of the numerator and denominator is decreased by 1 , the fraction becomes 1/2 . Find the fraction graphically.
Answers
Answer: 4/7
Step-by-step explanation:
Lets say the fraction is a/b (a is the numerator and b is the denominator)
Sum of the numerator and the denominator of a fraction is 3 less than twice the denominator
a + b = 2b - 3
If the numerator and denominator are both decrease by 1, the numerator become half the denominator.
a - 1 = 1/2 (b - 1)
Now we do the algebra. We start with the equation we just wrote.
2a - 2 = b - 1
b = 2a - 1
From the first equation,
a + b = 2b - 3
a = b - 3
We can substitute b = 2
a − 1 into this.
a = 2a - 1 - 3
- a = - 4
a = 4
b = 2a - 1 = 2 (4) - 1 = 7
Fraction is
a = 4
b = 7
a/b = 4/7
Check:
Sum of the numerator (4) and the denominator(7) of a fraction is 3 less than twice the denominator.
(4) (7) = 2 (7) - 3 Correct
If the numerator (4) and denominator (7)are both decrease by 1, the numerator become half the denominator.
3 = 1/2 (6) Correct
That is why the answer is 4/7.