The denominator of a rational number is greater than its numerator by 7.13
is subtracted from the numerator and 2 is added to its denominator, the new
tor of a rational number are in the ratio 3:4. If the
1
number becomes
5
the rational number
If a so
place
plac
Find the rational number.
Answers
Answer:
Let the numerator of the fraction be x and the denominator of the fraction be ( x + 7 ) as it is 7 more than the numerator.
∴ Fraction = \dfrac{x}{x+7}
x+7
x
Given that if 3 is subtracted from the numerator and 2 is added to its denominator , the new number becomes 1/5
As numerator was x, 3 subtracted from numerator = ( x - 3 )
As denominator was x + 7 , 2 added to denominator = ( x + 7 + 2 )
= x + 9
New fraction =\dfrac{x-3}{x+9}
x+9
x−3
According to the question, new fraction is equal to 1 / 5.
1 / 5 = ( x - 3 ) / ( x + 9 )
x + 9 = 5( x - 3 )
x + 9 = 5x - 15
9 + 15 = 5x - x
24 = 4x
24 / 4 = x
6 = x
Therefore the required fraction is \dfrac{x}{x+7} =\dfrac{6}{6+7}=\dfrac{6}{13}
x+7
x
=
6+7
6
=
13
6
Rational number = 6 / 13