Question

33. The numerator of a fraction is 6 less than the denominator. If one is added to it
denominator, it becomes 1/3 find the fraction.​

Answer 1

$\maltese$Given :-

• Numerator of a fraction is 6 less than denominator
• One is added to denominator it becomes 1/3

$\maltese$ To find:-

• The fraction

$\maltese$ Solution:-

Let the denominator is x

Numerator is x-6

Then the fraction is $\dfrac{x-6}{x}$

If one is added to denominator it becomes 1/3

$\dfrac{x-6}{x+1} =\dfrac{1}{3}$

Cross multiplication

$3(x-6)=1(x+1)$

$3x-18=x+1$

$3x-x = 1+18$

$2x = 19$

$x=\dfrac{19}{2}$

$x = 9.5$

So, the fraction is x-6/x substitute value of x

$\dfrac{x-6}{x}$

$\dfrac{9.5-6}{9.5}$

$\dfrac{3.5}{9.5}$

So, the required fraction is 3.5/9.5

$\maltese$Verification:-

Hence Numerator should be 6 less than denominator

We got fraction 3.5/9.5

Numerator ia 3.5

Denominator is 9.5

9.5 - 3.5 = 6

Since , Numerator is 6 less than denominator

Verified !

If one is added to denominator It should be equal to 1/3

The fraction is 3.5/9.5

$\dfrac{3.5}{9.5+1} = \dfrac{1}{3}$

$\dfrac{3.5}{10.5} = \dfrac{1}{3}$

$\dfrac{35}{105}= \dfrac{1}{3}$

$\dfrac{7}{21} =\dfrac{1}{3}$

$\dfrac{1}{3} = \dfrac{1}{3}$

Hence verified !