Question

In a given fraction, the denominator is greater than the numerator by 2, if 7 is added to the numerator, the resulting fraction becomes greater than the given fraction by 1.Find the fraction.

Answer 1

Question :

In a given fraction , the denominator is greater than the numerator by 2, if 7 is added to the numerator, the resulting fraction becomes greater than the given fraction by 1 . Find the fraction .

Solution :

What is a fraction ?

• A fraction is a decimal number , which can be written in the  form of $\rm \dfrac{x}{y}$ , where x denotes numerator and y denotes denominator .

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According to question ,

" The denominator is greater than the numerator by 2 " ,

Let numerator be ' x ' , then

Denominator = ' x + 2 '

So , Given fraction is  $\rm \dfrac{x}{x+2}$

" If 7 is added to the numerator, the resulting fraction becomes greater than the given fraction by 1 "

If 7 is added to numerator , numerator becomes ' x + 7 '

Resulting fraction is  $\rm \dfrac{x+7}{x+2}$

The resulting fraction becomes greater than the given fraction by 1

$:\implies \sf \dfrac{x+7}{x+2}=\dfrac{x}{x+2}+1$

$:\implies \sf \dfrac{x+7}{x+2}=\dfrac{x+x+2}{x+2}$

$:\implies \sf x+7=x+x+2$

$:\implies \sf x+7=2x+2$

$:\implies \sf 7-2 =2x-x$

$:\implies \sf 5=x$

$:\implies \textsf{\textbf{\pink{x = 5 }}}\ \; \; \bigstar$

So , Fraction is  $\sf \dfrac{x}{x+2}=\dfrac{5}{5+2}=\green{\dfrac{\textsf{\textbf{5}}}{\textsf{\textbf{7}}}}\ \; \; \bigstar$

Answer 2

Given :-

In a given fraction, the denominator is greater than the numerator by 2, if 7 is added to the numerator, the resulting fraction becomes greater than the given fraction by 1.

To Find :-

Fraction

Solution :-

At first lets assume the numerator as x. Then, the numerator is greater by 2. So, New numerator becomes x + 2. Now,

7 is added to only denominator. So, the denominator become x + 7.

Now,

The fraction become greater than by 1. So, new fraction is (x + 1/x)+ 1

Let the fraction be

$\sf \dfrac{x + 7}{x + 2} =\dfrac{x + 1}{x} + 1$

$\sf \dfrac{x + 7}{x + 2} = \dfrac{x + x + 2}{x + 2}$

Cancelling x + 2 from both sides

$\sf x + 7 = x + x + 2$

x + 7 = 2x + 2

x - 2x = 2 - 7

-x = -5

x = 5

Numerator = 5

$\sf Denominator = 5 + 2 = 7$

$\sf \pink {Fraction = \dfrac{5}{7}}$.