Question

the numerator of a fraction is 7 less than the denominator. if the numerator is increased by 2 and the denominator by 9 we again get the same fraction.Find the fraction

Answer 1

Given, numerator of a fraction is 7 less than the denominator.
Let, the denominator be x
Then the numerator will be x - 7
In the second case it is given that ,
Numerator is increased by 2 i.e. = x - 7 + 2 = x - 5
Denominator is increased by 9 i.e. = x + 9
                    x - 7 / x = x - 5 / x + 9
Now let's cross multiply
                ( x - 7 )( x + 9 ) = x ( x - 5 )
               x^2 + 9x - 7x - 63 = x^2 - 5x
x^2 gets cancelled
                          2x - 63 = -5x
                              7x = 63
                                x = 9
∴ The required fraction = 9-7 / 9 = 2/9.

Hope my answer helps you..
                    

Answer 2

The answer of the fraction is 2/9.

According to the question

Given :

Numerator of a fraction is 7 less than the denominator. if the numerator is increased by 2 and the denominator by 9 we again get the same fraction

To Find  :

The Fraction

Solution :

Let the Denominator be x

then the Numerator will be ( x-7)

In the second case it is given that ,

Numerator is increased by 2 i.e. = x-7+2

                                                      =x-5

Denominator is increased by 9 i.e. = x+9

∴ $\frac{x-7}{x} = \frac{x-5}{x+9}$

∴$(x-7) (x+9)=x(x-5)$ $\longrightarrow$( cross multiply)

  $x^{2} + 9x-7x-63=x^{2} -5x$

∴$2x-63 = -5x$

  $7x = 63$

  $x = 63 / 7$ $\Longrightarrow x = 9$

∴ The required fraction is $\frac{9-7}{9}$  = $\frac{2}{9}$

Answer : The Fraction is 2/9.

 What is fraction ?

• Fraction, In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator.

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