Question

The denominator of a fraction is 4 more than the numerator. if the numerator is increased by 2 and the denominator is increased by 5 the fraction obtained is 5/12 find the frCtion

Answer 1

Let the numerator be x .

so, denominator = x + 4

if ,

numerator = x + 2

and, denominator = x + 4 + 5 = x + 9

so, fraction = $\frac{5}{12}$

$\textbf{According to the Question,}$

$\frac{x + 2}{x + 9} = {\frac{5}{12}}$

solve by cross multiplication,

$= > 12(x + 2) = 5(x + 9) \\ \\ = > 12x + 24 = 5x + 45$

take the like terms to one side :-

$= > 12x - 5x = 45 - 24 \\ \\ = > 7x = 21 \\ \\ = > x = \frac{21}{7} \\ \\ = > x = 3$
thus ,

numerator = x = 3

and, denominator = x + 4 = 3 + 4 = 7

hence, fraction = $\frac{3}{7}$ .

Answer 2

Answer:

Let the numerator be x .

so, denominator = x + 4

if ,

numerator = x + 2

and, denominator = x + 4 + 5 = x + 9

so, fraction = \frac{5}{12}

12

5

\textbf{According to the Question,}According to the Question,

\frac{x + 2}{x + 9} = {\frac{5}{12}}

x+9

x+2

=

12

5

solve by cross multiplication,

\begin{gathered} = > 12(x + 2) = 5(x + 9) \\ \\ = > 12x + 24 = 5x + 45 \end{gathered}

=>12(x+2)=5(x+9)

=>12x+24=5x+45

take the like terms to one side :-

\begin{gathered} = > 12x - 5x = 45 - 24 \\ \\ = > 7x = 21 \\ \\ = > x = \frac{21}{7} \\ \\ = > x = 3\end{gathered}

=>12x−5x=45−24

=>7x=21

=>x=

7

21

=>x=3

thus ,

numerator = x = 3

and, denominator = x + 4 = 3 + 4 = 7

hence, fraction = \frac{3}{7}

7

3

.