Question

The sum of numerator and denominator of a faction is 13.If 3 is added to numerator and 5

to denominator, the fraction becomes 1/2Find the fraction.​

Answer 1

Answer:

4/9

Step-by-step explanation:

Hope it's understandable

Answer 2

Answer:

The fraction is $\sf \dfrac{4}{9}$

Step-by-step explanation:

Question says that,

In a fraction

Numerator + Denominator = 13.

If 3 is added to numerator and 5 to the denominator the fraction becomes ½.

Find the fraction.

Step 1 : Let's assume :

➪ Numerator = $x$

➪ Denominator will be = $(13 - x)$

Now,

add 3 to the numerator

Numerator now will be : $(x + 3)$

And also,

5 added to the denominator

So, denominator now will be :

$\to (x - 13) + 5$

$\to (13 - x + 5)$

$\to {\boldsymbol{ (18 - x)}}$

Step 2 : Find the value of $\boldsymbol x :$

The fraction now is ½.

${ \underline{\boldsymbol{According \: to \: the \: question :}}}$

$\implies \dfrac{(x + 3)}{(18 - x)} = \dfrac{1}{2}$

$\implies 2(x + 3) = 1(18 - x)$

$\implies 2x + 6 = 18 - x$

$\implies 2x + x = 18 - 6$

$\implies 3x = 12$

$\implies x = \dfrac{12}{3}$

$\implies \boldsymbol { x = 4 }$

∴ The numerator is 4

Step 3 : Find the denominator :

Therefore, the denominator will be :

$\to (13 - 4)$

$\to \sf 9$

Step 4 : Express the fraction :

The fraction is :

$\to \sf \dfrac{Numerator}{Denominator}$

$\to \sf \dfrac{4}{9}$

_____________________

Verification :

Given,

$\to\sf \dfrac{4 + 3}{9 + 5} = \dfrac{1}{2}$

Let's check it.

$\to \sf \dfrac{7}{14} = \dfrac{1}{2}$

$\to \sf \dfrac{1}{2} = \dfrac{1}{2}$

Hence, proved