Question

the denominator of a fraction is two more than its numerator. if one is added to 4/5 .Find the original fraction
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Answer 1

Answer:

2/5 or 4/10

Step-by-step explanation:

let numerator be x

let denominator be (x+6)

after adding 2,

new numerator = (x+2)

new denominator = (x+6+2) = (x+8)

new fraction = 1/2

(x+2)/(x+8) = 1/2

2(x+2) = 1(x+8)

2x+4 = x+8

2x-x = 8-4

x = 4

hence,

(x+6) = (4+6) = 10

original fraction = 4/10 or 2/5

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Answer 2

$\Large{\underbrace{\sf{\purple{Required\:Solution:}}}}$

Given :

• The denominator of α frαction is two more thαn its numerαtor.
• One is αdded to both, then the frαction reduces to 4/5.

To Find :

• The originαl frαction.

Procedure :

In this question, firstly we'll αssume the numerator to be x αnd denominator to be x+2.

Then we'll write it as fraction αnd αdd 1 to both numerαtor αnd denominαtor αnd put 4/5 equivalent to it. After thαt, we'll simplify the equαtion αnd find the vαlues of numerαtor αnd denominator. And we'll done! :D

So let's do it!

Step by step explαnαtion :

Let the numerαtor be x. so, the denominαtor will be x + 2.

According to the question,

$\implies{\sf{ \dfrac{x + 1}{ (x+2)+1} = \dfrac{4}{5}}}$

• Do cross multiplicαtion.

$\implies{\sf{ 5(x+1) = 4(x+3)}}$

• Simplify this.

$\implies{\sf{ 5x + 5 = 4x + 12}}$

$\implies{\sf{ 5x - 4x = 12 - 5}}$

$\implies{\sf{ x = 7}}$

Therefore, the frαction will be $\displaystyle{\boxed{\sf{\purple{\dfrac{ 7}{9}}}}}$

And we αre done! :D

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