Question

in fractions if 1 is added in the numerator and 1 is subtracted from denominator then it's value becomes 1 Similarly if twice is made of its numerator and 1 is added to its value also becomes 1 Find the fraction​

Answer 1

Answer:

the fraction is ⅓

Step-by-step explanation:

let , the numerator of fraction is x

and the denominator of fraction is y

and the fraction is x/y

Now

if 1 is added to numertor ie. x+1

and 1 is subtracted from denominator ie. y-1

Then , the fraction becomes 1 ie.

$\frac{x + 1}{y - 1} = 1 \: \: \: \: \: \: \: \\ x + 1 = y - 1 \\ \: \: \: x - y = - 1 - 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x - y = - 2 \: \: \: \: \: .... \: \: eq.(1)$

Now,

similarly, twice is made of its numerator and 1 is added ie. 2x + 1

Then, the fraction becomes 1 ie.

$\frac{2x + 1}{y} = 1 \\ 2x + 1 = y \\ \: \: \: \: \: \: \:2x - y = - 1 \: \: \: \: .... \: \: \: \: \: \: \: \: eq. (2)$

Now,

Using elimination method

$\: \: \: \: \: \: \: \: x - y = - 2 \\ \: \: \: \: \: \: \: 2x - y = - 1 \\ \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: + \: \: \: \: \: \: \: + \\ \: \: \: \: \: \: \: - x = - 1 \\ \: \: \: \: \: \: \: \: x = 1$

So,we get the value of x = 1

then put the value of x = 1 in eq (1).

so, x - y = -2

1 - y = -2

- y = -2 -1

- y = - 3

so, y = 3

Now , we get the value of x = 1 and y = 3

And, the numerator = x = 1

Also, the denominator = y = 3

And the fraction = x/y = ⅓

Hence we get the fraction

I think this will help you

Answer 2

let , the numerator of fraction is x

and the denominator of fraction is y

and the fraction is x/y

Now

if 1 is added to numertor ie. x+1

and 1 is subtracted from denominator ie. y-1

Then , the fraction becomes 1 ie.

{x + 1}{y - 1} = 1

x + 1 = y - 1

x - y = - 1

- 1 x - y = - 2 eq.(1)

y−1

x+1

=1

x+1=y−1

x−y=−1−1

x−y=−2....eq.(1)

Now,

similarly, twice is made of its numerator and 1 is added ie. 2x + 1

Then, the fraction becomes 1 ie.

{2x + 1}{y} = 1

2x + 1 = y

2x - y = - 1 ...eq. (2)y

2x+1

=1

2x+1=y

2x−y=−1....eq.(2)

Now,

Using elimination method

- y = - 2

2x - y = - 1

- x = - 1

x = 1

x−y=−2

2x−y=−1

−++

−x=−1

x=1

So,we get the value of x = 1

then put the value of x = 1 in eq (1).

so, x - y = -2

1 - y = -2

- y = -2 -1

- y = - 3

so, y = 3

Now , we get the value of x = 1 and y = 3

And, the numerator = x = 1

Also, the denominator = y = 3

And the fraction = x/y = ⅓

Hence we get the fraction

hope it's help u !!