Question

The denominator of a fraction is 3 more than it's numerator if 2 is added to the numerator us 5 is added to the denominator the fraction become 1/2 . Find the fraction

Answer 1

Answer :

Fraction = 4 / 7

Explanation :

According to the question :

Let the numerator be ' n '

• Denominator ( D ) = n + 3
• Numerator ( N ) , 2 added = n + 2
• Denominator ( D ) , 5 added = ( n + 3 ) + 5
• Fraction = N / D

Equation :

→ n + 2 / ( n + 3 ) + 5 = 1 / 2

→ 1 ( n + 3 ) + 5 = 2 ( n + 2 )

⋆ ( 1 × n + 1 × 3 ) + 5 = ( 2 × n + 2 × 2 )

→ 1n + ( 3 + 5 ) = 2n + 4

→ 1n + 8 = 2n + 4

→ 2n - 1n = 8 - 4

→ 1n = 4

→ n = 4

To find :

Numerator ( N ) = 4

Denominator = N + 3 = 4 + 3 = 7

Fraction = N / D = 4 / 7

♥ So, It's Done ♥ !!

Answer 2

Question:-

The denominator of a fraction is 3 more than it's numerator if 2 is added to the numerator & if 5 is added to the denominator the fraction become 1/2 . Find the fraction.

Given:-

The denominator of a fraction is 3 more than it's numerator if 2 is added to the numerator & if 5 is added to the denominator the fraction become 1/2 .

Solution:-

To find the fraction

{ According to given }

Let, numerater be " x " .... ( 1 )

& denominator be x + 3 .... ( 2 )

Hence, according to given

»-»» Numerator = x + 2 .... ( 3 )

Denominator of a fraction is 3 more

than it's numerator .

»-»» Denominator = (x + 3 ) + 5 ...( 4 )

According to given { after ( 3 ) & ( 4 ) }

fraction become 1/2 .

${ \sf{ \purple{ \dashrightarrow}{ \bf{ \frac{(x + 2)}{(x + 3) + 5} = \frac{1}{2} }}}}$

${ \sf{ \purple{ \dashrightarrow}{ \bf{2(x + 2) = 1[(x + 3) + 5]}}}}$

${ \sf{ \purple{ \dashrightarrow}{ \bf{2x + 4 = x + 3 + 5}}}}$

${ \sf{ \purple{ \dashrightarrow}{ \bf{2x + 4= x + 8}}}}$

${ \sf{ \purple{ \dashrightarrow}{ \bf{2x - x= 8 - 4}}}}</p><p>$

${ \sf{ \purple{ \dashrightarrow}{ \bf{x= 4}}}}</p><p>$

Hence,

»-»» Numerator = x = 4

»-»» Denominator = x + 3 = 5 + 3 = 8

${ \sf{ \purple{ \dashrightarrow}{ \bf{ \frac{Numerator}{Denominator} = \frac{4}{8} = \frac{1}{2} }}}}$

& According to ( 3 ) & ( 4 )

»-»» Numerator = x + 2 = 4 + 2 = 6

»-»» Denominator =( x + 3)+ 5

= (4 + 3) + 5 = 7 + 5 = 12

${ \sf{ \purple{ \dashrightarrow}{ \bf{ \frac{Numerator}{Denominator} = \frac{6}{12} = \frac{1}{2} }}}}$

i hope it helps you.