Question

the numerator of a fraction is 7 less than the denominator.if 3 is added to the numerator and 2 is added to the denominator the value of the fraction becomes 2/3 .find the original fraction
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Answer 1

Answer:

Fraction = 9/16

Step-by-step explanation:

Given:

• Numerator of the fraction = 7 less than the denominator
• If 3 is added to the numerator and 2 is added to the denominator, fraction becomes 2/3.

To Find:

• The fraction

Solution:

Let us assume the denominator of the fraction as x.

Hence by given,

Numerator = Denominator - 7

Nummerator = x - 7

Hence the fraction is given by,

$\tt{Fraction=\dfrac{x-7}{x} }$

By given adding 3 to the numerator and 2 to the denominator, the fraction becomes 2/3.

Hence,

$\tt{\dfrac{x-7+3}{x+2} =\dfrac{2}{3} }$

$\tt{\dfrac{x-4}{x+2}=\dfrac{2}{3} }$

Cross multiplying we get,

3 (x - 4) = 2 (x + 2)

3x - 12 = 2x + 4

3x - 2x = 4 + 12

x = 16

Hence the denominator of the fraction is 16.

Now,

Numerator = x - 7

Numerator = 16 - 7

Numerator = 9

Therefore numerator of the fraction is 9.

Hence the fraction is 9/16.

Verification:

Numerator = Denominator - 7

9 = 16 - 7

9 = 9

Adding 3 to numerator and 2 to denominator the fraction becomes 2/3

(9 + 3)/(16 + 2) = 2/3

12/18 = 2/3

2/3 = 2/3

Hence verified.

Answer 2

${ \bf{ \underline{ \purple{ \underline{Given \: data}}}}:-}$

• The numerator of a fraction is 7 less than the denominator.
• 3 is added to the numerator and 2 is added to the denominator
• the value of the fraction becomes 2/3.

${ \bf{ \underline{ \purple{ \underline{Solution}}}}:-}$

Let,numerator be x and denominator be y.

{According to given data}

• Numerator = y - 7 ..... ( 1 )

• Denominator = y ..... ( 2 )

{3 is added to the numerator and 2 is added to the denominator}

From eq. ( 1 ) & eq. ( 2 )

• Numerator = y - 7 + 3 = y - 4 ....( 3 )

• Denominator = y + 2 ..... ( 4 )

{According to given data}

${ \red{ \tt {\dashrightarrow { \green{ \frac{Numerator }{Denominator} = \frac{2}{3} }}}}}$

{from ( 3 ) & ( 4 )}

${ \red{ \tt {\dashrightarrow { \green{ \frac{y - 4 }{y + 2} = \frac{2}{3} }}}}}$

{ cross multiplication}

${ \red{ \tt {\dashrightarrow { \green{3(y - 4) = 2(y + 2 )}}}}}$

${ \red{ \tt {\dashrightarrow { \green{3y - 12= 2y + 4}}}}}$

{Now, collect same term }

${ \red{ \tt {\dashrightarrow { \green{3y -2y= 4 + 12}}}}}$

${ \red{ \tt {\dashrightarrow { \green{y= 16}}}}}$

Put value of y in eq. ( 1 ) to find numerator.

• Numerator = y - 7

• Numerator = 16 - 7

• Numerator = 9

Hence, original fraction is

${ \red{ \tt {\dashrightarrow { \green{ \frac{Numerator }{Denominator} = \frac{9}{16} }}}}}$

Hope it helps you.