Question

the numerator of a fraction is 6 less than the denominator. if 1 is added to both the numerator and the denominator, the fraction becomes 1/2. find the fraction.​

Answer 1

Answer:

Let the numerator be x

then,denominator =x+6

(atq)

if 1 is added to numerator and denominator

new fraction=x+1/x+6+1

Now,

x+1/x+7=1/2

2(x+1)=1(x+7)

2x+2=x+7

2x-x=7-2

x=5

so,numerator=5

and denominator=11

so fraction 5/11

Answer 2

Given:

• The numerator of a fraction is 6 less than the denominator .If 1 is added to both, the numerator and denominator the fraction becomes $\sf{\frac{1}{2}}$ .

To Find:

• Original Fraction

Solution:

$:\implies\sf{Let\:Denominator\:be=x}$

As Given that The numerator of a fraction is 6 less than the denominator .

 So,

$:\implies\sf{Numerator=x-6}$

Now,

If 1 is added to both, the numerator and denominator the fraction becomes 1/2

$:\implies \sf{Numerator=x-6+1=x-5}$

$:\implies \sf{Denominator=x+1}$

$\boxed{\boxed{\pmb{\sf{\purple{According\: to\: the\: question}}}}}$

$:\implies \sf{\dfrac{x-5}{x+1}=\dfrac{1}{2}}$

$:\implies \sf{2(x-5)=1(x+1)}$

$:\implies \sf{2x-10=x+1}$

$:\implies \sf{2x-x=1+10}$

$:\implies \underline{\boxed{\frak{x=11}}} \: \blue{ \bigstar}$

• Hence, the value of x is 11 .

Therefore,

$:\implies \sf{Numerator=11-6}$

$:\implies \sf{5}$

$:\implies \sf{Denominator=x}$

$:\implies \sf{11}$

$:\implies \underline{\boxed{\frak{ \frac{5}{11} }}} \: \pink{ \bigstar}$

• The Fraction is ${\bf{ \frac{5}{11}} }$ .