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 become 1/2. find the fraction​

Answer 1

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 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 ${\bf{ \frac{5}{11}} }$ .