Question

the numerator of a fraction is 6 less than the denominator if 1 is added to the both numerator and denominator it become 1 by 2 find the fraction

Answer 1

x-6
$\frac{x - 6 + 1}{x + 1} = \frac{1}{2}$

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,

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

$:\implies \sf{5}$

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

$:\implies \sf{11}$

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

• So, fraction is ${\bf{ \frac{5}{11}} }$ .