Question

3) The numerator of a fraction is 6 less than the denominator. If 1 is added to both numerator and denominator, the fraction becomes 1/2. Find the fraction.

Answer 1

Answer:

6/12

Step-by-step explanation:

LET THE FRACTION BE "X"

SO, According to the question,

= x-6+1 = 1

x+1 2

So , x-5 Cross multiplied with 1

x+1 2

= 2x - 10 = x +1

= 2x - x = 1+10

= x = 11 ans

SO; ACCORDING TO THE QUESTION,

11-6+1 = 1

11+1 2

6 = 1

12 2 ANSWER

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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 $\sf{\frac{1}{2}}$

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

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

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

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

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

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

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

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

• Hence, the value of x is 11 .

Therefore,

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

$:\implies \sf{5}$

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

$:\implies \sf{11}$

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

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