Question

The numerator of fraction is 6 less
then the denominator . If 1 Is added
to both, the numerator and
denominator
The fraction becomes 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 :

$\longmapsto\tt{Let\:Denominator\:be=x}$

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

$\longmapsto\tt{Numerator=x-6}$

Now ,

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

$\longmapsto\tt{Numerator=x-6+1=x-5}$

$\longmapsto\tt{Denominator=x+1}$

A.T.Q :

$\longmapsto\tt{\dfrac{x-5}{x+1}=\dfrac{1}{2}}$

$\longmapsto\tt{2(x-5)=1(x+1)}$

$\longmapsto\tt{2x-10=x+1}$

$\longmapsto\tt{2x-x=1+10}$

$\longmapsto\tt\bf{x=11}$

Value of x is 11 .

Therefore :

$\longmapsto\tt{Numerator=11-6}$

$\longmapsto\tt\bf{5}$

$\longmapsto\tt{Denominator=x}$

$\longmapsto\tt\bf{11}$

So , The Fraction is 5/11 .

Answer 2

Question :-

• The numerator of fraction is 6 less then the denominator . If 1 is added to both the numerator and denominator, the fraction becomes 1/2. Find the fraction

Answer :-

• The required fraction is 5/11.

Explanation :-

Given :-

• The numerator of fraction is 6 less then the denominator.
• If 1 is added to both the numerator and denominator, the fraction becomes 1/2.

To Find :-

• The fraction?

Solution :-

• Let denominator be n
• As it is given that numerator is 6 less than the denominator. So, numerator is (n - 6).

According to the question,

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

Therefore,

↦ $\sf \dfrac{(n - 6) + 1}{n + 1} = \dfrac{1}{2}$

By cross multiplication,

↦ $\sf 2(n - 6 + 1) = n + 1$

↦ $\sf 2(n - 5) = n + 1$

↦ $\sf 2n - 10 = n + 1$

↦ $\sf 2n - n = 1 + 10$

➦ $\bf \red{n = 11}$

Hence,

⇒ Denominator = n

➠ Denominator = 11

Also,

⇒ Numerator = n - 6

⇒ Numerator = 11 - 6

➠ Numerator = 5

And,

⇒ Fraction = Numerator/Denominator

➠ Fraction = 5/11

∴ Required fraction is 5/11.

Let's Verify :-

We know that,

↪ $\sf \dfrac{(n - 6) + 1}{n + 1} = \dfrac{1}{2}$

Put n = 11 we get,

↪ $\sf \dfrac{(11 - 6) + 1}{11 + 1} = \dfrac{1}{2}$

↪ $\sf \dfrac{5 + 1}{12} = \dfrac{1}{2}$

↪ $\sf {\cancel{\dfrac{6}{12}}} = \dfrac{1}{2}$

↪ $\sf \dfrac{1}{2} = \dfrac{1}{2}$

➢ $\bf \purple{LHS = RHS}$

Hence, Verified ✔

Learn more on brainly :-

Question (1) :-

• The denominator of the rational number is twice the numerator. if the numerator is deceased by 3 and the denominator is increased by 7, the number obtained is 2/7. Find the rational number.

Answer :-

• brainly.in/question/43501561

Question (2) :-

• The denominator of a rational number is less than its numerator than 5.If 5 is added to the numerator, the new number becomes 11/6.Find the original rational number.

Answer :-

• brainly.in/question/43273890

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