Question

The numerator of a 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

Answer:

Let the denominator be x. Hence Numerator = (x-4)

When 1 is added to both numerator and denominator it becomes:(x-3)/(x+1) which is equal to 1/2

=> 2(x-3)=x+1

=> 2x -6 = x + 1

X = 7

Fraction is 3/7

Step-by-step explanation:

hope it helps you

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

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬