Question

The denominator of a fraction is 8 more than the numerator. If 5 is added to the numerator and denominator the fraction becomes ½. Find the fraction.​

Answer 1

Given:

• The denominator of a fraction is 8 more than numerator.

• If 5 is added to the numerator and denominator the fraction becomes ½.

Need To find:

• Original Fraction ?

Solution:

Let the numerator of a fraction be x.

Then, The denominator of fraction will be (x + 8).

Now,

According to the Question,

• 5 is added to numerator = (x + 5)
• 5 is added to denominator = (x + 8+ 5)

➜(x + 5)/(x + 8 + 5) = 1/2

➜ (x + 5)/(x + 13) = 1/2

➜ 2(x + 5) = x + 13

➜ 2x + 10 = x + 13

➜ 2x - x = 13 - 10

➜ x = 3

Hence,

• Numerator of the fraction, x = 3
• Denominator of the fraction, (x + 8) = 3 + 8 = 11

Therefore, The Required fraction is 3/11.

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Answer 2

Answer:

The fraction is 3/11 ✔

Step-by-step explanation:

Given that,

The denominator of a fraction is 8 more than it's numerator.

Here, In the fraction if 5 is added to both the numerator and the denominator the fraction is now ½. So, we need to find the original fraction.

Step 1 :

Considering the numerator as "x"

Then, it's denominator will be (x + 8)

Step 2 :

Adding 5 to both the numerator as well as denominator :

• Numerator now will be (x + 5)
• And also, the denominator (x + 13)

★ According to the question :

• The fraction now is ½.

Step 3 :

Solving for "x" :

➙ (x + 5)/(x + 13) = ½

➙ 2(x + 5) = (x + 13)

➙ 2x + 10 = x + 13

➙ 2x - x = 13 - 10

➙ x = 3.

Therefore,

• Value of "x" or, the numerator is 3.

Hence,

• The denominator will be 11.

The fraction is 3/11