Question

The denominator of a fraction is 8 more than its numerator. If 1 is subtracted from the numerator and 3 is added to the denominator, the fraction becomes 1/2. Find the fraction

pleases help as soon as possible..thank you so much

Answer 1

Answer:

The fraction is 13/21.

Step-by-step explanation:

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

Let x be the numerator: x

So the denominator is: x + 8

$\frac{x}{x + 8}$

If 1 is subtracted from the numerator and 3 is added to the denominator, the fraction becomes 1/2.

It will become:

$\frac{x - 1}{x + 8 + 3} = \frac{1}{2}$

$\frac{x - 1}{x + 11} = \frac{1}{2}$

Now, by using cross multiplication, multiply (x - 1) by 2 and (x+11) by 1.

It will become:

2x - 2 = x + 11

Now transpose and combine the same values. Make sure to change the integer sign. If the integer is positive, change it to negative when you transpose it.

2x - x = 11 + 2

x = 13

So the value of x is 13. Now to check if it is correct. Go back to the equation($\frac{x - 1}{x + 11} = \frac{1}{2}$)

Put the value of x in it.

$\frac{13-1}{13+11} = \frac{1}{2}$

$\frac{12}{24} = \frac{1}{2}$

12/24 is equivalent to 1/2 so that is correct.

Now, to find the main fraction. Go back to the original equation which is;

($\frac{x}{x + 8}$)

Put the value of x.

$\frac{13}{8 + 13}$

= 13/21

Not a verified expert but I put much effort to answer your question. Hope it helps:)