Question

a) The numerator of fraction is 3 less than denominator. If 5 is subtracted from both numerator and denominator, the fraction becomes 4⁄5. Express the equation algebraically and upload your workout in the google classroom. b) What is the fractional number?

Answer 1

Answer: 17/20

Explanation:

Let's define:

N = numerator

D = denominator.

The fraction is N/D.

We know that:

"The numerator of fraction is 3 less than denominator. "

N = D - 3

" If 5 is subtracted from both numerator and denominator, the fraction becomes 4⁄5."

(N - 5)/(D - 5) = 4/5.

Then we have a system of equations of two variables:

N = D - 3

(N - 5)/(D - 5) = 4/5.

The first step to solve this, is to replace the first equation into the second, in that way we can work with only one variable.

(D - 3 - 5)/(D - 5) = 4/5.

Now we can solve this for D.

(D - 8)/(D - 5) = 4/5

D - 8 = (D - 5)*(4/5) = (4/5)*D - 4

D - (4/5)*D = -4 + 8 = 4

(1/5)*D = 4

D = 4*5 = 20

And here we can use the first equation to find the value of N.

N = D - 3 = 20 - 3 = 17

Then our fraction is:

N/D = 17/20