Question

10. The numerator of a fraction is 5 less than the denominator. If 2 is
added to both numerator and denominator, it becomes 4/5. Find the
fraction.

Answer 1

Answer:

18/23

Step-by-step explanation:

Let the denominator = x

numerator = x - 5

A.T.Q.

x-5/x + 2/2 = 4/5

x-3/x+2 =4/5

5(x-3) = 4(x +2)

5x - 15 = 4x + 8

5x-4x = 8+15

x= 23

Fraction => 18/23

Answer 2

Answer: 9/14

Step-by-step explanation: If “The numerator of the fraction is five less than the denominator,” then you could write the denominator as x and the numerator as x-5.

That means that the missing fraction is (x-5)/x.

Now you must “add one to the numerator and denominator.”

So the new fraction is (x-5+1)/9x+1) or (x-4)/(x+1).

According to the question, this equals 2/3.

Therefore, we can set up an equation: (x-4)/(x+1) = 2/3.

To solve, cross multiply: 3(x-4) = 2(x+1)

Solve for x:

3x-12 = 2x+2

x=14

Remember, this is only x. You must still plug it into the fraction: (14-5)/14.

Simplify: (9/14).