The numerator of a fraction is less than the denominator. If Sara adds 1 to the numerator and adds 2 to the denominator, the fraction is 1/2, when expressed in it's simplest form. FIND the original fraction.

when you multiply the numerator by 2 and add 16 to the denominator, the original fraction is reduced by 1/3.

this means the original fraction is equal to 2/3 times what it was originally.

your equation is:

(x-5) * 2 divided by x + 16

is equal to 2/3 * (x-5) / x

this is equivalent to:

(x-5) * 2 / (x + 16) = ((x-5) * 2) / 3x

multiply both sides of the equation by (x+16) and by (3x) and you get:

(x-5) * 2 * (3x) = (x-5) * 2 * (x+16)

divide both sides of this equation by (x-5) and you get:

2 * 3x = 2 * (x + 16)

simplify to get:

6x = 2x + 32

subtract 2x from both sides of this equation to get:

4x = 32

divide both sides of this equation by 4 to get:

x = 8

that's your solution.

your original fraction is (8-5) / 8 = 3/8

your final fraction is (3 * 2) / (8 + 16) = 6 / 24 = 1/4

your original fraction of 3/8 * 2/3 = 6/24 = 1/4.

this is the same as your original fraction being reduced by 1/3.

3/8 - 1/3 * 3/8 = 3/8 - 3/24 = 9/24 - 3/24 = 6/24 = 1/4.

the questions was what is the original fraction.

the answer is that the original fraction is 3/8.