Question

the sum of the numerator and the denominator of the fraction is 11. if 1 is added to the numerator and 2 is subtract from the denominator it becomes 2/3 to find the fraction​

Answer 1

Answer:

3/8

Step-by-step explanation:

Write an equation for each statement:

:

the sum of the numerator and denominator of a fraction is 11.

n + d = 11

n = (11-d); use this form for substitution

:

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

(n+1)/(d-2) = 2/3

Cross multiply

3(n+1) = 2(d-2)

3n + 3 = 2d - 4

3n = 2d - 4 - 3

3n = 2d - 7

replace n with (11-d)

3(11-d) = 2d - 7

33 - 3d = 2d - 7

33 + 7 = 2d + 3d

40 = 5d

d = 40/5

d = 8

then

n = 11 - 8

n = 3

3/8 is the fraction

see if that checks out in the statement:

"if 1 is added to the numerator and 2 is subtracted from the denominator,it becomes 2/3."

(3+1)/(8-2) = 4/6  which is 2/3