Simplify the following:
(6+1/2) y+(2+5/6) y+1/4+3/4+2+4
Put 6+1/2 over the common denominator 2. 6+1/2 = (2×6)/2+1/2:
(2×6)/2+1/2 y+(2+5/6) y+1/4+3/4+2+4
2×6 = 12:
(1/212+1/2) y+(2+5/6) y+1/4+3/4+2+4
12/2+1/2 = (12+1)/2:
(12+1)/2 y+(2+5/6) y+1/4+3/4+2+4
12+1 = 13:
(13 y)/2+(2+5/6) y+1/4+3/4+2+4
Put 2+5/6 over the common denominator 6. 2+5/6 = (6×2)/6+5/6:
(13 y)/2+(6×2)/6+5/6 y+1/4+3/4+2+4
6×2 = 12:
(13 y)/2+(1/612+5/6) y+1/4+3/4+2+4
12/6+5/6 = (12+5)/6:
(13 y)/2+(12+5)/6 y+1/4+3/4+2+4
12+5 = 17:
(13 y)/2+(17 y)/6+1/4+3/4+2+4
Put each term in (13 y)/2+(17 y)/6+1/4+3/4+2+4 over the common denominator 12: (13 y)/2+(17 y)/6+1/4+3/4+2+4 = (78 y)/12+(34 y)/12+3/12+9/12+24/12+48/12:
(78 y)/12+(34 y)/12+3/12+9/12+24/12+48/12
(78 y)/12+(34 y)/12+3/12+9/12+24/12+48/12 = (78 y+34 y+3+9+24+48)/12:
(78 y+34 y+3+9+24+48)/12
Grouping like terms, 78 y+34 y+3+9+24+48 = (78 y+34 y)+(48+3+24+9):
((78 y+34 y)+(48+3+24+9))/12
78 y+34 y = 112 y:
(112 y+(48+3+24+9))/12
48+3+24+9 = 84:
(112 y+84)/12
Factor 28 out of 112 y+84:
28 (4 y+3)/12
The gcd of 28 and 12 is 4, so (28 (4 y+3))/12 = ((4×7) (4 y+3))/(4×3) = 4/4×(7 (4 y+3))/3 = (7 (4 y+3))/3:
Answer: |7/3 (4y + 3)
