1/2+ (2/3 / 3/4) - (4/5 * 5/6)=
Simplify the following:
1/2+((2/3)/3)/4-4/5×5/6
(2/3)/3 = 2/(3×3):
1/2+2/(3×3)/4-4/5×5/6
4/5×5/6 = (4×5)/(5×6):
1/2+2/(3×3)×1/4-(4×5)/(5×6)
2/(3×3)×1/4 = 2/(3×3×4):
1/2+2/(3×3×4)-(4×5)/(5×6)
2/4 = 2/(2×2) = 1/2:
1/2+1/(3×3×2)-(4×5)/(5×6)
(4×5)/(5×6) = 5/5×4/6 = 4/6:
1/2+1/(3×3×2)-4/6
The gcd of 4 and 6 is 2, so 4/6 = (2×2)/(2×3) = 2/2×2/3 = 2/3:
1/2+1/(3×3×2)-2/3
3×3 = 9:
1/2+1/(9×2)-2/3
9×2 = 18:
1/2+1/18-2/3
Put 1/2+1/18-2/3 over the common denominator 18. 1/2+1/18-2/3 = 9/18+1/18+(6 (-2))/18:
9/18+1/18+(6 (-2))/18
6 (-2) = -12:
9/18+1/18+-12/18
9/18+1/18-12/18 = (9+1-12)/18:
(9+1-12)/18
9+1 = 10:
10-12/18
10-12 = -(12-10):
-(12-10)/18
2/18 = 2/(2×9) = 1/9:
Answer: | (-1)/9