Simplify the following:
9/10-(1+1/2)-(-(3+2/5))
(-1)^2 = 1:
9/10-(1+1/2)+3+2/5
Put 1+1/2 over the common denominator 2. 1+1/2 = 2/2+1/2:
9/10-2/2+1/2+3+2/5
2/2+1/2 = (2+1)/2:
9/10-(2+1)/2+3+2/5
2+1 = 3:
9/10-3/2+3+2/5
Put 9/10-3/2+3+2/5 over the common denominator 10. 9/10-3/2+3+2/5 = 9/10+(5 (-3))/10+(10×3)/10+(2×2)/10:
9/10+(5 (-3))/10+(10×3)/10+(2×2)/10
5 (-3) = -15:
9/10+-15/10+(10×3)/10+(2×2)/10
10×3 = 30:
9/10-15/10+30/10+(2×2)/10
2×2 = 4:
9/10-15/10+30/10+4/10
9/10-(15)/10+30/10+4/10 = (9-15+30+4)/10:
(9-15+30+4)/10
| 1 |
| 3 | 0
| | 9
+ | | 4
| 4 | 3:
43-15/10
| 3 | 13
| 4 | 3
- | 1 | 5
| 2 | 8:
28/10
The gcd of 28 and 10 is 2, so 28/10 = (2×14)/(2×5) = 2/2×14/5 = 14/5:
Answer: |
| 14/5
Simplify the following:
9/10-(1+1/2)-(-(3+2/5))
(-1)^2 = 1:
9/10-(1+1/2)+3+2/5
Put 1+1/2 over the common denominator 2. 1+1/2 = 2/2+1/2:
9/10-2/2+1/2+3+2/5
2/2+1/2 = (2+1)/2:
9/10-(2+1)/2+3+2/5
2+1 = 3:
9/10-3/2+3+2/5
Put 9/10-3/2+3+2/5 over the common denominator 10. 9/10-3/2+3+2/5 = 9/10+(5 (-3))/10+(10×3)/10+(2×2)/10:
9/10+(5 (-3))/10+(10×3)/10+(2×2)/10
5 (-3) = -15:
9/10+-15/10+(10×3)/10+(2×2)/10
10×3 = 30:
9/10-15/10+30/10+(2×2)/10
2×2 = 4:
9/10-15/10+30/10+4/10
9/10-(15)/10+30/10+4/10 = (9-15+30+4)/10:
(9-15+30+4)/10
| 1 |
| 3 | 0
| | 9
+ | | 4
| 4 | 3:
43-15/10
| 3 | 13
| 4 | 3
- | 1 | 5
| 2 | 8:
28/10
The gcd of 28 and 10 is 2, so 28/10 = (2×14)/(2×5) = 2/2×14/5 = 14/5:
Answer: |
| 14/5