Answer:
75/2
Explanation:
Simplify the following:
8×4 - 5 (3 + 1/5 - (2 + 1/2)) + (4 - 1)^2
Put 2 + 1/2 over the common denominator 2. 2 + 1/2 = (2×2)/2 + 1/2:
8×4 - 5 (3 + 1/5 - (2×2)/2 + 1/2) + (4 - 1)^2
2×2 = 4:
8×4 - 5 (3 + 1/5 - (4/2 + 1/2)) + (4 - 1)^2
4/2 + 1/2 = (4 + 1)/2:
8×4 - 5 (3 + 1/5 - (4 + 1)/2) + (4 - 1)^2
4 + 1 = 5:
8×4 - 5 (3 + 1/5 - 5/2) + (4 - 1)^2
Put 3 + 1/5 - 5/2 over the common denominator 10. 3 + 1/5 - 5/2 = (10×3)/10 + 2/10 + (5 (-5))/10:
8×4 - 5(10×3)/10 + 2/10 + (5 (-5))/10 + (4 - 1)^2
10×3 = 30:
8×4 - 5 (30/10 + 2/10 + (5 (-5))/10) + (4 - 1)^2
5 (-5) = -25:
8×4 - 5 (30/10 + 2/10 + (-25)/10) + (4 - 1)^2
30/10 + 2/10 - 25/10 = (30 + 2 - 25)/10:
8×4 - 5(30 + 2 - 25)/10 + (4 - 1)^2
30 + 2 = 32:
8×4 - 5 (32 - 25)/10 + (4 - 1)^2
| 2 | 12
| 3 | 2
- | 2 | 5
| 0 | 7:
8×4 - 5×7/10 + (4 - 1)^2
-5×7/10 = (-5×7)/10:
8×4 + (-5×7)/10 + (4 - 1)^2
The gcd of -5 and 10 is 5, so (-5×7)/10 = ((5 (-1)) 7)/(5×2) = 5/5×(-7)/2 = (-7)/2:
8×4 + (-1×7)/2 + (4 - 1)^2
4 - 1 = 3:
8×4 - 7/2 + 3^2
8×4 = 32:
32 - 7/2 + 3^2
3^2 = 9:
32 - 7/2 + 9
Put 32 - 7/2 + 9 over the common denominator 2. 32 - 7/2 + 9 = (2×32)/2 - 7/2 + (2×9)/2:
(2×32)/2 - 7/2 + (2×9)/2
2×32 = 64:
64/2 - 7/2 + (2×9)/2
2×9 = 18:
64/2 - 7/2 + 18/2
64/2 - 7/2 + 18/2 = (64 - 7 + 18)/2:
(64 - 7 + 18)/2
| 1 |
| 6 | 4
+ | 1 | 8
| 8 | 2:
(82 - 7)/2
| 7 | 12
| 8 | 2
- | | 7
| 7 | 5:
Answer: 75/2