Simplify the following:
52×81/63+58-98745×5
52×81/63 = (52×81)/63:
(52×81)/63+58-98745×5
The gcd of 81 and 63 is 9, so (52×81)/63 = (52 (9×9))/(9×7) = 9/9×(52×9)/7 = (52×9)/7:
(52×9)/7+58-98745×5
52×9 = 468:
468/7+58-98745×5
-98745×5 = -493725:
468/7+58+-493725
Put 468/7+58-493725 over the common denominator 7. 468/7+58-493725 = 468/7+(7×58)/7+(7 (-493725))/7:
468/7+(7×58)/7+(7 (-493725))/7
7×58 = 406:
468/7+406/7+(7 (-493725))/7
7 (-493725) = -3456075:
468/7+406/7+-3456075/7
468/7+406/7-(3456075)/7 = (468+406-3456075)/7:
(468+406-3456075)/7
| | 1 |
| 4 | 6 | 8
+ | 4 | 0 | 6
| 8 | 7 | 4:
874-3456075/7
874-3456075 = -(3456075-874):
-(3456075-874)/7
| | | | 5 | 10 | |
| 3 | 4 | 5 | 6 | 0 | 7 | 5
- | | | | | 8 | 7 | 4
| 3 | 4 | 5 | 5 | 2 | 0 | 1:
Answer: |
| (-3,455,201)/7
