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Consolidated Statements of Cash Flows (Unaudited) - USD ($)
$ in Millions
 9 Months Ended
May 31, 2020
May 31, 2019
Cash flows from operating activities:    
Net income $ 174.6 $ 234.3
Adjustments to reconcile net income to net cash flows from operating activities:    
Depreciation and amortization 75.3 65.7
Share-based payment expense 32.5 22.9
Loss on sale or disposal of property, plant, and equipment 0.2 0.6
Asset impairment 1.4 0.0
Deferred income taxes 0.3 0.2
Change in assets and liabilities, net of effect of acquisitions, divestitures, and exchange rate changes:    
Accounts receivable 119.9 72.1
Inventories 1.0 20.5
Prepayments and other current assets 13.2 (23.6)
Accounts payable (14.7) (71.5)
Other current liabilities (38.5) (21.6)
Other 13.1 12.4
Net cash provided by operating activities 378.3 312.0
Cash flows from investing activities:    
Purchases of property, plant, and equipment (38.3) (39.8)
Proceeds from sale of property, plant, and equipment 0.2 0.0
Acquisition of businesses, net of cash acquired (303.0) 0.0
Other investing activities (1.9) 2.9
Net cash used for investing activities (343.0) (36.9)
Cash flows from financing activities:    
Borrowings on credit facility 400.0 86.5
Repayments of borrowings on credit facility (2.5) (86.5)
Repayments of long-term debt (350.7) (0.3)
Repurchases of common stock 0.0 (48.7)
Proceeds from stock option exercises and other 0.7 0.5
Payments of taxes withheld on net settlement of equity awards (5.1) (4.9)
Dividends paid (15.6) (15.6)
Net cash provided by (used for) financing activities 26.8 (69.0)
Effect of exchange rate changes on cash and cash equivalents (2.5) (1.5)
Net change in cash and cash equivalents 59.6 204.6
Cash and cash equivalents at beginning of period 461.0 129.1
Cash and cash equivalents at end of period 520.6 333.7
Supplemental cash flow information:    
Income taxes paid during the period 32.1 89.0
Interest paid during the period $ 26.9 $ 24.8