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Consolidated Statements of Cash Flows (Unaudited) - USD ($)
$ in Millions
 3 Months Ended
Nov. 30, 2018
Nov. 30, 2017
Cash flows from operating activities:    
Net income $ 79.6 $ 71.5
Adjustments to reconcile net income to net cash flows from operating activities:    
Depreciation and amortization 21.3 19.0
Share-based payment expense 7.8 8.5
Loss on sale or disposal of property, plant, and equipment 0.4 0.1
Deferred income taxes (0.1) (0.1)
Change in assets and liabilities, net of effect of acquisitions, divestitures, and exchange rate changes:    
Accounts receivable 102.0 57.6
Inventories (9.2) (11.1)
Prepayments and other current assets (14.8) (9.3)
Accounts payable (61.5) (32.5)
Other current liabilities (1.6) 25.5
Other 7.9 10.6
Net cash provided by operating activities 131.8 139.8
Cash flows from investing activities:    
Purchases of property, plant, and equipment (14.0) (10.3)
Other investing activities 2.7 0.0
Net cash used for investing activities (11.3) (10.3)
Cash flows from financing activities:    
Borrowings on credit facility 55.4 0.0
Repayments of borrowings on credit facility (55.4) 0.0
Repayments of long-term debt (0.1) (0.1)
Repurchases of common stock (25.0) 0.0
Proceeds from stock option exercises and other 0.1 0.8
Payments of taxes withheld on net settlement of equity awards (3.9) (6.0)
Dividends paid (5.2) (5.5)
Net cash used for financing activities (34.1) (10.8)
Effect of exchange rate changes on cash and cash equivalents (0.7) (1.2)
Net change in cash and cash equivalents 85.7 117.5
Cash and cash equivalents at beginning of period 129.1 311.1
Cash and cash equivalents at end of period 214.8 428.6
Supplemental cash flow information:    
Income taxes paid during the period 6.1 2.7
Interest paid during the period $ 13.5 $ 12.7