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Consolidated Statements of Cash Flows (Unaudited) - USD ($)
$ in Millions
 3 Months Ended
Nov. 30, 2020
Nov. 30, 2019
Cash flows from operating activities:    
Net income $ 59.6 $ 57.0
Adjustments to reconcile net income to net cash flows from operating activities:    
Depreciation and amortization 25.0 24.2
Share-based payment expense 7.7 16.7
Asset impairment 4.0 0.0
Accounts receivable 56.3 66.3
Inventories 4.1 4.9
Prepayments and other current assets (20.3) (3.3)
Accounts payable (9.2) (22.7)
Other (3.3) (13.5)
Net cash provided by operating activities 123.9 129.6
Cash flows from investing activities:    
Purchases of property, plant, and equipment (11.4) (11.6)
Proceeds from sale of property, plant, and equipment 0.4 0.0
Acquisition of businesses, net of cash acquired 0.0 (302.0)
Other investing activities (3.1) (1.5)
Net cash used for investing activities (14.1) (315.1)
Cash flows from financing activities:    
Issuance of long-term debt 493.9 0.0
Repayments of long-term debt (395.1) (0.4)
Repurchases of common stock (255.2) 0.0
Proceeds from stock option exercises and other 0.3 0.2
Payments of taxes withheld on net settlement of equity awards (3.0) (4.1)
Dividends paid (5.0) (5.2)
Net cash used for financing activities (164.1) (9.5)
Effect of exchange rate changes on cash and cash equivalents 0.6 0.6
Net change in cash and cash equivalents (53.7) (194.4)
Cash and cash equivalents at beginning of period 560.7 461.0
Cash and cash equivalents at end of period 507.0 266.6
Supplemental cash flow information:    
Income taxes paid during the period 9.3 4.6
Interest paid during the period $ 15.1 $ 12.9