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Comprehensive Income - Changes in Components of Accumulated Other Comprehensive Income (Loss) Items (Details) - USD ($) $ in Millions	3 Months Ended						9 Months Ended
	May 31, 2020	Feb. 29, 2020	Nov. 30, 2019	May 31, 2019	Feb. 28, 2019	Nov. 30, 2018	May 31, 2020	May 31, 2019
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	$ 2,045.1	$ 1,987.3	$ 1,918.9	$ 1,801.8	$ 1,750.9	$ 1,716.8	$ 1,918.9	$ 1,716.8
Other comprehensive (loss) income before reclassifications							(15.6)	(11.7)
Amounts reclassified from accumulated other comprehensive loss							5.4	4.4
Net current period other comprehensive (loss) income	(12.0)	(2.0)	3.8	(7.4)	6.3	(6.2)	(10.2)	(7.3)
Ending balance	2,095.7	2,045.1	1,987.3	1,884.9	1,801.8	1,750.9	2,095.7	1,884.9
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	(149.6)	(147.6)	(151.4)	(114.7)	(121.0)	(114.8)	(151.4)	(114.8)
Net current period other comprehensive (loss) income	(12.0)	(2.0)	3.8	(7.4)	6.3	(6.2)
Ending balance	(161.6)	$ (149.6)	(147.6)	(122.1)	$ (114.7)	(121.0)	(161.6)	(122.1)
Foreign Currency Items
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance			(65.4)			(53.9)	(65.4)	(53.9)
Other comprehensive (loss) income before reclassifications							(15.6)	(12.6)
Amounts reclassified from accumulated other comprehensive loss							0.0	0.0
Net current period other comprehensive (loss) income							(15.6)	(12.6)
Ending balance	(81.0)			(66.5)			(81.0)	(66.5)
Defined Benefit Pension Plans
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance			$ (86.0)			$ (60.9)	(86.0)	(60.9)
Other comprehensive (loss) income before reclassifications							0.0	0.9
Amounts reclassified from accumulated other comprehensive loss							5.4	4.4
Net current period other comprehensive (loss) income							5.4	5.3
Ending balance	$ (80.6)			$ (55.6)			$ (80.6)	$ (55.6)

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A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

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Amount after tax, before reclassification adjustments of other comprehensive income (loss).

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