The smallest fraction, which should be added to the sum

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The smallest fraction, which should be added to the sum of
2 1 , 3 1 , 4 1 , and 5 1
2 3 4 5

to make the result a whole number, is

2	1	+ 3	1	+ 4	1	+ 5	1
	2		3		4		5

= (2 + 3 + 4 + 5) +		1	+	1	+	1	+	1
		2		3		4		5

= 14 +		30 + 20 + 15 + 12
		60

= 14 +	77	= 14 + 1	17
	60		60

= 15	77
	60

∴ Required answer = 1 –	77	=	60 − 17	=	43
	60		60		60

2	1	, 3	1	, 4	1	, and 5	1
	2		3		4		5