The sum of three mixed numbers is 22 7/10. Two of the numbers are 5 2/3 and 9 5/6. what's the third number?

Addition/Subtraction of fractions.
5 2/3 + 9 5/6 + x = 22 7/10
Hence
x = 22 7/10 - 5 2/3 - 9 5/6
#1 step bring to Improper (top heavy) fractions.
227/10 - 17/3 - 59/6
#2 step bring to a common denominator of '30'.
227/30 - 17/30 - 59/30
#3 Bring the numerators to the equivalent fraction.
227(3)/30 - 17(10)/30 - 59(5)/30
#4 step multiply out the numerators
681/30 - 170/30 - 295/30
#5step subtract the numerators
216/30
#7 step bring to a mixed fraction
7 6/30 = 7 1/5
Answer is '7 1/5'
Hope that helps!!!!

17/3 + 59/6 + x = 227/10
54/6 + 59/6 + x = 227/10
112/6 + x = 227/10
x = 681/30 - 560/30
x = 121 / 30
x = 4 1/30

5 2/3 + 9 5/6 + x = 22 7/10
x = 22 7/10 - 5 2/3 - 9 5/6
x = (22-5-9) + (7/10-2/3-5/6)
x = 8 + (-4/5)
x = 7 1/5