2 1/4 was subtracted twice from a number; then 1/8 was subtracted three times and 2/3 was subtracted twice. The resulting number is 3 11/24. Find the number

We will call the unknown number x.

x - 2 1/4 - 1/8 (3) - 2/3 (2) = 3 11/24

x - 2 1/4 - (1/8) (3/1) - (2/3) (2/1) = 3 11/24

x - 2 1/4 - 3/8 - 4/3 = 3 11/24

We need a common denominator. 24 is the first number that 4, 8 and 3 all both divide evenly into.

x - 2 6/24 - 9/24 - 32/24 = 3 11/24

x - 2 15/24 - 32/24 = 3 11/24

x - 2 47/24 = 3 11/24

x - 3 23/24 = 3 11/24

Cancel the 3 23/34 by adding to both sides:

x - 3 23/24 + 3 23/24 = 3 11/24 + 3 23/24

x = 6 34/24 = 7 10/24 = 7 5/12