10, 2: (18, 5 - (5 2/3 1.75 - 3 2/3 1.75) : 2 1/3)
Firstly, solve the expressions inside the parentheses:
5 2/3 1.75 = 17/3 7/4 = 119/12
3 2/3 1.75 = 11/3 7/4 = 77/12
Now subtract these two values: 119/12 - 77/12 = 42/12 = 3.5
Now substitute this value back into the original expression:
10, 2: (18, 5 - 3.5 : 2 1/3)
Next, simplify the division:
3.5 : 2 1/3 = 3.5 : 7/3 = 3.5 * 3/7 = 10.5/7 = 1.5
10, 2: (18, 5 - 1.5)
Now subtract the values inside the parentheses:
18, 5 - 1.5 = 17.5
Finally, substitute this value back into the original expression:
10, 2: 17.5
Now perform the division:
10, 2 / 17.5 = 80.64 : 1.6 - 3.4 : 1/6
Firstly, divide 80.64 by 1.6:
80.64 / 1.6 = 50.4
Now substitute this value back into the expression:
50.4 - 3.4 : 1/6
Now divide 3.4 by 1/6:
3.4 / (1/6) = 3.4 * 6 = 20.4
50.4 - 20.4
Finally, subtract the values:
50.4 - 20.4 = 30
Therefore, the final answer is 30.
10, 2: (18, 5 - (5 2/3 1.75 - 3 2/3 1.75) : 2 1/3)
Firstly, solve the expressions inside the parentheses:
5 2/3 1.75 = 17/3 7/4 = 119/12
3 2/3 1.75 = 11/3 7/4 = 77/12
Now subtract these two values: 119/12 - 77/12 = 42/12 = 3.5
Now substitute this value back into the original expression:
10, 2: (18, 5 - 3.5 : 2 1/3)
Next, simplify the division:
3.5 : 2 1/3 = 3.5 : 7/3 = 3.5 * 3/7 = 10.5/7 = 1.5
Now substitute this value back into the original expression:
10, 2: (18, 5 - 1.5)
Now subtract the values inside the parentheses:
18, 5 - 1.5 = 17.5
Finally, substitute this value back into the original expression:
10, 2: 17.5
Now perform the division:
10, 2 / 17.5 = 80.64 : 1.6 - 3.4 : 1/6
Firstly, divide 80.64 by 1.6:
80.64 / 1.6 = 50.4
Now substitute this value back into the expression:
50.4 - 3.4 : 1/6
Now divide 3.4 by 1/6:
3.4 / (1/6) = 3.4 * 6 = 20.4
Now substitute this value back into the expression:
50.4 - 20.4
Finally, subtract the values:
50.4 - 20.4 = 30
Therefore, the final answer is 30.