Question

((2 - 12 1/2 : (1/40 + 1/5 + (-(2)-(-6 2/3)) : (-1 2 /3 +1 5/6)) : 8 = ?

Answer 1

2 - 12 1/2) : (-1/40 + 1/5) + (- (-2) - (-6 2/3)) : (-1 2/3 + 1 5/6)) : 8 = - 1

1) 2 - 12 1/2 = - 10 1/2

2) -1/40 + 1/5 = 1/5 - 1/40 = 8/40 - 1/40 = 7/40

3) -(-2) - (-6 2/3) = 2 + 6 2/3 = 8 2/3

4) -1 2/3 + 1 5/6 = 1 5/6 - 1 2/3 = 1 5/6 - 1 4/6 = 1/6

5) -10 1/2 : 7/40 = -21/2 * 40/7 = - 3/1 * 20/1 = - 60

6) 8 2/3 : 1/6 = 26/3 * 6/1 = 52

7) -60 + 52 = - 8

8) -8 : 8 = -1

Answer 2

Let's break down the expression step by step to simplify it.

Step 1: Simplify the expression inside the parentheses. -(2) = -2 (-6 2/3) = -6 - 2/3 = -18/3 - 2/3 = -20/3

So the expression becomes: 2 - 12 1/2 : (1/40 + 1/5 + (-2 - (-20/3)) : (-1 2/3 + 1 5/6)) : 8

Step 2: Perform the operations inside the parentheses. (-1 2/3) = -1 - 2/3 = -3/3 - 2/3 = -5/3 (1 5/6) = 1 + 5/6 = 6/6 + 5/6 = 11/6

The expression now becomes: 2 - 12 1/2 : (1/40 + 1/5 + (-2 - (-20/3)) : (-5/3 + 11/6)) : 8

Step 3: Simplify the subtraction inside the expression. -2 - (-20/3) = -2 + 20/3 = -6/3 + 20/3 = 14/3

The expression simplifies to: 2 - 12 1/2 : (1/40 + 1/5 + 14/3 : (-5/3 + 11/6)) : 8

Step 4: Simplify the addition inside the expression. 1/40 + 1/5 = 1/40 + 8/40 = 9/40

The expression becomes: 2 - 12 1/2 : (9/40 + 14/3 : (-5/3 + 11/6)) : 8

Step 5: Simplify the subtraction and addition inside the expression. -5/3 + 11/6 = -10/6 + 11/6 = 1/6

The expression simplifies to: 2 - 12 1/2 : (9/40 + 14/3 : 1/6) : 8

Step 6: Simplify the division inside the expression. 9/40 + 14/3 : 1/6 = 9/40 + (14/3) * (6/1) = 9/40 + 84/3 = 9/40 + 28 = 9/40 + 280/40 = 289/40

The expression becomes: 2 - 12 1/2 : 289/40 : 8

Step 7: Simplify the subtraction inside the expression. 12 1/2 = 12 + 1/2 = 24/2 + 1/2 = 25/2

The expression simplifies to: 2 - 25/2 : 289/40 : 8

Step 8: Simplify the division inside the expression. 25/2 : 289/40 = 25/2 * 40/289 = 1000/578 = 500/289

The expression becomes: 2 - 500/289 : 8

Step 9: Simplify the subtraction inside the expression. 2 - 500/289 = 2 * 289/289 - 500/289 = (578 - 500)/289 = 78/289

The expression simplifies to: 78/289 : 8

Step 10: Simplify the division inside the expression. 78/289 : 8 = 78/289 * 1/8 = 78/2312 = 39/1156

Therefore, the final result of the expression ((2 - 12 1/2) : (1/40 + 1/5 + (-(2)-(-6 2/3)) : (-1 2 /3 +1 5/6)) : 8) is 39/1156.