Solve 4+[2+(8-5)div1(4+1)]div[10-(4-2)+6(1+1)-6]+2=

$$4 + [ 2 + ( 8 - 5 ) \div 1 ( 4 + 1 ) ] \div [ 10 - ( 4 - 2 ) + 6 ( 1 + 1 ) - 6 ] + 2 =$$

Evaluate

$$\frac{101}{14}\approx 7.214285714$$

Solution Steps

Subtract 5 from 8 to get 3.

$$4+\frac{2+\frac{3}{1}\left(4+1\right)}{10-\left(4-2\right)+6\left(1+1\right)-6}+2$$

Anything divided by one gives itself.

$$4+\frac{2+3\left(4+1\right)}{10-\left(4-2\right)+6\left(1+1\right)-6}+2$$

Add 4 and 1 to get 5.

$$4+\frac{2+3\times 5}{10-\left(4-2\right)+6\left(1+1\right)-6}+2$$

Multiply 3 and 5 to get 15.

$$4+\frac{2+15}{10-\left(4-2\right)+6\left(1+1\right)-6}+2$$

Add 2 and 15 to get 17.

$$4+\frac{17}{10-\left(4-2\right)+6\left(1+1\right)-6}+2$$

Subtract 2 from 4 to get 2.

$$4+\frac{17}{10-2+6\left(1+1\right)-6}+2$$

Subtract 2 from 10 to get 8.

$$4+\frac{17}{8+6\left(1+1\right)-6}+2$$

Add 1 and 1 to get 2.

$$4+\frac{17}{8+6\times 2-6}+2$$

Multiply 6 and 2 to get 12.

$$4+\frac{17}{8+12-6}+2$$

Add 8 and 12 to get 20.

$$4+\frac{17}{20-6}+2$$

Subtract 6 from 20 to get 14.

$$4+\frac{17}{14}+2$$

Convert 4 to fraction \frac{56}{14}.

$$\frac{56}{14}+\frac{17}{14}+2$$

Since \frac{56}{14} and \frac{17}{14} have the same denominator, add them by adding their numerators.

$$\frac{56+17}{14}+2$$

Add 56 and 17 to get 73.

$$\frac{73}{14}+2$$

Convert 2 to fraction \frac{28}{14}.

$$\frac{73}{14}+\frac{28}{14}$$

Since \frac{73}{14} and \frac{28}{14} have the same denominator, add them by adding their numerators.

$$\frac{73+28}{14}$$

Add 73 and 28 to get 101.

$$\frac{101}{14}$$

Factor

$$\frac{101}{2 \cdot 7} = 7\frac{3}{14} = 7.214285714285714$$