Solve -{31/2-[-(71/5-4)+(20/5-2)]-5}

$$- \{ 3 \frac { 1 } { 2 } - [ - ( 7 \frac { 1 } { 5 } - 4 ) + ( \frac { 20 } { 5 } - 2 ) ] - 5 \}$$

Evaluate

$$\frac{3}{10}=0.3$$

Solution Steps

Multiply 3 and 2 to get 6.

$$-\left(\frac{6+1}{2}-\left(-\left(\frac{7\times 5+1}{5}-4\right)+\frac{20}{5}-2\right)-5\right)$$

Add 6 and 1 to get 7.

$$-\left(\frac{7}{2}-\left(-\left(\frac{7\times 5+1}{5}-4\right)+\frac{20}{5}-2\right)-5\right)$$

Multiply 7 and 5 to get 35.

$$-\left(\frac{7}{2}-\left(-\left(\frac{35+1}{5}-4\right)+\frac{20}{5}-2\right)-5\right)$$

Add 35 and 1 to get 36.

$$-\left(\frac{7}{2}-\left(-\left(\frac{36}{5}-4\right)+\frac{20}{5}-2\right)-5\right)$$

Convert 4 to fraction \frac{20}{5}.

$$-\left(\frac{7}{2}-\left(-\left(\frac{36}{5}-\frac{20}{5}\right)+\frac{20}{5}-2\right)-5\right)$$

Since \frac{36}{5} and \frac{20}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\left(\frac{7}{2}-\left(-\frac{36-20}{5}+\frac{20}{5}-2\right)-5\right)$$

Subtract 20 from 36 to get 16.

$$-\left(\frac{7}{2}-\left(-\frac{16}{5}+\frac{20}{5}-2\right)-5\right)$$

Since -\frac{16}{5} and \frac{20}{5} have the same denominator, add them by adding their numerators.

$$-\left(\frac{7}{2}-\left(\frac{-16+20}{5}-2\right)-5\right)$$

Add -16 and 20 to get 4.

$$-\left(\frac{7}{2}-\left(\frac{4}{5}-2\right)-5\right)$$

Convert 2 to fraction \frac{10}{5}.

$$-\left(\frac{7}{2}-\left(\frac{4}{5}-\frac{10}{5}\right)-5\right)$$

Since \frac{4}{5} and \frac{10}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\left(\frac{7}{2}-\frac{4-10}{5}-5\right)$$

Subtract 10 from 4 to get -6.

$$-\left(\frac{7}{2}-\left(-\frac{6}{5}\right)-5\right)$$

The opposite of -\frac{6}{5} is \frac{6}{5}.

$$-\left(\frac{7}{2}+\frac{6}{5}-5\right)$$

Least common multiple of 2 and 5 is 10. Convert \frac{7}{2} and \frac{6}{5} to fractions with denominator 10.

$$-\left(\frac{35}{10}+\frac{12}{10}-5\right)$$

Since \frac{35}{10} and \frac{12}{10} have the same denominator, add them by adding their numerators.

$$-\left(\frac{35+12}{10}-5\right)$$

Add 35 and 12 to get 47.

$$-\left(\frac{47}{10}-5\right)$$

Convert 5 to fraction \frac{50}{10}.

$$-\left(\frac{47}{10}-\frac{50}{10}\right)$$

Since \frac{47}{10} and \frac{50}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{47-50}{10}$$

Subtract 50 from 47 to get -3.

$$-\left(-\frac{3}{10}\right)$$

The opposite of -\frac{3}{10} is \frac{3}{10}.

$$\frac{3}{10}$$

Factor

$$\frac{3}{2 \cdot 5} = 0.3$$