Solve 7/2-[(3/2-1/5)*5+2div(1/3div1)-frac{5}{2}]

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

Evaluate

$$-\frac{13}{2}=-6.5$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{1}{5} to fractions with denominator 10.

$$\frac{7}{2}-\left(\left(\frac{15}{10}-\frac{2}{10}\right)\times 5+\frac{2}{\frac{\frac{1}{3}}{1}}-\frac{5}{2}\right)$$

Since \frac{15}{10} and \frac{2}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}-\left(\frac{15-2}{10}\times 5+\frac{2}{\frac{\frac{1}{3}}{1}}-\frac{5}{2}\right)$$

Subtract 2 from 15 to get 13.

$$\frac{7}{2}-\left(\frac{13}{10}\times 5+\frac{2}{\frac{\frac{1}{3}}{1}}-\frac{5}{2}\right)$$

Express \frac{13}{10}\times 5 as a single fraction.

$$\frac{7}{2}-\left(\frac{13\times 5}{10}+\frac{2}{\frac{\frac{1}{3}}{1}}-\frac{5}{2}\right)$$

Multiply 13 and 5 to get 65.

$$\frac{7}{2}-\left(\frac{65}{10}+\frac{2}{\frac{\frac{1}{3}}{1}}-\frac{5}{2}\right)$$

Reduce the fraction \frac{65}{10} to lowest terms by extracting and canceling out 5.

$$\frac{7}{2}-\left(\frac{13}{2}+\frac{2}{\frac{\frac{1}{3}}{1}}-\frac{5}{2}\right)$$

Divide 2 by \frac{\frac{1}{3}}{1} by multiplying 2 by the reciprocal of \frac{\frac{1}{3}}{1}.

$$\frac{7}{2}-\left(\frac{13}{2}+\frac{2}{\frac{1}{3}}-\frac{5}{2}\right)$$

Divide 2 by \frac{1}{3} by multiplying 2 by the reciprocal of \frac{1}{3}.

$$\frac{7}{2}-\left(\frac{13}{2}+2\times 3-\frac{5}{2}\right)$$

Multiply 2 and 3 to get 6.

$$\frac{7}{2}-\left(\frac{13}{2}+6-\frac{5}{2}\right)$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{7}{2}-\left(\frac{13}{2}+\frac{12}{2}-\frac{5}{2}\right)$$

Since \frac{13}{2} and \frac{12}{2} have the same denominator, add them by adding their numerators.

$$\frac{7}{2}-\left(\frac{13+12}{2}-\frac{5}{2}\right)$$

Add 13 and 12 to get 25.

$$\frac{7}{2}-\left(\frac{25}{2}-\frac{5}{2}\right)$$

Since \frac{25}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}-\frac{25-5}{2}$$

Subtract 5 from 25 to get 20.

$$\frac{7}{2}-\frac{20}{2}$$

Since \frac{7}{2} and \frac{20}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-20}{2}$$

Subtract 20 from 7 to get -13.

$$-\frac{13}{2}$$

Factor

$$-\frac{13}{2} = -6\frac{1}{2} = -6.5$$