Solve 9-(3/2)-[8/3+(8-7)-(6-3-2/5)-3/10]=

$$9 - ( \frac { 3 } { 2 } ) - [ \frac { 8 } { 3 } + ( 8 - 7 ) - ( 6 - 3 - \frac { 2 } { 5 } ) - \frac { 3 } { 10 } ] =$$

Evaluate

$$\frac{101}{15}\approx 6.733333333$$

Solution Steps

Convert 9 to fraction \frac{18}{2}.

$$\frac{18}{2}-\frac{3}{2}-\left(\frac{8}{3}+8-7-\left(6-3-\frac{2}{5}\right)-\frac{3}{10}\right)$$

Since \frac{18}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-3}{2}-\left(\frac{8}{3}+8-7-\left(6-3-\frac{2}{5}\right)-\frac{3}{10}\right)$$

Subtract 3 from 18 to get 15.

$$\frac{15}{2}-\left(\frac{8}{3}+8-7-\left(6-3-\frac{2}{5}\right)-\frac{3}{10}\right)$$

Convert 8 to fraction \frac{24}{3}.

$$\frac{15}{2}-\left(\frac{8}{3}+\frac{24}{3}-7-\left(6-3-\frac{2}{5}\right)-\frac{3}{10}\right)$$

Since \frac{8}{3} and \frac{24}{3} have the same denominator, add them by adding their numerators.

$$\frac{15}{2}-\left(\frac{8+24}{3}-7-\left(6-3-\frac{2}{5}\right)-\frac{3}{10}\right)$$

Add 8 and 24 to get 32.

$$\frac{15}{2}-\left(\frac{32}{3}-7-\left(6-3-\frac{2}{5}\right)-\frac{3}{10}\right)$$

Convert 7 to fraction \frac{21}{3}.

$$\frac{15}{2}-\left(\frac{32}{3}-\frac{21}{3}-\left(6-3-\frac{2}{5}\right)-\frac{3}{10}\right)$$

Since \frac{32}{3} and \frac{21}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15}{2}-\left(\frac{32-21}{3}-\left(6-3-\frac{2}{5}\right)-\frac{3}{10}\right)$$

Subtract 21 from 32 to get 11.

$$\frac{15}{2}-\left(\frac{11}{3}-\left(6-3-\frac{2}{5}\right)-\frac{3}{10}\right)$$

Subtract 3 from 6 to get 3.

$$\frac{15}{2}-\left(\frac{11}{3}-\left(3-\frac{2}{5}\right)-\frac{3}{10}\right)$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{15}{2}-\left(\frac{11}{3}-\left(\frac{15}{5}-\frac{2}{5}\right)-\frac{3}{10}\right)$$

Since \frac{15}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15}{2}-\left(\frac{11}{3}-\frac{15-2}{5}-\frac{3}{10}\right)$$

Subtract 2 from 15 to get 13.

$$\frac{15}{2}-\left(\frac{11}{3}-\frac{13}{5}-\frac{3}{10}\right)$$

Least common multiple of 3 and 5 is 15. Convert \frac{11}{3} and \frac{13}{5} to fractions with denominator 15.

$$\frac{15}{2}-\left(\frac{55}{15}-\frac{39}{15}-\frac{3}{10}\right)$$

Since \frac{55}{15} and \frac{39}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15}{2}-\left(\frac{55-39}{15}-\frac{3}{10}\right)$$

Subtract 39 from 55 to get 16.

$$\frac{15}{2}-\left(\frac{16}{15}-\frac{3}{10}\right)$$

Least common multiple of 15 and 10 is 30. Convert \frac{16}{15} and \frac{3}{10} to fractions with denominator 30.

$$\frac{15}{2}-\left(\frac{32}{30}-\frac{9}{30}\right)$$

Since \frac{32}{30} and \frac{9}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15}{2}-\frac{32-9}{30}$$

Subtract 9 from 32 to get 23.

$$\frac{15}{2}-\frac{23}{30}$$

Least common multiple of 2 and 30 is 30. Convert \frac{15}{2} and \frac{23}{30} to fractions with denominator 30.

$$\frac{225}{30}-\frac{23}{30}$$

Since \frac{225}{30} and \frac{23}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{225-23}{30}$$

Subtract 23 from 225 to get 202.

$$\frac{202}{30}$$

Reduce the fraction \frac{202}{30} to lowest terms by extracting and canceling out 2.

$$\frac{101}{15}$$

Factor

$$\frac{101}{3 \cdot 5} = 6\frac{11}{15} = 6.733333333333333$$