Solve 2/7-[4/3-(1/2+2/5)+frac{3}{2}]-frac{8}{3}

$$\frac { 2 } { 7 } - [ \frac { 4 } { 3 } - ( \frac { 1 } { 2 } + \frac { 2 } { 5 } ) + \frac { 3 } { 2 } ] - \frac { 8 } { 3 }$$

Evaluate

$$-\frac{151}{35}\approx -4.314285714$$

Solution Steps

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

$$\frac{2}{7}-\left(\frac{4}{3}-\left(\frac{5}{10}+\frac{4}{10}\right)+\frac{3}{2}\right)-\frac{8}{3}$$

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

$$\frac{2}{7}-\left(\frac{4}{3}-\frac{5+4}{10}+\frac{3}{2}\right)-\frac{8}{3}$$

Add 5 and 4 to get 9.

$$\frac{2}{7}-\left(\frac{4}{3}-\frac{9}{10}+\frac{3}{2}\right)-\frac{8}{3}$$

Least common multiple of 3 and 10 is 30. Convert \frac{4}{3} and \frac{9}{10} to fractions with denominator 30.

$$\frac{2}{7}-\left(\frac{40}{30}-\frac{27}{30}+\frac{3}{2}\right)-\frac{8}{3}$$

Since \frac{40}{30} and \frac{27}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{7}-\left(\frac{40-27}{30}+\frac{3}{2}\right)-\frac{8}{3}$$

Subtract 27 from 40 to get 13.

$$\frac{2}{7}-\left(\frac{13}{30}+\frac{3}{2}\right)-\frac{8}{3}$$

Least common multiple of 30 and 2 is 30. Convert \frac{13}{30} and \frac{3}{2} to fractions with denominator 30.

$$\frac{2}{7}-\left(\frac{13}{30}+\frac{45}{30}\right)-\frac{8}{3}$$

Since \frac{13}{30} and \frac{45}{30} have the same denominator, add them by adding their numerators.

$$\frac{2}{7}-\frac{13+45}{30}-\frac{8}{3}$$

Add 13 and 45 to get 58.

$$\frac{2}{7}-\frac{58}{30}-\frac{8}{3}$$

Reduce the fraction \frac{58}{30} to lowest terms by extracting and canceling out 2.

$$\frac{2}{7}-\frac{29}{15}-\frac{8}{3}$$

Least common multiple of 7 and 15 is 105. Convert \frac{2}{7} and \frac{29}{15} to fractions with denominator 105.

$$\frac{30}{105}-\frac{203}{105}-\frac{8}{3}$$

Since \frac{30}{105} and \frac{203}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30-203}{105}-\frac{8}{3}$$

Subtract 203 from 30 to get -173.

$$-\frac{173}{105}-\frac{8}{3}$$

Least common multiple of 105 and 3 is 105. Convert -\frac{173}{105} and \frac{8}{3} to fractions with denominator 105.

$$-\frac{173}{105}-\frac{280}{105}$$

Since -\frac{173}{105} and \frac{280}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-173-280}{105}$$

Subtract 280 from -173 to get -453.

$$\frac{-453}{105}$$

Reduce the fraction \frac{-453}{105} to lowest terms by extracting and canceling out 3.

$$-\frac{151}{35}$$

Factor

$$-\frac{151}{35} = -4\frac{11}{35} = -4.314285714285714$$