Solve -5/3+3/8/3-2{4+frac{2/3}}

$$\frac { \frac { - 5 } { 3 } + \frac { 3 } { 8 } } { 3 - \frac { 2 } { 4 + \frac { 2 } { 3 } } }$$

Evaluate

$$-\frac{217}{432}\approx -0.502314815$$

Solution Steps

Fraction \frac{-5}{3} can be rewritten as -\frac{5}{3} by extracting the negative sign.

$$\frac{-\frac{5}{3}+\frac{3}{8}}{3-\frac{2}{4+\frac{2}{3}}}$$

Least common multiple of 3 and 8 is 24. Convert -\frac{5}{3} and \frac{3}{8} to fractions with denominator 24.

$$\frac{-\frac{40}{24}+\frac{9}{24}}{3-\frac{2}{4+\frac{2}{3}}}$$

Since -\frac{40}{24} and \frac{9}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-40+9}{24}}{3-\frac{2}{4+\frac{2}{3}}}$$

Add -40 and 9 to get -31.

$$\frac{-\frac{31}{24}}{3-\frac{2}{4+\frac{2}{3}}}$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{-\frac{31}{24}}{3-\frac{2}{\frac{12}{3}+\frac{2}{3}}}$$

Since \frac{12}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{31}{24}}{3-\frac{2}{\frac{12+2}{3}}}$$

Add 12 and 2 to get 14.

$$\frac{-\frac{31}{24}}{3-\frac{2}{\frac{14}{3}}}$$

Divide 2 by \frac{14}{3} by multiplying 2 by the reciprocal of \frac{14}{3}.

$$\frac{-\frac{31}{24}}{3-2\times \frac{3}{14}}$$

Express 2\times \frac{3}{14} as a single fraction.

$$\frac{-\frac{31}{24}}{3-\frac{2\times 3}{14}}$$

Multiply 2 and 3 to get 6.

$$\frac{-\frac{31}{24}}{3-\frac{6}{14}}$$

Reduce the fraction \frac{6}{14} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{31}{24}}{3-\frac{3}{7}}$$

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

$$\frac{-\frac{31}{24}}{\frac{21}{7}-\frac{3}{7}}$$

Since \frac{21}{7} and \frac{3}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{31}{24}}{\frac{21-3}{7}}$$

Subtract 3 from 21 to get 18.

$$\frac{-\frac{31}{24}}{\frac{18}{7}}$$

Divide -\frac{31}{24} by \frac{18}{7} by multiplying -\frac{31}{24} by the reciprocal of \frac{18}{7}.

$$-\frac{31}{24}\times \frac{7}{18}$$

Multiply -\frac{31}{24} times \frac{7}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-31\times 7}{24\times 18}$$

Do the multiplications in the fraction \frac{-31\times 7}{24\times 18}.

$$\frac{-217}{432}$$

Fraction \frac{-217}{432} can be rewritten as -\frac{217}{432} by extracting the negative sign.

$$-\frac{217}{432}$$

Factor

$$-\frac{217}{432} = -0.5023148148148148$$