Solve 21/3div(1/5-31/2)*81/3

$$2 \frac { 1 } { 3 } \div ( \frac { 1 } { 5 } - 3 \frac { 1 } { 2 } ) \times 8 \frac { 1 } { 3 }$$

Evaluate

$$-\frac{1750}{297}\approx -5.892255892$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{\frac{6+1}{3}}{\frac{1}{5}-\frac{3\times 2+1}{2}}\times \frac{8\times 3+1}{3}$$

Add 6 and 1 to get 7.

$$\frac{\frac{7}{3}}{\frac{1}{5}-\frac{3\times 2+1}{2}}\times \frac{8\times 3+1}{3}$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{7}{3}}{\frac{1}{5}-\frac{6+1}{2}}\times \frac{8\times 3+1}{3}$$

Add 6 and 1 to get 7.

$$\frac{\frac{7}{3}}{\frac{1}{5}-\frac{7}{2}}\times \frac{8\times 3+1}{3}$$

Least common multiple of 5 and 2 is 10. Convert \frac{1}{5} and \frac{7}{2} to fractions with denominator 10.

$$\frac{\frac{7}{3}}{\frac{2}{10}-\frac{35}{10}}\times \frac{8\times 3+1}{3}$$

Since \frac{2}{10} and \frac{35}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{3}}{\frac{2-35}{10}}\times \frac{8\times 3+1}{3}$$

Subtract 35 from 2 to get -33.

$$\frac{\frac{7}{3}}{-\frac{33}{10}}\times \frac{8\times 3+1}{3}$$

Divide \frac{7}{3} by -\frac{33}{10} by multiplying \frac{7}{3} by the reciprocal of -\frac{33}{10}.

$$\frac{7}{3}\left(-\frac{10}{33}\right)\times \frac{8\times 3+1}{3}$$

Multiply \frac{7}{3} times -\frac{10}{33} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-10\right)}{3\times 33}\times \frac{8\times 3+1}{3}$$

Do the multiplications in the fraction \frac{7\left(-10\right)}{3\times 33}.

$$\frac{-70}{99}\times \frac{8\times 3+1}{3}$$

Fraction \frac{-70}{99} can be rewritten as -\frac{70}{99} by extracting the negative sign.

$$-\frac{70}{99}\times \frac{8\times 3+1}{3}$$

Multiply 8 and 3 to get 24.

$$-\frac{70}{99}\times \frac{24+1}{3}$$

Add 24 and 1 to get 25.

$$-\frac{70}{99}\times \frac{25}{3}$$

Multiply -\frac{70}{99} times \frac{25}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-70\times 25}{99\times 3}$$

Do the multiplications in the fraction \frac{-70\times 25}{99\times 3}.

$$\frac{-1750}{297}$$

Fraction \frac{-1750}{297} can be rewritten as -\frac{1750}{297} by extracting the negative sign.

$$-\frac{1750}{297}$$

Factor

$$-\frac{1750}{297} = -5\frac{265}{297} = -5.892255892255892$$