Solve (-41/3-31/2)*2+22/3div(-1/2)

$$( - 4 \frac { 1 } { 3 } - 3 \frac { 1 } { 2 } ) \times 2 + 2 \frac { 2 } { 3 } \div ( - \frac { 1 } { 2 } )$$

Evaluate

$$-21$$

Solution Steps

Multiply 4 and 3 to get 12.

$$\left(-\frac{12+1}{3}-\frac{3\times 2+1}{2}\right)\times 2+\frac{\frac{2\times 3+2}{3}}{-\frac{1}{2}}$$

Add 12 and 1 to get 13.

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

Multiply 3 and 2 to get 6.

$$\left(-\frac{13}{3}-\frac{6+1}{2}\right)\times 2+\frac{\frac{2\times 3+2}{3}}{-\frac{1}{2}}$$

Add 6 and 1 to get 7.

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

Least common multiple of 3 and 2 is 6. Convert -\frac{13}{3} and \frac{7}{2} to fractions with denominator 6.

$$\left(-\frac{26}{6}-\frac{21}{6}\right)\times 2+\frac{\frac{2\times 3+2}{3}}{-\frac{1}{2}}$$

Since -\frac{26}{6} and \frac{21}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-26-21}{6}\times 2+\frac{\frac{2\times 3+2}{3}}{-\frac{1}{2}}$$

Subtract 21 from -26 to get -47.

$$-\frac{47}{6}\times 2+\frac{\frac{2\times 3+2}{3}}{-\frac{1}{2}}$$

Express -\frac{47}{6}\times 2 as a single fraction.

$$\frac{-47\times 2}{6}+\frac{\frac{2\times 3+2}{3}}{-\frac{1}{2}}$$

Multiply -47 and 2 to get -94.

$$\frac{-94}{6}+\frac{\frac{2\times 3+2}{3}}{-\frac{1}{2}}$$

Reduce the fraction \frac{-94}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{47}{3}+\frac{\frac{2\times 3+2}{3}}{-\frac{1}{2}}$$

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

$$-\frac{47}{3}+\frac{\left(2\times 3+2\right)\times 2}{3\left(-1\right)}$$

Multiply 2 and 3 to get 6.

$$-\frac{47}{3}+\frac{\left(6+2\right)\times 2}{3\left(-1\right)}$$

Add 6 and 2 to get 8.

$$-\frac{47}{3}+\frac{8\times 2}{3\left(-1\right)}$$

Multiply 8 and 2 to get 16.

$$-\frac{47}{3}+\frac{16}{3\left(-1\right)}$$

Multiply 3 and -1 to get -3.

$$-\frac{47}{3}+\frac{16}{-3}$$

Fraction \frac{16}{-3} can be rewritten as -\frac{16}{3} by extracting the negative sign.

$$-\frac{47}{3}-\frac{16}{3}$$

Since -\frac{47}{3} and \frac{16}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-47-16}{3}$$

Subtract 16 from -47 to get -63.

$$\frac{-63}{3}$$

Divide -63 by 3 to get -21.

$$-21$$

Factor

$$-21$$