Solve 41/2*[(-12/3)div3]div3/4

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

Evaluate

$$-\frac{10}{3}\approx -3.333333333$$

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{\frac{8+1}{2}\times \frac{-\frac{1\times 3+2}{3}}{3}}{\frac{3}{4}}$$

Add 8 and 1 to get 9.

$$\frac{\frac{9}{2}\times \frac{-\frac{1\times 3+2}{3}}{3}}{\frac{3}{4}}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{9}{2}\times \frac{-\frac{3+2}{3}}{3}}{\frac{3}{4}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{9}{2}\times \frac{-\frac{5}{3}}{3}}{\frac{3}{4}}$$

Express \frac{-\frac{5}{3}}{3} as a single fraction.

$$\frac{\frac{9}{2}\times \frac{-5}{3\times 3}}{\frac{3}{4}}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{9}{2}\times \frac{-5}{9}}{\frac{3}{4}}$$

Fraction \frac{-5}{9} can be rewritten as -\frac{5}{9} by extracting the negative sign.

$$\frac{\frac{9}{2}\left(-\frac{5}{9}\right)}{\frac{3}{4}}$$

Multiply \frac{9}{2} times -\frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9\left(-5\right)}{2\times 9}}{\frac{3}{4}}$$

Cancel out 9 in both numerator and denominator.

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

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

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

Divide -\frac{5}{2} by \frac{3}{4} by multiplying -\frac{5}{2} by the reciprocal of \frac{3}{4}.

$$-\frac{5}{2}\times \frac{4}{3}$$

Multiply -\frac{5}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\times 4}{2\times 3}$$

Do the multiplications in the fraction \frac{-5\times 4}{2\times 3}.

$$\frac{-20}{6}$$

Reduce the fraction \frac{-20}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{10}{3}$$

Factor

$$-\frac{10}{3} = -3\frac{1}{3} = -3.3333333333333335$$