Solve 4*1/3*-2-(-1/2)^2/4*frac{1{3}}

$$\frac { 4 \cdot \frac { 1 } { 3 } \cdot - 2 - ( - \frac { 1 } { 2 } ) ^ { 2 } } { 4 \times \frac { 1 } { 3 } }$$

Evaluate

$$-\frac{35}{16}=-2.1875$$

Solution Steps

Multiply 4 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{\frac{4}{3}\left(-2\right)-\left(-\frac{1}{2}\right)^{2}}{4\times \frac{1}{3}}$$

Express \frac{4}{3}\left(-2\right) as a single fraction.

$$\frac{\frac{4\left(-2\right)}{3}-\left(-\frac{1}{2}\right)^{2}}{4\times \frac{1}{3}}$$

Multiply 4 and -2 to get -8.

$$\frac{\frac{-8}{3}-\left(-\frac{1}{2}\right)^{2}}{4\times \frac{1}{3}}$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$\frac{-\frac{8}{3}-\left(-\frac{1}{2}\right)^{2}}{4\times \frac{1}{3}}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

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

Least common multiple of 3 and 4 is 12. Convert -\frac{8}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{-\frac{32}{12}-\frac{3}{12}}{4\times \frac{1}{3}}$$

Since -\frac{32}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-32-3}{12}}{4\times \frac{1}{3}}$$

Subtract 3 from -32 to get -35.

$$\frac{-\frac{35}{12}}{4\times \frac{1}{3}}$$

Multiply 4 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{-\frac{35}{12}}{\frac{4}{3}}$$

Divide -\frac{35}{12} by \frac{4}{3} by multiplying -\frac{35}{12} by the reciprocal of \frac{4}{3}.

$$-\frac{35}{12}\times \frac{3}{4}$$

Multiply -\frac{35}{12} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-35\times 3}{12\times 4}$$

Do the multiplications in the fraction \frac{-35\times 3}{12\times 4}.

$$\frac{-105}{48}$$

Reduce the fraction \frac{-105}{48} to lowest terms by extracting and canceling out 3.

$$-\frac{35}{16}$$

Factor

$$-\frac{35}{16} = -2\frac{3}{16} = -2.1875$$