Solve 4*-1/12*5/3-{left(frac{2/3right)}^2}{4*-1/12}

$$\frac{ 4 \times - \frac{ 1 }{ 12 } \times \frac{ 5 }{ 3 } - { \left( \frac{ 2 }{ 3 } \right) }^{ 2 } }{ 4 \times - \frac{ 1 }{ 12 } }$$

Evaluate

$$3$$

Solution Steps

Express 4\left(-\frac{1}{12}\right) as a single fraction.

$$\frac{\frac{4\left(-1\right)}{12}\times \frac{5}{3}-\left(\frac{2}{3}\right)^{2}}{4\left(-\frac{1}{12}\right)}$$

Multiply 4 and -1 to get -4.

$$\frac{\frac{-4}{12}\times \frac{5}{3}-\left(\frac{2}{3}\right)^{2}}{4\left(-\frac{1}{12}\right)}$$

Reduce the fraction \frac{-4}{12} to lowest terms by extracting and canceling out 4.

$$\frac{-\frac{1}{3}\times \frac{5}{3}-\left(\frac{2}{3}\right)^{2}}{4\left(-\frac{1}{12}\right)}$$

Multiply -\frac{1}{3} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-5}{3\times 3}-\left(\frac{2}{3}\right)^{2}}{4\left(-\frac{1}{12}\right)}$$

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

$$\frac{\frac{-5}{9}-\left(\frac{2}{3}\right)^{2}}{4\left(-\frac{1}{12}\right)}$$

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

$$\frac{-\frac{5}{9}-\left(\frac{2}{3}\right)^{2}}{4\left(-\frac{1}{12}\right)}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{-\frac{5}{9}-\frac{4}{9}}{4\left(-\frac{1}{12}\right)}$$

Since -\frac{5}{9} and \frac{4}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-5-4}{9}}{4\left(-\frac{1}{12}\right)}$$

Subtract 4 from -5 to get -9.

$$\frac{\frac{-9}{9}}{4\left(-\frac{1}{12}\right)}$$

Divide -9 by 9 to get -1.

$$\frac{-1}{4\left(-\frac{1}{12}\right)}$$

Express 4\left(-\frac{1}{12}\right) as a single fraction.

$$\frac{-1}{\frac{4\left(-1\right)}{12}}$$

Multiply 4 and -1 to get -4.

$$\frac{-1}{\frac{-4}{12}}$$

Reduce the fraction \frac{-4}{12} to lowest terms by extracting and canceling out 4.

$$\frac{-1}{-\frac{1}{3}}$$

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

$$-\left(-3\right)$$

Multiply -1 and -3 to get 3.

$$3$$

Factor

$$3$$