Solve [2/3div(-4)-1/4*(-0.4)]div(1/3)^2-(-2)

$$[ \frac { 2 } { 3 } \div ( - 4 ) - \frac { 1 } { 4 } \times ( - 0.4 ) ] \div ( \frac { 1 } { 3 } ) ^ { 2 } - ( - 2 )$$

Evaluate

$$1.4$$

Solution Steps

Express \frac{\frac{2}{3}}{-4} as a single fraction.

$$\frac{\frac{2}{3\left(-4\right)}-\frac{1}{4}\left(-0.4\right)}{\left(\frac{1}{3}\right)^{2}}-\left(-2\right)$$

Multiply 3 and -4 to get -12.

$$\frac{\frac{2}{-12}-\frac{1}{4}\left(-0.4\right)}{\left(\frac{1}{3}\right)^{2}}-\left(-2\right)$$

Reduce the fraction \frac{2}{-12} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{1}{6}-\frac{1}{4}\left(-0.4\right)}{\left(\frac{1}{3}\right)^{2}}-\left(-2\right)$$

Convert decimal number -0.4 to fraction -\frac{4}{10}. Reduce the fraction -\frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{1}{6}-\frac{1}{4}\left(-\frac{2}{5}\right)}{\left(\frac{1}{3}\right)^{2}}-\left(-2\right)$$

Multiply \frac{1}{4} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{1}{6}-\frac{1\left(-2\right)}{4\times 5}}{\left(\frac{1}{3}\right)^{2}}-\left(-2\right)$$

Do the multiplications in the fraction \frac{1\left(-2\right)}{4\times 5}.

$$\frac{-\frac{1}{6}-\frac{-2}{20}}{\left(\frac{1}{3}\right)^{2}}-\left(-2\right)$$

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

$$\frac{-\frac{1}{6}-\left(-\frac{1}{10}\right)}{\left(\frac{1}{3}\right)^{2}}-\left(-2\right)$$

The opposite of -\frac{1}{10} is \frac{1}{10}.

$$\frac{-\frac{1}{6}+\frac{1}{10}}{\left(\frac{1}{3}\right)^{2}}-\left(-2\right)$$

Least common multiple of 6 and 10 is 30. Convert -\frac{1}{6} and \frac{1}{10} to fractions with denominator 30.

$$\frac{-\frac{5}{30}+\frac{3}{30}}{\left(\frac{1}{3}\right)^{2}}-\left(-2\right)$$

Since -\frac{5}{30} and \frac{3}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-5+3}{30}}{\left(\frac{1}{3}\right)^{2}}-\left(-2\right)$$

Add -5 and 3 to get -2.

$$\frac{\frac{-2}{30}}{\left(\frac{1}{3}\right)^{2}}-\left(-2\right)$$

Reduce the fraction \frac{-2}{30} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{1}{15}}{\left(\frac{1}{3}\right)^{2}}-\left(-2\right)$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{-\frac{1}{15}}{\frac{1}{9}}-\left(-2\right)$$

Divide -\frac{1}{15} by \frac{1}{9} by multiplying -\frac{1}{15} by the reciprocal of \frac{1}{9}.

$$-\frac{1}{15}\times 9-\left(-2\right)$$

Express -\frac{1}{15}\times 9 as a single fraction.

$$\frac{-9}{15}-\left(-2\right)$$

Reduce the fraction \frac{-9}{15} to lowest terms by extracting and canceling out 3.

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

The opposite of -2 is 2.

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

Convert 2 to fraction \frac{10}{5}.

$$-\frac{3}{5}+\frac{10}{5}$$

Since -\frac{3}{5} and \frac{10}{5} have the same denominator, add them by adding their numerators.

$$\frac{-3+10}{5}$$

Add -3 and 10 to get 7.

$$\frac{7}{5}$$

Factor

$$\frac{7}{5} = 1\frac{2}{5} = 1.4$$