Solve [(-0.5)^2-1/36div(-1/3)^3]*2/3-(1/3)^2div2.5*1.5

$$[ ( - 0.5 ) ^ { 2 } - \frac { 1 } { 36 } \div ( - \frac { 1 } { 3 } ) ^ { 3 } ] \times \frac { 2 } { 3 } - ( \frac { 1 } { 3 } ) ^ { 2 } \div 2.5 \times 1.5$$

Evaluate

$$0.6$$

Solution Steps

Calculate -0.5 to the power of 2 and get 0.25.

$$\left(0.25-\frac{\frac{1}{36}}{\left(-\frac{1}{3}\right)^{3}}\right)\times \frac{2}{3}-\frac{\left(\frac{1}{3}\right)^{2}}{2.5}\times 1.5$$

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$\left(0.25-\frac{\frac{1}{36}}{-\frac{1}{27}}\right)\times \frac{2}{3}-\frac{\left(\frac{1}{3}\right)^{2}}{2.5}\times 1.5$$

Divide \frac{1}{36} by -\frac{1}{27} by multiplying \frac{1}{36} by the reciprocal of -\frac{1}{27}.

$$\left(0.25-\frac{1}{36}\left(-27\right)\right)\times \frac{2}{3}-\frac{\left(\frac{1}{3}\right)^{2}}{2.5}\times 1.5$$

Multiply \frac{1}{36} and -27 to get \frac{-27}{36}.

$$\left(0.25-\frac{-27}{36}\right)\times \frac{2}{3}-\frac{\left(\frac{1}{3}\right)^{2}}{2.5}\times 1.5$$

Reduce the fraction \frac{-27}{36} to lowest terms by extracting and canceling out 9.

$$\left(0.25-\left(-\frac{3}{4}\right)\right)\times \frac{2}{3}-\frac{\left(\frac{1}{3}\right)^{2}}{2.5}\times 1.5$$

The opposite of -\frac{3}{4} is \frac{3}{4}.

$$\left(0.25+\frac{3}{4}\right)\times \frac{2}{3}-\frac{\left(\frac{1}{3}\right)^{2}}{2.5}\times 1.5$$

Convert decimal number 0.25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\left(\frac{1}{4}+\frac{3}{4}\right)\times \frac{2}{3}-\frac{\left(\frac{1}{3}\right)^{2}}{2.5}\times 1.5$$

Since \frac{1}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{1+3}{4}\times \frac{2}{3}-\frac{\left(\frac{1}{3}\right)^{2}}{2.5}\times 1.5$$

Add 1 and 3 to get 4.

$$\frac{4}{4}\times \frac{2}{3}-\frac{\left(\frac{1}{3}\right)^{2}}{2.5}\times 1.5$$

Divide 4 by 4 to get 1.

$$1\times \frac{2}{3}-\frac{\left(\frac{1}{3}\right)^{2}}{2.5}\times 1.5$$

Multiply 1 and \frac{2}{3} to get \frac{2}{3}.

$$\frac{2}{3}-\frac{\left(\frac{1}{3}\right)^{2}}{2.5}\times 1.5$$

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

$$\frac{2}{3}-\frac{\frac{1}{9}}{2.5}\times 1.5$$

Express \frac{\frac{1}{9}}{2.5} as a single fraction.

$$\frac{2}{3}-\frac{1}{9\times 2.5}\times 1.5$$

Multiply 9 and 2.5 to get 22.5.

$$\frac{2}{3}-\frac{1}{22.5}\times 1.5$$

Expand \frac{1}{22.5} by multiplying both numerator and the denominator by 10.

$$\frac{2}{3}-\frac{10}{225}\times 1.5$$

Reduce the fraction \frac{10}{225} to lowest terms by extracting and canceling out 5.

$$\frac{2}{3}-\frac{2}{45}\times 1.5$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{2}{3}-\frac{2}{45}\times \frac{3}{2}$$

Multiply \frac{2}{45} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}-\frac{2\times 3}{45\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2}{3}-\frac{3}{45}$$

Reduce the fraction \frac{3}{45} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}-\frac{1}{15}$$

Least common multiple of 3 and 15 is 15. Convert \frac{2}{3} and \frac{1}{15} to fractions with denominator 15.

$$\frac{10}{15}-\frac{1}{15}$$

Since \frac{10}{15} and \frac{1}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-1}{15}$$

Subtract 1 from 10 to get 9.

$$\frac{9}{15}$$

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

$$\frac{3}{5}$$

Factor

$$\frac{3}{5} = 0.6$$