Solve 14/5*(32/3-15/6)+(1/2)^3=

$$1 \frac { 4 } { 5 } \cdot ( 3 \frac { 2 } { 3 } - 1 \frac { 5 } { 6 } ) + ( \frac { 1 } { 2 } ) ^ { 3 } =$$

Evaluate

$$\frac{137}{40}=3.425$$

Solution Steps

Multiply 1 and 5 to get 5.

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

Add 5 and 4 to get 9.

$$\frac{9}{5}\left(\frac{3\times 3+2}{3}-\frac{1\times 6+5}{6}\right)+\left(\frac{1}{2}\right)^{3}$$

Multiply 3 and 3 to get 9.

$$\frac{9}{5}\left(\frac{9+2}{3}-\frac{1\times 6+5}{6}\right)+\left(\frac{1}{2}\right)^{3}$$

Add 9 and 2 to get 11.

$$\frac{9}{5}\left(\frac{11}{3}-\frac{1\times 6+5}{6}\right)+\left(\frac{1}{2}\right)^{3}$$

Multiply 1 and 6 to get 6.

$$\frac{9}{5}\left(\frac{11}{3}-\frac{6+5}{6}\right)+\left(\frac{1}{2}\right)^{3}$$

Add 6 and 5 to get 11.

$$\frac{9}{5}\left(\frac{11}{3}-\frac{11}{6}\right)+\left(\frac{1}{2}\right)^{3}$$

Least common multiple of 3 and 6 is 6. Convert \frac{11}{3} and \frac{11}{6} to fractions with denominator 6.

$$\frac{9}{5}\left(\frac{22}{6}-\frac{11}{6}\right)+\left(\frac{1}{2}\right)^{3}$$

Since \frac{22}{6} and \frac{11}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{5}\times \frac{22-11}{6}+\left(\frac{1}{2}\right)^{3}$$

Subtract 11 from 22 to get 11.

$$\frac{9}{5}\times \frac{11}{6}+\left(\frac{1}{2}\right)^{3}$$

Multiply \frac{9}{5} times \frac{11}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 11}{5\times 6}+\left(\frac{1}{2}\right)^{3}$$

Do the multiplications in the fraction \frac{9\times 11}{5\times 6}.

$$\frac{99}{30}+\left(\frac{1}{2}\right)^{3}$$

Reduce the fraction \frac{99}{30} to lowest terms by extracting and canceling out 3.

$$\frac{33}{10}+\left(\frac{1}{2}\right)^{3}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{33}{10}+\frac{1}{8}$$

Least common multiple of 10 and 8 is 40. Convert \frac{33}{10} and \frac{1}{8} to fractions with denominator 40.

$$\frac{132}{40}+\frac{5}{40}$$

Since \frac{132}{40} and \frac{5}{40} have the same denominator, add them by adding their numerators.

$$\frac{132+5}{40}$$

Add 132 and 5 to get 137.

$$\frac{137}{40}$$

Factor

$$\frac{137}{2 ^ {3} \cdot 5} = 3\frac{17}{40} = 3.425$$