Solve 31/1[(1/2+2/5)*2/3]

$$3 \frac { 1 } { 1 } [ ( \frac { 1 } { 2 } + \frac { 2 } { 5 } ) \times \frac { 2 } { 3 } ]$$

Evaluate

$$\frac{12}{5}=2.4$$

Solution Steps

Multiply 3 and 1 to get 3.

$$\frac{3+1}{1}\left(\frac{1}{2}+\frac{2}{5}\right)\times \frac{2}{3}$$

Add 3 and 1 to get 4.

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

Anything divided by one gives itself.

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

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{2}{5} to fractions with denominator 10.

$$4\left(\frac{5}{10}+\frac{4}{10}\right)\times \frac{2}{3}$$

Since \frac{5}{10} and \frac{4}{10} have the same denominator, add them by adding their numerators.

$$4\times \frac{5+4}{10}\times \frac{2}{3}$$

Add 5 and 4 to get 9.

$$4\times \frac{9}{10}\times \frac{2}{3}$$

Express 4\times \frac{9}{10} as a single fraction.

$$\frac{4\times 9}{10}\times \frac{2}{3}$$

Multiply 4 and 9 to get 36.

$$\frac{36}{10}\times \frac{2}{3}$$

Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$\frac{18}{5}\times \frac{2}{3}$$

Multiply \frac{18}{5} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{18\times 2}{5\times 3}$$

Do the multiplications in the fraction \frac{18\times 2}{5\times 3}.

$$\frac{36}{15}$$

Reduce the fraction \frac{36}{15} to lowest terms by extracting and canceling out 3.

$$\frac{12}{5}$$

Factor

$$\frac{2 ^ {2} \cdot 3}{5} = 2\frac{2}{5} = 2.4$$