Solve 2/3+[3/5(2/3-1/2)]

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

Evaluate

$$\frac{23}{30}\approx 0.766666667$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

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

Since \frac{4}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}+\frac{3}{5}\times \frac{4-3}{6}$$

Subtract 3 from 4 to get 1.

$$\frac{2}{3}+\frac{3}{5}\times \frac{1}{6}$$

Multiply \frac{3}{5} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}+\frac{3\times 1}{5\times 6}$$

Do the multiplications in the fraction \frac{3\times 1}{5\times 6}.

$$\frac{2}{3}+\frac{3}{30}$$

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

$$\frac{2}{3}+\frac{1}{10}$$

Least common multiple of 3 and 10 is 30. Convert \frac{2}{3} and \frac{1}{10} to fractions with denominator 30.

$$\frac{20}{30}+\frac{3}{30}$$

Since \frac{20}{30} and \frac{3}{30} have the same denominator, add them by adding their numerators.

$$\frac{20+3}{30}$$

Add 20 and 3 to get 23.

$$\frac{23}{30}$$

Factor

$$\frac{23}{2 \cdot 3 \cdot 5} = 0.7666666666666667$$