Solve 2/5(9/10-4/6)

$$\frac { 2 } { 5 } ( \frac { 9 } { 10 } - \frac { 4 } { 6 } )$$

Evaluate

$$\frac{7}{75}\approx 0.093333333$$

Solution Steps

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}\left(\frac{9}{10}-\frac{2}{3}\right)$$

Least common multiple of 10 and 3 is 30. Convert \frac{9}{10} and \frac{2}{3} to fractions with denominator 30.

$$\frac{2}{5}\left(\frac{27}{30}-\frac{20}{30}\right)$$

Since \frac{27}{30} and \frac{20}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}\times \frac{27-20}{30}$$

Subtract 20 from 27 to get 7.

$$\frac{2}{5}\times \frac{7}{30}$$

Multiply \frac{2}{5} times \frac{7}{30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 7}{5\times 30}$$

Do the multiplications in the fraction \frac{2\times 7}{5\times 30}.

$$\frac{14}{150}$$

Reduce the fraction \frac{14}{150} to lowest terms by extracting and canceling out 2.

$$\frac{7}{75}$$

Factor

$$\frac{7}{3 \cdot 5 ^ {2}} = 0.09333333333333334$$