Solve 2/5left(3/4-1/6right)

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

Evaluate

$$\frac{7}{30}\approx 0.233333333$$

Solution Steps

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{2}{5}\left(\frac{9}{12}-\frac{2}{12}\right)$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}\times \frac{9-2}{12}$$

Subtract 2 from 9 to get 7.

$$\frac{2}{5}\times \frac{7}{12}$$

Multiply \frac{2}{5} times \frac{7}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 7}{5\times 12}$$

Do the multiplications in the fraction \frac{2\times 7}{5\times 12}.

$$\frac{14}{60}$$

Reduce the fraction \frac{14}{60} to lowest terms by extracting and canceling out 2.

$$\frac{7}{30}$$

Factor

$$\frac{7}{2 \cdot 3 \cdot 5} = 0.23333333333333334$$