Solve [(2/5-3/4)*2/3]:3

$$[ ( \frac { 2 } { 5 } - \frac { 3 } { 4 } ) \cdot \frac { 2 } { 3 } ] : 3$$

Evaluate

$$-\frac{7}{90}\approx -0.077777778$$

Solution Steps

Least common multiple of 5 and 4 is 20. Convert \frac{2}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{\left(\frac{8}{20}-\frac{15}{20}\right)\times \frac{2}{3}}{3}$$

Since \frac{8}{20} and \frac{15}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8-15}{20}\times \frac{2}{3}}{3}$$

Subtract 15 from 8 to get -7.

$$\frac{-\frac{7}{20}\times \frac{2}{3}}{3}$$

Multiply -\frac{7}{20} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-7\times 2}{20\times 3}}{3}$$

Do the multiplications in the fraction \frac{-7\times 2}{20\times 3}.

$$\frac{\frac{-14}{60}}{3}$$

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

$$\frac{-\frac{7}{30}}{3}$$

Express \frac{-\frac{7}{30}}{3} as a single fraction.

$$\frac{-7}{30\times 3}$$

Multiply 30 and 3 to get 90.

$$\frac{-7}{90}$$

Fraction \frac{-7}{90} can be rewritten as -\frac{7}{90} by extracting the negative sign.

$$-\frac{7}{90}$$

Factor

$$-\frac{7}{90} = -0.07777777777777778$$