Solve |(2/5-3/4)2/3|:3

$$| ( \frac { 2 } { 5 } - \frac { 3 } { 4 } ) \frac { 2 } { 3 } | : 3$$

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.

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

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{7}{30} is \frac{7}{30}.

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

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

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

Multiply 30 and 3 to get 90.

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

Factor

$$\frac{7}{2 \cdot 3 ^ {2} \cdot 5} = 0.07777777777777778$$