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

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

Evaluate

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

Solution Steps

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

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

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

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

Subtract 15 from 8 to get -7.

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

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

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

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

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

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

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

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}.

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

Factor

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