Solve 2/3+(1/6-5/4)*2/3=

$$\frac { 2 } { 3 } + ( \frac { 1 } { 6 } - \frac { 5 } { 4 } ) \cdot \frac { 2 } { 3 } =$$

Evaluate

$$-\frac{1}{18}\approx -0.055555556$$

Solution Steps

Least common multiple of 6 and 4 is 12. Convert \frac{1}{6} and \frac{5}{4} to fractions with denominator 12.

$$\frac{2}{3}+\left(\frac{2}{12}-\frac{15}{12}\right)\times \frac{2}{3}$$

Since \frac{2}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}+\frac{2-15}{12}\times \frac{2}{3}$$

Subtract 15 from 2 to get -13.

$$\frac{2}{3}-\frac{13}{12}\times \frac{2}{3}$$

Multiply -\frac{13}{12} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}+\frac{-13\times 2}{12\times 3}$$

Do the multiplications in the fraction \frac{-13\times 2}{12\times 3}.

$$\frac{2}{3}+\frac{-26}{36}$$

Reduce the fraction \frac{-26}{36} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}-\frac{13}{18}$$

Least common multiple of 3 and 18 is 18. Convert \frac{2}{3} and \frac{13}{18} to fractions with denominator 18.

$$\frac{12}{18}-\frac{13}{18}$$

Since \frac{12}{18} and \frac{13}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-13}{18}$$

Subtract 13 from 12 to get -1.

$$-\frac{1}{18}$$

Factor

$$-\frac{1}{18} = -0.05555555555555555$$