Solve (1/6+2/3-5/12)(1-2/3)

$$( \frac { 1 } { 6 } + \frac { 2 } { 3 } - \frac { 5 } { 12 } ) ( 1 - \frac { 2 } { 3 } )$$

Evaluate

$$\frac{5}{36}\approx 0.138888889$$

Solution Steps

Least common multiple of 6 and 3 is 6. Convert \frac{1}{6} and \frac{2}{3} to fractions with denominator 6.

$$\left(\frac{1}{6}+\frac{4}{6}-\frac{5}{12}\right)\left(1-\frac{2}{3}\right)$$

Since \frac{1}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\left(\frac{1+4}{6}-\frac{5}{12}\right)\left(1-\frac{2}{3}\right)$$

Add 1 and 4 to get 5.

$$\left(\frac{5}{6}-\frac{5}{12}\right)\left(1-\frac{2}{3}\right)$$

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

$$\left(\frac{10}{12}-\frac{5}{12}\right)\left(1-\frac{2}{3}\right)$$

Since \frac{10}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-5}{12}\left(1-\frac{2}{3}\right)$$

Subtract 5 from 10 to get 5.

$$\frac{5}{12}\left(1-\frac{2}{3}\right)$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{5}{12}\left(\frac{3}{3}-\frac{2}{3}\right)$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{12}\times \frac{3-2}{3}$$

Subtract 2 from 3 to get 1.

$$\frac{5}{12}\times \frac{1}{3}$$

Multiply \frac{5}{12} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 1}{12\times 3}$$

Do the multiplications in the fraction \frac{5\times 1}{12\times 3}.

$$\frac{5}{36}$$

Factor

$$\frac{5}{2 ^ {2} \cdot 3 ^ {2}} = 0.1388888888888889$$