Solve 1/3[1/2(1/4-1/3)+frac{1}{6})=

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

Evaluate

$$\frac{1}{24}\approx 0.041666667$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

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

Since \frac{3}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 3 to get -1.

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

Multiply \frac{1}{2} times -\frac{1}{12} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-1\right)}{2\times 12}.

$$\frac{1}{3}\left(\frac{-1}{24}+\frac{1}{6}\right)$$

Fraction \frac{-1}{24} can be rewritten as -\frac{1}{24} by extracting the negative sign.

$$\frac{1}{3}\left(-\frac{1}{24}+\frac{1}{6}\right)$$

Least common multiple of 24 and 6 is 24. Convert -\frac{1}{24} and \frac{1}{6} to fractions with denominator 24.

$$\frac{1}{3}\left(-\frac{1}{24}+\frac{4}{24}\right)$$

Since -\frac{1}{24} and \frac{4}{24} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}\times \frac{-1+4}{24}$$

Add -1 and 4 to get 3.

$$\frac{1}{3}\times \frac{3}{24}$$

Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.

$$\frac{1}{3}\times \frac{1}{8}$$

Multiply \frac{1}{3} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{3\times 8}$$

Do the multiplications in the fraction \frac{1\times 1}{3\times 8}.

$$\frac{1}{24}$$

Factor

$$\frac{1}{2 ^ {3} \cdot 3} = 0.041666666666666664$$