Solve 1/4+1/4[1/3-1/2)

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

Evaluate

$$\frac{5}{24}\approx 0.208333333$$

Solution Steps

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

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

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}+\frac{1}{4}\times \frac{2-3}{6}$$

Subtract 3 from 2 to get -1.

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

Multiply \frac{1}{4} times -\frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-1\right)}{4\times 6}.

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

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

$$\frac{1}{4}-\frac{1}{24}$$

Least common multiple of 4 and 24 is 24. Convert \frac{1}{4} and \frac{1}{24} to fractions with denominator 24.

$$\frac{6}{24}-\frac{1}{24}$$

Since \frac{6}{24} and \frac{1}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-1}{24}$$

Subtract 1 from 6 to get 5.

$$\frac{5}{24}$$

Factor

$$\frac{5}{2 ^ {3} \cdot 3} = 0.20833333333333334$$