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

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

Evaluate

$$\frac{7}{12}\approx 0.583333333$$

Solution Steps

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

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

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

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

Subtract 2 from 3 to get 1.

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

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

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

Since \frac{2}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$1-\frac{2+3}{12}$$

Add 2 and 3 to get 5.

$$1-\frac{5}{12}$$

Convert 1 to fraction \frac{12}{12}.

$$\frac{12}{12}-\frac{5}{12}$$

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

$$\frac{12-5}{12}$$

Subtract 5 from 12 to get 7.

$$\frac{7}{12}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3} = 0.5833333333333334$$