Solve 1/6-3/8-5/12+2/3=

$$\frac { 1 } { 6 } - \frac { 3 } { 8 } - \frac { 5 } { 12 } + \frac { 2 } { 3 } =$$

Evaluate

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

Solution Steps

Least common multiple of 6 and 8 is 24. Convert \frac{1}{6} and \frac{3}{8} to fractions with denominator 24.

$$\frac{4}{24}-\frac{9}{24}-\frac{5}{12}+\frac{2}{3}$$

Since \frac{4}{24} and \frac{9}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-9}{24}-\frac{5}{12}+\frac{2}{3}$$

Subtract 9 from 4 to get -5.

$$-\frac{5}{24}-\frac{5}{12}+\frac{2}{3}$$

Least common multiple of 24 and 12 is 24. Convert -\frac{5}{24} and \frac{5}{12} to fractions with denominator 24.

$$-\frac{5}{24}-\frac{10}{24}+\frac{2}{3}$$

Since -\frac{5}{24} and \frac{10}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-10}{24}+\frac{2}{3}$$

Subtract 10 from -5 to get -15.

$$\frac{-15}{24}+\frac{2}{3}$$

Reduce the fraction \frac{-15}{24} to lowest terms by extracting and canceling out 3.

$$-\frac{5}{8}+\frac{2}{3}$$

Least common multiple of 8 and 3 is 24. Convert -\frac{5}{8} and \frac{2}{3} to fractions with denominator 24.

$$-\frac{15}{24}+\frac{16}{24}$$

Since -\frac{15}{24} and \frac{16}{24} have the same denominator, add them by adding their numerators.

$$\frac{-15+16}{24}$$

Add -15 and 16 to get 1.

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

Factor

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