Solve 2/3-1/4+3/5-5/6

$$\frac { 2 } { 3 } - \frac { 1 } { 4 } + \frac { 3 } { 5 } - \frac { 5 } { 6 }$$

Evaluate

$$\frac{11}{60}\approx 0.183333333$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

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

Since \frac{8}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 8 to get 5.

$$\frac{5}{12}+\frac{3}{5}-\frac{5}{6}$$

Least common multiple of 12 and 5 is 60. Convert \frac{5}{12} and \frac{3}{5} to fractions with denominator 60.

$$\frac{25}{60}+\frac{36}{60}-\frac{5}{6}$$

Since \frac{25}{60} and \frac{36}{60} have the same denominator, add them by adding their numerators.

$$\frac{25+36}{60}-\frac{5}{6}$$

Add 25 and 36 to get 61.

$$\frac{61}{60}-\frac{5}{6}$$

Least common multiple of 60 and 6 is 60. Convert \frac{61}{60} and \frac{5}{6} to fractions with denominator 60.

$$\frac{61}{60}-\frac{50}{60}$$

Since \frac{61}{60} and \frac{50}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{61-50}{60}$$

Subtract 50 from 61 to get 11.

$$\frac{11}{60}$$

Factor

$$\frac{11}{2 ^ {2} \cdot 3 \cdot 5} = 0.18333333333333332$$