Solve 1/5+2/3:1/5-5/12=

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

Evaluate

$$\frac{187}{60}\approx 3.116666667$$

Solution Steps

Divide \frac{2}{3} by \frac{1}{5} by multiplying \frac{2}{3} by the reciprocal of \frac{1}{5}.

$$\frac{1}{5}+\frac{2}{3}\times 5-\frac{5}{12}$$

Express \frac{2}{3}\times 5 as a single fraction.

$$\frac{1}{5}+\frac{2\times 5}{3}-\frac{5}{12}$$

Multiply 2 and 5 to get 10.

$$\frac{1}{5}+\frac{10}{3}-\frac{5}{12}$$

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{10}{3} to fractions with denominator 15.

$$\frac{3}{15}+\frac{50}{15}-\frac{5}{12}$$

Since \frac{3}{15} and \frac{50}{15} have the same denominator, add them by adding their numerators.

$$\frac{3+50}{15}-\frac{5}{12}$$

Add 3 and 50 to get 53.

$$\frac{53}{15}-\frac{5}{12}$$

Least common multiple of 15 and 12 is 60. Convert \frac{53}{15} and \frac{5}{12} to fractions with denominator 60.

$$\frac{212}{60}-\frac{25}{60}$$

Since \frac{212}{60} and \frac{25}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{212-25}{60}$$

Subtract 25 from 212 to get 187.

$$\frac{187}{60}$$

Factor

$$\frac{11 \cdot 17}{2 ^ {2} \cdot 3 \cdot 5} = 3\frac{7}{60} = 3.1166666666666667$$