Solve 2/5+3/10-1/20/2/3+1/2+5/6

$$\frac { 2 / 5 + 3 / 10 - 1 / 20 } { 2 / 3 + 1 / 2 + 5 / 6 }$$

Evaluate

$$\frac{13}{40}=0.325$$

Solution Steps

Least common multiple of 5 and 10 is 10. Convert \frac{2}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{\frac{4}{10}+\frac{3}{10}-\frac{1}{20}}{\frac{2}{3}+\frac{1}{2}+\frac{5}{6}}$$

Since \frac{4}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+3}{10}-\frac{1}{20}}{\frac{2}{3}+\frac{1}{2}+\frac{5}{6}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{7}{10}-\frac{1}{20}}{\frac{2}{3}+\frac{1}{2}+\frac{5}{6}}$$

Least common multiple of 10 and 20 is 20. Convert \frac{7}{10} and \frac{1}{20} to fractions with denominator 20.

$$\frac{\frac{14}{20}-\frac{1}{20}}{\frac{2}{3}+\frac{1}{2}+\frac{5}{6}}$$

Since \frac{14}{20} and \frac{1}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14-1}{20}}{\frac{2}{3}+\frac{1}{2}+\frac{5}{6}}$$

Subtract 1 from 14 to get 13.

$$\frac{\frac{13}{20}}{\frac{2}{3}+\frac{1}{2}+\frac{5}{6}}$$

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

$$\frac{\frac{13}{20}}{\frac{4}{6}+\frac{3}{6}+\frac{5}{6}}$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13}{20}}{\frac{4+3}{6}+\frac{5}{6}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{13}{20}}{\frac{7}{6}+\frac{5}{6}}$$

Since \frac{7}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13}{20}}{\frac{7+5}{6}}$$

Add 7 and 5 to get 12.

$$\frac{\frac{13}{20}}{\frac{12}{6}}$$

Divide 12 by 6 to get 2.

$$\frac{\frac{13}{20}}{2}$$

Express \frac{\frac{13}{20}}{2} as a single fraction.

$$\frac{13}{20\times 2}$$

Multiply 20 and 2 to get 40.

$$\frac{13}{40}$$

Factor

$$\frac{13}{2 ^ {3} \cdot 5} = 0.325$$