Solve 2/5+3/10-1/20/2/3+1/9+5/6

$$\frac { 2 / 5 + 3 / 10 - 1 / 20 } { 2 / 3 + 1 / 9 + 5 / 6 }$$

Evaluate

$$\frac{117}{290}\approx 0.403448276$$

Solution Steps

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

$$\frac{\frac{4}{10}+\frac{3}{10}-\frac{1}{20}}{\frac{2}{3}+\frac{1}{9}+\frac{5}{6}}$$

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

$$\frac{\frac{4+3}{10}-\frac{1}{20}}{\frac{2}{3}+\frac{1}{9}+\frac{5}{6}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{7}{10}-\frac{1}{20}}{\frac{2}{3}+\frac{1}{9}+\frac{5}{6}}$$

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

$$\frac{\frac{14}{20}-\frac{1}{20}}{\frac{2}{3}+\frac{1}{9}+\frac{5}{6}}$$

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

$$\frac{\frac{14-1}{20}}{\frac{2}{3}+\frac{1}{9}+\frac{5}{6}}$$

Subtract 1 from 14 to get 13.

$$\frac{\frac{13}{20}}{\frac{2}{3}+\frac{1}{9}+\frac{5}{6}}$$

Least common multiple of 3 and 9 is 9. Convert \frac{2}{3} and \frac{1}{9} to fractions with denominator 9.

$$\frac{\frac{13}{20}}{\frac{6}{9}+\frac{1}{9}+\frac{5}{6}}$$

Since \frac{6}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13}{20}}{\frac{6+1}{9}+\frac{5}{6}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{13}{20}}{\frac{7}{9}+\frac{5}{6}}$$

Least common multiple of 9 and 6 is 18. Convert \frac{7}{9} and \frac{5}{6} to fractions with denominator 18.

$$\frac{\frac{13}{20}}{\frac{14}{18}+\frac{15}{18}}$$

Since \frac{14}{18} and \frac{15}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13}{20}}{\frac{14+15}{18}}$$

Add 14 and 15 to get 29.

$$\frac{\frac{13}{20}}{\frac{29}{18}}$$

Divide \frac{13}{20} by \frac{29}{18} by multiplying \frac{13}{20} by the reciprocal of \frac{29}{18}.

$$\frac{13}{20}\times \frac{18}{29}$$

Multiply \frac{13}{20} times \frac{18}{29} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 18}{20\times 29}$$

Do the multiplications in the fraction \frac{13\times 18}{20\times 29}.

$$\frac{234}{580}$$

Reduce the fraction \frac{234}{580} to lowest terms by extracting and canceling out 2.

$$\frac{117}{290}$$

Factor

$$\frac{3 ^ {2} \cdot 13}{2 \cdot 5 \cdot 29} = 0.40344827586206894$$