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

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

Evaluate

$$\frac{17}{30}\approx 0.566666667$$

Solution Steps

Convert 1 to fraction \frac{5}{5}.

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

Since \frac{5}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 5 to get 2.

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

Least common multiple of 5 and 10 is 10. Convert \frac{2}{5} and \frac{1}{10} to fractions with denominator 10.

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

Since \frac{4}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

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

Add 4 and 1 to get 5.

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

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

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

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

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

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

$$\frac{1}{6}+\frac{2}{5}$$

Least common multiple of 6 and 5 is 30. Convert \frac{1}{6} and \frac{2}{5} to fractions with denominator 30.

$$\frac{5}{30}+\frac{12}{30}$$

Since \frac{5}{30} and \frac{12}{30} have the same denominator, add them by adding their numerators.

$$\frac{5+12}{30}$$

Add 5 and 12 to get 17.

$$\frac{17}{30}$$

Factor

$$\frac{17}{2 \cdot 3 \cdot 5} = 0.5666666666666667$$