Solve 1-(2/6+4/10-17/5)

$$1 - ( \frac { 2 } { 6 } + \frac { 4 } { 10 } - \frac { 17 } { 5 } )$$

Evaluate

$$\frac{11}{3}\approx 3.666666667$$

Solution Steps

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$1-\left(\frac{1}{3}+\frac{4}{10}-\frac{17}{5}\right)$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$1-\left(\frac{1}{3}+\frac{2}{5}-\frac{17}{5}\right)$$

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{2}{5} to fractions with denominator 15.

$$1-\left(\frac{5}{15}+\frac{6}{15}-\frac{17}{5}\right)$$

Since \frac{5}{15} and \frac{6}{15} have the same denominator, add them by adding their numerators.

$$1-\left(\frac{5+6}{15}-\frac{17}{5}\right)$$

Add 5 and 6 to get 11.

$$1-\left(\frac{11}{15}-\frac{17}{5}\right)$$

Least common multiple of 15 and 5 is 15. Convert \frac{11}{15} and \frac{17}{5} to fractions with denominator 15.

$$1-\left(\frac{11}{15}-\frac{51}{15}\right)$$

Since \frac{11}{15} and \frac{51}{15} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{11-51}{15}$$

Subtract 51 from 11 to get -40.

$$1-\frac{-40}{15}$$

Reduce the fraction \frac{-40}{15} to lowest terms by extracting and canceling out 5.

$$1-\left(-\frac{8}{3}\right)$$

The opposite of -\frac{8}{3} is \frac{8}{3}.

$$1+\frac{8}{3}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{3}{3}+\frac{8}{3}$$

Since \frac{3}{3} and \frac{8}{3} have the same denominator, add them by adding their numerators.

$$\frac{3+8}{3}$$

Add 3 and 8 to get 11.

$$\frac{11}{3}$$

Factor

$$\frac{11}{3} = 3\frac{2}{3} = 3.6666666666666665$$