Solve (1/3+1/2)1/13/5-frac{17}{18}

$$( \frac { 1 } { 3 } + \frac { 1 } { 2 } ) \frac { 1 } { 1 } \frac { 3 } { 5 } - \frac { 17 } { 18 }$$

Evaluate

$$-\frac{4}{9}\approx -0.444444444$$

Solution Steps

Divide 1 by 1 to get 1.

$$\left(\frac{1}{3}+\frac{1}{2}\right)\times 1\times \frac{3}{5}-\frac{17}{18}$$

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

$$\left(\frac{2}{6}+\frac{3}{6}\right)\times 1\times \frac{3}{5}-\frac{17}{18}$$

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

$$\frac{2+3}{6}\times 1\times \frac{3}{5}-\frac{17}{18}$$

Add 2 and 3 to get 5.

$$\frac{5}{6}\times 1\times \frac{3}{5}-\frac{17}{18}$$

Multiply \frac{5}{6} and 1 to get \frac{5}{6}.

$$\frac{5}{6}\times \frac{3}{5}-\frac{17}{18}$$

Multiply \frac{5}{6} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 3}{6\times 5}-\frac{17}{18}$$

Cancel out 5 in both numerator and denominator.

$$\frac{3}{6}-\frac{17}{18}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}-\frac{17}{18}$$

Least common multiple of 2 and 18 is 18. Convert \frac{1}{2} and \frac{17}{18} to fractions with denominator 18.

$$\frac{9}{18}-\frac{17}{18}$$

Since \frac{9}{18} and \frac{17}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-17}{18}$$

Subtract 17 from 9 to get -8.

$$\frac{-8}{18}$$

Reduce the fraction \frac{-8}{18} to lowest terms by extracting and canceling out 2.

$$-\frac{4}{9}$$

Factor

$$-\frac{4}{9} = -0.4444444444444444$$