Solve 4/5-2/15+11/6-21/2

$$\frac{ 4 }{ 5 } - \frac{ 2 }{ 15 } +1 \frac{ 1 }{ 6 } -2 \frac{ 1 }{ 2 }$$

Evaluate

$$-\frac{2}{3}\approx -0.666666667$$

Solution Steps

Least common multiple of 5 and 15 is 15. Convert \frac{4}{5} and \frac{2}{15} to fractions with denominator 15.

$$\frac{12}{15}-\frac{2}{15}+\frac{1\times 6+1}{6}-\frac{2\times 2+1}{2}$$

Since \frac{12}{15} and \frac{2}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-2}{15}+\frac{1\times 6+1}{6}-\frac{2\times 2+1}{2}$$

Subtract 2 from 12 to get 10.

$$\frac{10}{15}+\frac{1\times 6+1}{6}-\frac{2\times 2+1}{2}$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

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

Multiply 1 and 6 to get 6.

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

Add 6 and 1 to get 7.

$$\frac{2}{3}+\frac{7}{6}-\frac{2\times 2+1}{2}$$

Least common multiple of 3 and 6 is 6. Convert \frac{2}{3} and \frac{7}{6} to fractions with denominator 6.

$$\frac{4}{6}+\frac{7}{6}-\frac{2\times 2+1}{2}$$

Since \frac{4}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$\frac{4+7}{6}-\frac{2\times 2+1}{2}$$

Add 4 and 7 to get 11.

$$\frac{11}{6}-\frac{2\times 2+1}{2}$$

Multiply 2 and 2 to get 4.

$$\frac{11}{6}-\frac{4+1}{2}$$

Add 4 and 1 to get 5.

$$\frac{11}{6}-\frac{5}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{11}{6} and \frac{5}{2} to fractions with denominator 6.

$$\frac{11}{6}-\frac{15}{6}$$

Since \frac{11}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-15}{6}$$

Subtract 15 from 11 to get -4.

$$\frac{-4}{6}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{3}$$

Factor

$$-\frac{2}{3} = -0.6666666666666666$$