Solve 8/5-(5/3-7/6)+10/3-frac{14}{15}+4

$$\frac { 8 } { 5 } - ( \frac { 5 } { 3 } - \frac { 7 } { 6 } ) + \frac { 10 } { 3 } - \frac { 14 } { 15 } + 4$$

Evaluate

$$\frac{15}{2}=7.5$$

Solution Steps

Least common multiple of 3 and 6 is 6. Convert \frac{5}{3} and \frac{7}{6} to fractions with denominator 6.

$$\frac{8}{5}-\left(\frac{10}{6}-\frac{7}{6}\right)+\frac{10}{3}-\frac{14}{15}+4$$

Since \frac{10}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{5}-\frac{10-7}{6}+\frac{10}{3}-\frac{14}{15}+4$$

Subtract 7 from 10 to get 3.

$$\frac{8}{5}-\frac{3}{6}+\frac{10}{3}-\frac{14}{15}+4$$

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

$$\frac{8}{5}-\frac{1}{2}+\frac{10}{3}-\frac{14}{15}+4$$

Least common multiple of 5 and 2 is 10. Convert \frac{8}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{16}{10}-\frac{5}{10}+\frac{10}{3}-\frac{14}{15}+4$$

Since \frac{16}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-5}{10}+\frac{10}{3}-\frac{14}{15}+4$$

Subtract 5 from 16 to get 11.

$$\frac{11}{10}+\frac{10}{3}-\frac{14}{15}+4$$

Least common multiple of 10 and 3 is 30. Convert \frac{11}{10} and \frac{10}{3} to fractions with denominator 30.

$$\frac{33}{30}+\frac{100}{30}-\frac{14}{15}+4$$

Since \frac{33}{30} and \frac{100}{30} have the same denominator, add them by adding their numerators.

$$\frac{33+100}{30}-\frac{14}{15}+4$$

Add 33 and 100 to get 133.

$$\frac{133}{30}-\frac{14}{15}+4$$

Least common multiple of 30 and 15 is 30. Convert \frac{133}{30} and \frac{14}{15} to fractions with denominator 30.

$$\frac{133}{30}-\frac{28}{30}+4$$

Since \frac{133}{30} and \frac{28}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{133-28}{30}+4$$

Subtract 28 from 133 to get 105.

$$\frac{105}{30}+4$$

Reduce the fraction \frac{105}{30} to lowest terms by extracting and canceling out 15.

$$\frac{7}{2}+4$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{7}{2}+\frac{8}{2}$$

Since \frac{7}{2} and \frac{8}{2} have the same denominator, add them by adding their numerators.

$$\frac{7+8}{2}$$

Add 7 and 8 to get 15.

$$\frac{15}{2}$$

Factor

$$\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5$$