Solve -3/5+(4/5+8/15-1/6):(frac{13}{3}-frac{11}{4}-1)+frac{8}{3}-frac{2}{3}*(+frac{18}{5})

$$- \frac { 3 } { 5 } + ( \frac { 4 } { 5 } + \frac { 8 } { 15 } - \frac { 1 } { 6 } ) : ( \frac { 13 } { 3 } - \frac { 11 } { 4 } - 1 ) + \frac { 8 } { 3 } - \frac { 2 } { 3 } \cdot ( + \frac { 18 } { 5 } )$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Least common multiple of 5 and 15 is 15. Convert \frac{4}{5} and \frac{8}{15} to fractions with denominator 15.

$$-\frac{3}{5}+\frac{\frac{12}{15}+\frac{8}{15}-\frac{1}{6}}{\frac{13}{3}-\frac{11}{4}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Since \frac{12}{15} and \frac{8}{15} have the same denominator, add them by adding their numerators.

$$-\frac{3}{5}+\frac{\frac{12+8}{15}-\frac{1}{6}}{\frac{13}{3}-\frac{11}{4}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Add 12 and 8 to get 20.

$$-\frac{3}{5}+\frac{\frac{20}{15}-\frac{1}{6}}{\frac{13}{3}-\frac{11}{4}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Reduce the fraction \frac{20}{15} to lowest terms by extracting and canceling out 5.

$$-\frac{3}{5}+\frac{\frac{4}{3}-\frac{1}{6}}{\frac{13}{3}-\frac{11}{4}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Least common multiple of 3 and 6 is 6. Convert \frac{4}{3} and \frac{1}{6} to fractions with denominator 6.

$$-\frac{3}{5}+\frac{\frac{8}{6}-\frac{1}{6}}{\frac{13}{3}-\frac{11}{4}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Since \frac{8}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{5}+\frac{\frac{8-1}{6}}{\frac{13}{3}-\frac{11}{4}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Subtract 1 from 8 to get 7.

$$-\frac{3}{5}+\frac{\frac{7}{6}}{\frac{13}{3}-\frac{11}{4}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Least common multiple of 3 and 4 is 12. Convert \frac{13}{3} and \frac{11}{4} to fractions with denominator 12.

$$-\frac{3}{5}+\frac{\frac{7}{6}}{\frac{52}{12}-\frac{33}{12}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Since \frac{52}{12} and \frac{33}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{5}+\frac{\frac{7}{6}}{\frac{52-33}{12}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Subtract 33 from 52 to get 19.

$$-\frac{3}{5}+\frac{\frac{7}{6}}{\frac{19}{12}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Convert 1 to fraction \frac{12}{12}.

$$-\frac{3}{5}+\frac{\frac{7}{6}}{\frac{19}{12}-\frac{12}{12}}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Since \frac{19}{12} and \frac{12}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{5}+\frac{\frac{7}{6}}{\frac{19-12}{12}}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Subtract 12 from 19 to get 7.

$$-\frac{3}{5}+\frac{\frac{7}{6}}{\frac{7}{12}}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Divide \frac{7}{6} by \frac{7}{12} by multiplying \frac{7}{6} by the reciprocal of \frac{7}{12}.

$$-\frac{3}{5}+\frac{7}{6}\times \frac{12}{7}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Multiply \frac{7}{6} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{3}{5}+\frac{7\times 12}{6\times 7}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Cancel out 7 in both numerator and denominator.

$$-\frac{3}{5}+\frac{12}{6}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Divide 12 by 6 to get 2.

$$-\frac{3}{5}+2+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Convert 2 to fraction \frac{10}{5}.

$$-\frac{3}{5}+\frac{10}{5}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Since -\frac{3}{5} and \frac{10}{5} have the same denominator, add them by adding their numerators.

$$\frac{-3+10}{5}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Add -3 and 10 to get 7.

$$\frac{7}{5}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Least common multiple of 5 and 3 is 15. Convert \frac{7}{5} and \frac{8}{3} to fractions with denominator 15.

$$\frac{21}{15}+\frac{40}{15}-\frac{2}{3}\times \frac{18}{5}$$

Since \frac{21}{15} and \frac{40}{15} have the same denominator, add them by adding their numerators.

$$\frac{21+40}{15}-\frac{2}{3}\times \frac{18}{5}$$

Add 21 and 40 to get 61.

$$\frac{61}{15}-\frac{2}{3}\times \frac{18}{5}$$

Multiply \frac{2}{3} times \frac{18}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{61}{15}-\frac{2\times 18}{3\times 5}$$

Do the multiplications in the fraction \frac{2\times 18}{3\times 5}.

$$\frac{61}{15}-\frac{36}{15}$$

Since \frac{61}{15} and \frac{36}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{61-36}{15}$$

Subtract 36 from 61 to get 25.

$$\frac{25}{15}$$

Reduce the fraction \frac{25}{15} to lowest terms by extracting and canceling out 5.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$