Solve (2/5-1/9):1/3-(3/2+frac{1}{8}):frac{1}{3}

$$( \frac { 2 } { 5 } - \frac { 1 } { 9 } ) : \frac { 1 } { 3 } - ( \frac { 3 } { 2 } + \frac { 1 } { 8 } ) : \frac { 1 } { 3 }$$

Evaluate

$$-\frac{481}{120}\approx -4.008333333$$

Solution Steps

Least common multiple of 5 and 9 is 45. Convert \frac{2}{5} and \frac{1}{9} to fractions with denominator 45.

$$\frac{\frac{18}{45}-\frac{5}{45}}{\frac{1}{3}}-\frac{\frac{3}{2}+\frac{1}{8}}{\frac{1}{3}}$$

Since \frac{18}{45} and \frac{5}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{18-5}{45}}{\frac{1}{3}}-\frac{\frac{3}{2}+\frac{1}{8}}{\frac{1}{3}}$$

Subtract 5 from 18 to get 13.

$$\frac{\frac{13}{45}}{\frac{1}{3}}-\frac{\frac{3}{2}+\frac{1}{8}}{\frac{1}{3}}$$

Divide \frac{13}{45} by \frac{1}{3} by multiplying \frac{13}{45} by the reciprocal of \frac{1}{3}.

$$\frac{13}{45}\times 3-\frac{\frac{3}{2}+\frac{1}{8}}{\frac{1}{3}}$$

Express \frac{13}{45}\times 3 as a single fraction.

$$\frac{13\times 3}{45}-\frac{\frac{3}{2}+\frac{1}{8}}{\frac{1}{3}}$$

Multiply 13 and 3 to get 39.

$$\frac{39}{45}-\frac{\frac{3}{2}+\frac{1}{8}}{\frac{1}{3}}$$

Reduce the fraction \frac{39}{45} to lowest terms by extracting and canceling out 3.

$$\frac{13}{15}-\frac{\frac{3}{2}+\frac{1}{8}}{\frac{1}{3}}$$

Least common multiple of 2 and 8 is 8. Convert \frac{3}{2} and \frac{1}{8} to fractions with denominator 8.

$$\frac{13}{15}-\frac{\frac{12}{8}+\frac{1}{8}}{\frac{1}{3}}$$

Since \frac{12}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{13}{15}-\frac{\frac{12+1}{8}}{\frac{1}{3}}$$

Add 12 and 1 to get 13.

$$\frac{13}{15}-\frac{\frac{13}{8}}{\frac{1}{3}}$$

Divide \frac{13}{8} by \frac{1}{3} by multiplying \frac{13}{8} by the reciprocal of \frac{1}{3}.

$$\frac{13}{15}-\frac{13}{8}\times 3$$

Express \frac{13}{8}\times 3 as a single fraction.

$$\frac{13}{15}-\frac{13\times 3}{8}$$

Multiply 13 and 3 to get 39.

$$\frac{13}{15}-\frac{39}{8}$$

Least common multiple of 15 and 8 is 120. Convert \frac{13}{15} and \frac{39}{8} to fractions with denominator 120.

$$\frac{104}{120}-\frac{585}{120}$$

Since \frac{104}{120} and \frac{585}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{104-585}{120}$$

Subtract 585 from 104 to get -481.

$$-\frac{481}{120}$$

Factor

$$-\frac{481}{120} = -4\frac{1}{120} = -4.008333333333334$$