Solve (2/3-4/5)/(frac{5{4}+3/2)}div(frac{7}{2}-frac{3}{2})=

$$\frac { ( \frac { 2 } { 3 } - \frac { 4 } { 5 } ) } { ( \frac { 5 } { 4 } + \frac { 3 } { 2 } ) } \div ( \frac { 7 } { 2 } - \frac { 3 } { 2 } ) =$$

Evaluate

$$-\frac{4}{165}\approx -0.024242424$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{\frac{\frac{10}{15}-\frac{12}{15}}{\frac{5}{4}+\frac{3}{2}}}{\frac{7}{2}-\frac{3}{2}}$$

Since \frac{10}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{10-12}{15}}{\frac{5}{4}+\frac{3}{2}}}{\frac{7}{2}-\frac{3}{2}}$$

Subtract 12 from 10 to get -2.

$$\frac{\frac{-\frac{2}{15}}{\frac{5}{4}+\frac{3}{2}}}{\frac{7}{2}-\frac{3}{2}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{3}{2} to fractions with denominator 4.

$$\frac{\frac{-\frac{2}{15}}{\frac{5}{4}+\frac{6}{4}}}{\frac{7}{2}-\frac{3}{2}}$$

Since \frac{5}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-\frac{2}{15}}{\frac{5+6}{4}}}{\frac{7}{2}-\frac{3}{2}}$$

Add 5 and 6 to get 11.

$$\frac{\frac{-\frac{2}{15}}{\frac{11}{4}}}{\frac{7}{2}-\frac{3}{2}}$$

Divide -\frac{2}{15} by \frac{11}{4} by multiplying -\frac{2}{15} by the reciprocal of \frac{11}{4}.

$$\frac{-\frac{2}{15}\times \frac{4}{11}}{\frac{7}{2}-\frac{3}{2}}$$

Multiply -\frac{2}{15} times \frac{4}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-2\times 4}{15\times 11}}{\frac{7}{2}-\frac{3}{2}}$$

Do the multiplications in the fraction \frac{-2\times 4}{15\times 11}.

$$\frac{\frac{-8}{165}}{\frac{7}{2}-\frac{3}{2}}$$

Fraction \frac{-8}{165} can be rewritten as -\frac{8}{165} by extracting the negative sign.

$$\frac{-\frac{8}{165}}{\frac{7}{2}-\frac{3}{2}}$$

Since \frac{7}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{8}{165}}{\frac{7-3}{2}}$$

Subtract 3 from 7 to get 4.

$$\frac{-\frac{8}{165}}{\frac{4}{2}}$$

Divide 4 by 2 to get 2.

$$\frac{-\frac{8}{165}}{2}$$

Express \frac{-\frac{8}{165}}{2} as a single fraction.

$$\frac{-8}{165\times 2}$$

Multiply 165 and 2 to get 330.

$$\frac{-8}{330}$$

Reduce the fraction \frac{-8}{330} to lowest terms by extracting and canceling out 2.

$$-\frac{4}{165}$$

Factor

$$-\frac{4}{165} = -0.024242424242424242$$