Solve 1/2*(10/3-8/5)-(3/2+frac{7}{12}):frac{5}{3}

$$\frac { 1 } { 2 } \cdot ( \frac { 10 } { 3 } - \frac { 8 } { 5 } ) - ( \frac { 3 } { 2 } + \frac { 7 } { 12 } ) : \frac { 5 } { 3 }$$

Evaluate

$$-\frac{23}{60}\approx -0.383333333$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{10}{3} and \frac{8}{5} to fractions with denominator 15.

$$\frac{1}{2}\left(\frac{50}{15}-\frac{24}{15}\right)-\frac{\frac{3}{2}+\frac{7}{12}}{\frac{5}{3}}$$

Since \frac{50}{15} and \frac{24}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{50-24}{15}-\frac{\frac{3}{2}+\frac{7}{12}}{\frac{5}{3}}$$

Subtract 24 from 50 to get 26.

$$\frac{1}{2}\times \frac{26}{15}-\frac{\frac{3}{2}+\frac{7}{12}}{\frac{5}{3}}$$

Multiply \frac{1}{2} times \frac{26}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 26}{2\times 15}-\frac{\frac{3}{2}+\frac{7}{12}}{\frac{5}{3}}$$

Do the multiplications in the fraction \frac{1\times 26}{2\times 15}.

$$\frac{26}{30}-\frac{\frac{3}{2}+\frac{7}{12}}{\frac{5}{3}}$$

Reduce the fraction \frac{26}{30} to lowest terms by extracting and canceling out 2.

$$\frac{13}{15}-\frac{\frac{3}{2}+\frac{7}{12}}{\frac{5}{3}}$$

Least common multiple of 2 and 12 is 12. Convert \frac{3}{2} and \frac{7}{12} to fractions with denominator 12.

$$\frac{13}{15}-\frac{\frac{18}{12}+\frac{7}{12}}{\frac{5}{3}}$$

Since \frac{18}{12} and \frac{7}{12} have the same denominator, add them by adding their numerators.

$$\frac{13}{15}-\frac{\frac{18+7}{12}}{\frac{5}{3}}$$

Add 18 and 7 to get 25.

$$\frac{13}{15}-\frac{\frac{25}{12}}{\frac{5}{3}}$$

Divide \frac{25}{12} by \frac{5}{3} by multiplying \frac{25}{12} by the reciprocal of \frac{5}{3}.

$$\frac{13}{15}-\frac{25}{12}\times \frac{3}{5}$$

Multiply \frac{25}{12} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{15}-\frac{25\times 3}{12\times 5}$$

Do the multiplications in the fraction \frac{25\times 3}{12\times 5}.

$$\frac{13}{15}-\frac{75}{60}$$

Reduce the fraction \frac{75}{60} to lowest terms by extracting and canceling out 15.

$$\frac{13}{15}-\frac{5}{4}$$

Least common multiple of 15 and 4 is 60. Convert \frac{13}{15} and \frac{5}{4} to fractions with denominator 60.

$$\frac{52}{60}-\frac{75}{60}$$

Since \frac{52}{60} and \frac{75}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{52-75}{60}$$

Subtract 75 from 52 to get -23.

$$-\frac{23}{60}$$

Factor

$$-\frac{23}{60} = -0.38333333333333336$$