Solve 5/2-(3/4+1/2)+10/6*(frac{1}{2}-frac{3}{5}

$$\frac { 5 } { 2 } - ( \frac { 3 } { 4 } + \frac { 1 } { 2 } ) + \frac { 10 } { 6 } \cdot ( \frac { 1 } { 2 } - \frac { 3 } { 5 }$$

Evaluate

$$\frac{13}{12}\approx 1.083333333$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{5}{2}-\left(\frac{3}{4}+\frac{2}{4}\right)+\frac{10}{6}\left(\frac{1}{2}-\frac{3}{5}\right)$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{5}{2}-\frac{3+2}{4}+\frac{10}{6}\left(\frac{1}{2}-\frac{3}{5}\right)$$

Add 3 and 2 to get 5.

$$\frac{5}{2}-\frac{5}{4}+\frac{10}{6}\left(\frac{1}{2}-\frac{3}{5}\right)$$

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

$$\frac{10}{4}-\frac{5}{4}+\frac{10}{6}\left(\frac{1}{2}-\frac{3}{5}\right)$$

Since \frac{10}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-5}{4}+\frac{10}{6}\left(\frac{1}{2}-\frac{3}{5}\right)$$

Subtract 5 from 10 to get 5.

$$\frac{5}{4}+\frac{10}{6}\left(\frac{1}{2}-\frac{3}{5}\right)$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{4}+\frac{5}{3}\left(\frac{1}{2}-\frac{3}{5}\right)$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{3}{5} to fractions with denominator 10.

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

Since \frac{5}{10} and \frac{6}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{4}+\frac{5}{3}\times \frac{5-6}{10}$$

Subtract 6 from 5 to get -1.

$$\frac{5}{4}+\frac{5}{3}\left(-\frac{1}{10}\right)$$

Multiply \frac{5}{3} times -\frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{4}+\frac{5\left(-1\right)}{3\times 10}$$

Do the multiplications in the fraction \frac{5\left(-1\right)}{3\times 10}.

$$\frac{5}{4}+\frac{-5}{30}$$

Reduce the fraction \frac{-5}{30} to lowest terms by extracting and canceling out 5.

$$\frac{5}{4}-\frac{1}{6}$$

Least common multiple of 4 and 6 is 12. Convert \frac{5}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{15}{12}-\frac{2}{12}$$

Since \frac{15}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-2}{12}$$

Subtract 2 from 15 to get 13.

$$\frac{13}{12}$$

Factor

$$\frac{13}{2 ^ {2} \cdot 3} = 1\frac{1}{12} = 1.0833333333333333$$