Solve 5/9-(-3/4+1/2)+10/3(frac{1}{2}-frac{3}{5})=

$$\frac { 5 } { 9 } - ( - \frac { 3 } { 4 } + \frac { 1 } { 2 } ) + \frac { 10 } { 3 } ( \frac { 1 } { 2 } - \frac { 3 } { 5 } ) =$$

Evaluate

$$\frac{17}{36}\approx 0.472222222$$

Solution Steps

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

$$\frac{5}{9}-\left(-\frac{3}{4}+\frac{2}{4}\right)+\frac{10}{3}\left(\frac{1}{2}-\frac{3}{5}\right)$$

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

$$\frac{5}{9}-\frac{-3+2}{4}+\frac{10}{3}\left(\frac{1}{2}-\frac{3}{5}\right)$$

Add -3 and 2 to get -1.

$$\frac{5}{9}-\left(-\frac{1}{4}\right)+\frac{10}{3}\left(\frac{1}{2}-\frac{3}{5}\right)$$

The opposite of -\frac{1}{4} is \frac{1}{4}.

$$\frac{5}{9}+\frac{1}{4}+\frac{10}{3}\left(\frac{1}{2}-\frac{3}{5}\right)$$

Least common multiple of 9 and 4 is 36. Convert \frac{5}{9} and \frac{1}{4} to fractions with denominator 36.

$$\frac{20}{36}+\frac{9}{36}+\frac{10}{3}\left(\frac{1}{2}-\frac{3}{5}\right)$$

Since \frac{20}{36} and \frac{9}{36} have the same denominator, add them by adding their numerators.

$$\frac{20+9}{36}+\frac{10}{3}\left(\frac{1}{2}-\frac{3}{5}\right)$$

Add 20 and 9 to get 29.

$$\frac{29}{36}+\frac{10}{3}\left(\frac{1}{2}-\frac{3}{5}\right)$$

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

$$\frac{29}{36}+\frac{10}{3}\left(\frac{5}{10}-\frac{6}{10}\right)$$

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

$$\frac{29}{36}+\frac{10}{3}\times \frac{5-6}{10}$$

Subtract 6 from 5 to get -1.

$$\frac{29}{36}+\frac{10}{3}\left(-\frac{1}{10}\right)$$

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

$$\frac{29}{36}+\frac{10\left(-1\right)}{3\times 10}$$

Cancel out 10 in both numerator and denominator.

$$\frac{29}{36}+\frac{-1}{3}$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$\frac{29}{36}-\frac{1}{3}$$

Least common multiple of 36 and 3 is 36. Convert \frac{29}{36} and \frac{1}{3} to fractions with denominator 36.

$$\frac{29}{36}-\frac{12}{36}$$

Since \frac{29}{36} and \frac{12}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{29-12}{36}$$

Subtract 12 from 29 to get 17.

$$\frac{17}{36}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 3 ^ {2}} = 0.4722222222222222$$