Solve 5/2+3/5-(-2/3-5/4)=

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

Evaluate

$$\frac{301}{60}\approx 5.016666667$$

Solution Steps

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

$$\frac{25}{10}+\frac{6}{10}-\left(-\frac{2}{3}-\frac{5}{4}\right)$$

Since \frac{25}{10} and \frac{6}{10} have the same denominator, add them by adding their numerators.

$$\frac{25+6}{10}-\left(-\frac{2}{3}-\frac{5}{4}\right)$$

Add 25 and 6 to get 31.

$$\frac{31}{10}-\left(-\frac{2}{3}-\frac{5}{4}\right)$$

Least common multiple of 3 and 4 is 12. Convert -\frac{2}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{31}{10}-\left(-\frac{8}{12}-\frac{15}{12}\right)$$

Since -\frac{8}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{31}{10}-\frac{-8-15}{12}$$

Subtract 15 from -8 to get -23.

$$\frac{31}{10}-\left(-\frac{23}{12}\right)$$

The opposite of -\frac{23}{12} is \frac{23}{12}.

$$\frac{31}{10}+\frac{23}{12}$$

Least common multiple of 10 and 12 is 60. Convert \frac{31}{10} and \frac{23}{12} to fractions with denominator 60.

$$\frac{186}{60}+\frac{115}{60}$$

Since \frac{186}{60} and \frac{115}{60} have the same denominator, add them by adding their numerators.

$$\frac{186+115}{60}$$

Add 186 and 115 to get 301.

$$\frac{301}{60}$$

Factor

$$\frac{7 \cdot 43}{2 ^ {2} \cdot 3 \cdot 5} = 5\frac{1}{60} = 5.016666666666667$$