Solve 53/4+(3/4-3/5)-8+18/5-(frac{2}{3}-frac{1}{4})

$$5 \frac { 3 } { 4 } + ( \frac { 3 } { 4 } - \frac { 3 } { 5 } ) - 8 + \frac { 18 } { 5 } - ( \frac { 2 } { 3 } - \frac { 1 } { 4 } )$$

Evaluate

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

Solution Steps

Multiply 5 and 4 to get 20.

$$\frac{20+3}{4}+\frac{3}{4}-\frac{3}{5}-8+\frac{18}{5}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Add 20 and 3 to get 23.

$$\frac{23}{4}+\frac{3}{4}-\frac{3}{5}-8+\frac{18}{5}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Since \frac{23}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{23+3}{4}-\frac{3}{5}-8+\frac{18}{5}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Add 23 and 3 to get 26.

$$\frac{26}{4}-\frac{3}{5}-8+\frac{18}{5}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Reduce the fraction \frac{26}{4} to lowest terms by extracting and canceling out 2.

$$\frac{13}{2}-\frac{3}{5}-8+\frac{18}{5}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Least common multiple of 2 and 5 is 10. Convert \frac{13}{2} and \frac{3}{5} to fractions with denominator 10.

$$\frac{65}{10}-\frac{6}{10}-8+\frac{18}{5}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Since \frac{65}{10} and \frac{6}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-6}{10}-8+\frac{18}{5}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Subtract 6 from 65 to get 59.

$$\frac{59}{10}-8+\frac{18}{5}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Convert 8 to fraction \frac{80}{10}.

$$\frac{59}{10}-\frac{80}{10}+\frac{18}{5}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Since \frac{59}{10} and \frac{80}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{59-80}{10}+\frac{18}{5}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Subtract 80 from 59 to get -21.

$$-\frac{21}{10}+\frac{18}{5}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Least common multiple of 10 and 5 is 10. Convert -\frac{21}{10} and \frac{18}{5} to fractions with denominator 10.

$$-\frac{21}{10}+\frac{36}{10}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Since -\frac{21}{10} and \frac{36}{10} have the same denominator, add them by adding their numerators.

$$\frac{-21+36}{10}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Add -21 and 36 to get 15.

$$\frac{15}{10}-\left(\frac{2}{3}-\frac{1}{4}\right)$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

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

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{3}{2}-\left(\frac{8}{12}-\frac{3}{12}\right)$$

Since \frac{8}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}-\frac{8-3}{12}$$

Subtract 3 from 8 to get 5.

$$\frac{3}{2}-\frac{5}{12}$$

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

$$\frac{18}{12}-\frac{5}{12}$$

Since \frac{18}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-5}{12}$$

Subtract 5 from 18 to get 13.

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

Factor

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