Solve 89/10-(18/5+9/10)-(7/10+frac{3}{2})

$$\frac { 89 } { 10 } - ( \frac { 18 } { 5 } + \frac { 9 } { 10 } ) - ( \frac { 7 } { 10 } + \frac { 3 } { 2 } )$$

Evaluate

$$\frac{11}{5}=2.2$$

Solution Steps

Least common multiple of 5 and 10 is 10. Convert \frac{18}{5} and \frac{9}{10} to fractions with denominator 10.

$$\frac{89}{10}-\left(\frac{36}{10}+\frac{9}{10}\right)-\left(\frac{7}{10}+\frac{3}{2}\right)$$

Since \frac{36}{10} and \frac{9}{10} have the same denominator, add them by adding their numerators.

$$\frac{89}{10}-\frac{36+9}{10}-\left(\frac{7}{10}+\frac{3}{2}\right)$$

Add 36 and 9 to get 45.

$$\frac{89}{10}-\frac{45}{10}-\left(\frac{7}{10}+\frac{3}{2}\right)$$

Since \frac{89}{10} and \frac{45}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{89-45}{10}-\left(\frac{7}{10}+\frac{3}{2}\right)$$

Subtract 45 from 89 to get 44.

$$\frac{44}{10}-\left(\frac{7}{10}+\frac{3}{2}\right)$$

Reduce the fraction \frac{44}{10} to lowest terms by extracting and canceling out 2.

$$\frac{22}{5}-\left(\frac{7}{10}+\frac{3}{2}\right)$$

Least common multiple of 10 and 2 is 10. Convert \frac{7}{10} and \frac{3}{2} to fractions with denominator 10.

$$\frac{22}{5}-\left(\frac{7}{10}+\frac{15}{10}\right)$$

Since \frac{7}{10} and \frac{15}{10} have the same denominator, add them by adding their numerators.

$$\frac{22}{5}-\frac{7+15}{10}$$

Add 7 and 15 to get 22.

$$\frac{22}{5}-\frac{22}{10}$$

Reduce the fraction \frac{22}{10} to lowest terms by extracting and canceling out 2.

$$\frac{22}{5}-\frac{11}{5}$$

Since \frac{22}{5} and \frac{11}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-11}{5}$$

Subtract 11 from 22 to get 11.

$$\frac{11}{5}$$

Factor

$$\frac{11}{5} = 2\frac{1}{5} = 2.2$$