Solve [11/10+(3/2-2/5)]div((9/5+frac{3}{5})-3]

$$[ \frac { 11 } { 10 } + ( \frac { 3 } { 2 } - \frac { 2 } { 5 } ) ] \div ( ( \frac { 9 } { 5 } + \frac { 3 } { 5 } ) - 3 ]$$

Evaluate

$$-\frac{11}{3}\approx -3.666666667$$

Solution Steps

Least common multiple of 10 and 2 is 10. Convert \frac{11}{10} and \frac{3}{2} to fractions with denominator 10.

$$\frac{\frac{11}{10}+\frac{15}{10}-\frac{2}{5}}{\frac{9}{5}+\frac{3}{5}-3}$$

Since \frac{11}{10} and \frac{15}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{11+15}{10}-\frac{2}{5}}{\frac{9}{5}+\frac{3}{5}-3}$$

Add 11 and 15 to get 26.

$$\frac{\frac{26}{10}-\frac{2}{5}}{\frac{9}{5}+\frac{3}{5}-3}$$

Reduce the fraction \frac{26}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{13}{5}-\frac{2}{5}}{\frac{9}{5}+\frac{3}{5}-3}$$

Since \frac{13}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13-2}{5}}{\frac{9}{5}+\frac{3}{5}-3}$$

Subtract 2 from 13 to get 11.

$$\frac{\frac{11}{5}}{\frac{9}{5}+\frac{3}{5}-3}$$

Since \frac{9}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{11}{5}}{\frac{9+3}{5}-3}$$

Add 9 and 3 to get 12.

$$\frac{\frac{11}{5}}{\frac{12}{5}-3}$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{\frac{11}{5}}{\frac{12}{5}-\frac{15}{5}}$$

Since \frac{12}{5} and \frac{15}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11}{5}}{\frac{12-15}{5}}$$

Subtract 15 from 12 to get -3.

$$\frac{\frac{11}{5}}{-\frac{3}{5}}$$

Divide \frac{11}{5} by -\frac{3}{5} by multiplying \frac{11}{5} by the reciprocal of -\frac{3}{5}.

$$\frac{11}{5}\left(-\frac{5}{3}\right)$$

Multiply \frac{11}{5} times -\frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\left(-5\right)}{5\times 3}$$

Do the multiplications in the fraction \frac{11\left(-5\right)}{5\times 3}.

$$\frac{-55}{15}$$

Reduce the fraction \frac{-55}{15} to lowest terms by extracting and canceling out 5.

$$-\frac{11}{3}$$

Factor

$$-\frac{11}{3} = -3\frac{2}{3} = -3.6666666666666665$$