Solve 11/2-(31/2-52/2)-32/3-5

$$1 \frac { 1 } { 2 } - ( 3 \frac { 1 } { 2 } - 5 \frac { 2 } { 2 } ) - 3 \frac { 2 } { 3 } - 5$$

Evaluate

$$-\frac{14}{3}\approx -4.666666667$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{2+1}{2}-\left(\frac{3\times 2+1}{2}-\frac{5\times 2+2}{2}\right)-\frac{3\times 3+2}{3}-5$$

Add 2 and 1 to get 3.

$$\frac{3}{2}-\left(\frac{3\times 2+1}{2}-\frac{5\times 2+2}{2}\right)-\frac{3\times 3+2}{3}-5$$

Multiply 3 and 2 to get 6.

$$\frac{3}{2}-\left(\frac{6+1}{2}-\frac{5\times 2+2}{2}\right)-\frac{3\times 3+2}{3}-5$$

Add 6 and 1 to get 7.

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

Multiply 5 and 2 to get 10.

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

Add 10 and 2 to get 12.

$$\frac{3}{2}-\left(\frac{7}{2}-\frac{12}{2}\right)-\frac{3\times 3+2}{3}-5$$

Since \frac{7}{2} and \frac{12}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}-\frac{7-12}{2}-\frac{3\times 3+2}{3}-5$$

Subtract 12 from 7 to get -5.

$$\frac{3}{2}-\left(-\frac{5}{2}\right)-\frac{3\times 3+2}{3}-5$$

The opposite of -\frac{5}{2} is \frac{5}{2}.

$$\frac{3}{2}+\frac{5}{2}-\frac{3\times 3+2}{3}-5$$

Since \frac{3}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{3+5}{2}-\frac{3\times 3+2}{3}-5$$

Add 3 and 5 to get 8.

$$\frac{8}{2}-\frac{3\times 3+2}{3}-5$$

Divide 8 by 2 to get 4.

$$4-\frac{3\times 3+2}{3}-5$$

Multiply 3 and 3 to get 9.

$$4-\frac{9+2}{3}-5$$

Add 9 and 2 to get 11.

$$4-\frac{11}{3}-5$$

Convert 4 to fraction \frac{12}{3}.

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

Since \frac{12}{3} and \frac{11}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 11 from 12 to get 1.

$$\frac{1}{3}-5$$

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

$$\frac{1}{3}-\frac{15}{3}$$

Since \frac{1}{3} and \frac{15}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-15}{3}$$

Subtract 15 from 1 to get -14.

$$-\frac{14}{3}$$

Factor

$$-\frac{14}{3} = -4\frac{2}{3} = -4.666666666666667$$