Solve 1+1/2*(-3^2)+11/2*(-3)^2+1-1/2*3^2+(1-1/2)*9

$$1 + \frac { 1 } { 2 } \times ( - 3 ^ { 2 } ) + 1 \frac { 1 } { 2 } \times ( - 3 ) ^ { 2 } + 1 - \frac { 1 } { 2 } \times 3 ^ { 2 } + ( 1 - \frac { 1 } { 2 } ) \times 9$$

Evaluate

$$11$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$1+\frac{1}{2}\left(-9\right)+\frac{1\times 2+1}{2}\left(-3\right)^{2}+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Multiply \frac{1}{2} and -9 to get \frac{-9}{2}.

$$1+\frac{-9}{2}+\frac{1\times 2+1}{2}\left(-3\right)^{2}+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$1-\frac{9}{2}+\frac{1\times 2+1}{2}\left(-3\right)^{2}+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{2}{2}-\frac{9}{2}+\frac{1\times 2+1}{2}\left(-3\right)^{2}+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Since \frac{2}{2} and \frac{9}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-9}{2}+\frac{1\times 2+1}{2}\left(-3\right)^{2}+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Subtract 9 from 2 to get -7.

$$-\frac{7}{2}+\frac{1\times 2+1}{2}\left(-3\right)^{2}+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Multiply 1 and 2 to get 2.

$$-\frac{7}{2}+\frac{2+1}{2}\left(-3\right)^{2}+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Add 2 and 1 to get 3.

$$-\frac{7}{2}+\frac{3}{2}\left(-3\right)^{2}+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Calculate -3 to the power of 2 and get 9.

$$-\frac{7}{2}+\frac{3}{2}\times 9+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Express \frac{3}{2}\times 9 as a single fraction.

$$-\frac{7}{2}+\frac{3\times 9}{2}+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Multiply 3 and 9 to get 27.

$$-\frac{7}{2}+\frac{27}{2}+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Since -\frac{7}{2} and \frac{27}{2} have the same denominator, add them by adding their numerators.

$$\frac{-7+27}{2}+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Add -7 and 27 to get 20.

$$\frac{20}{2}+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Divide 20 by 2 to get 10.

$$10+1-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Add 10 and 1 to get 11.

$$11-\frac{1}{2}\times 3^{2}+\left(1-\frac{1}{2}\right)\times 9$$

Calculate 3 to the power of 2 and get 9.

$$11-\frac{1}{2}\times 9+\left(1-\frac{1}{2}\right)\times 9$$

Multiply \frac{1}{2} and 9 to get \frac{9}{2}.

$$11-\frac{9}{2}+\left(1-\frac{1}{2}\right)\times 9$$

Convert 11 to fraction \frac{22}{2}.

$$\frac{22}{2}-\frac{9}{2}+\left(1-\frac{1}{2}\right)\times 9$$

Since \frac{22}{2} and \frac{9}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-9}{2}+\left(1-\frac{1}{2}\right)\times 9$$

Subtract 9 from 22 to get 13.

$$\frac{13}{2}+\left(1-\frac{1}{2}\right)\times 9$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{13}{2}+\left(\frac{2}{2}-\frac{1}{2}\right)\times 9$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{2}+\frac{2-1}{2}\times 9$$

Subtract 1 from 2 to get 1.

$$\frac{13}{2}+\frac{1}{2}\times 9$$

Multiply \frac{1}{2} and 9 to get \frac{9}{2}.

$$\frac{13}{2}+\frac{9}{2}$$

Since \frac{13}{2} and \frac{9}{2} have the same denominator, add them by adding their numerators.

$$\frac{13+9}{2}$$

Add 13 and 9 to get 22.

$$\frac{22}{2}$$

Divide 22 by 2 to get 11.

$$11$$

Factor

$$11$$