Basic Math Examples

$4 {(\pm \frac{1}{2})}^{3} - 11 {(\pm \frac{1}{2})}^{2} - 6 (\pm \frac{1}{2}) + 9$

Step 1

Simplify each term.

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Step 1.1

Remove the plus-minus sign on $\pm \frac{1}{2}$ because it is raised to an even power.

$4 {(\pm \frac{1}{2})}^{3} - 11 {(\frac{1}{2})}^{2} - 6 (\pm \frac{1}{2}) + 9$

Step 1.2

Apply the product rule to $\frac{1}{2}$ .

$4 {(\pm \frac{1}{2})}^{3} - 11 \frac{1^{2}}{2^{2}} - 6 (\pm \frac{1}{2}) + 9$

Step 1.3

One to any power is one.

$4 {(\pm \frac{1}{2})}^{3} - 11 \frac{1}{2^{2}} - 6 (\pm \frac{1}{2}) + 9$

Step 1.4

Raise $2$ to the power of $2$ .

$4 {(\pm \frac{1}{2})}^{3} - 11 (\frac{1}{4}) - 6 (\pm \frac{1}{2}) + 9$

Step 1.5

Combine $- 11$ and $\frac{1}{4}$ .

$4 {(\pm \frac{1}{2})}^{3} + \frac{- 11}{4} - 6 (\pm \frac{1}{2}) + 9$

Step 1.6

Move the negative in front of the fraction.

$4 {(\pm \frac{1}{2})}^{3} - \frac{11}{4} - 6 (\pm \frac{1}{2}) + 9$

Step 2

To write $4 {(\pm \frac{1}{2})}^{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$4 {(\pm \frac{1}{2})}^{3} \cdot \frac{4}{4} - \frac{11}{4} - 6 (\pm \frac{1}{2}) + 9$

Step 3

Combine $4 {(\pm \frac{1}{2})}^{3}$ and $\frac{4}{4}$ .

$\frac{4 {(\pm \frac{1}{2})}^{3} \cdot 4}{4} - \frac{11}{4} - 6 (\pm \frac{1}{2}) + 9$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{4 {(\pm \frac{1}{2})}^{3} \cdot 4 - 11}{4} - 6 (\pm \frac{1}{2}) + 9$

Step 4.2

Multiply $4$ by $4$ .

$\frac{16 {(\pm \frac{1}{2})}^{3} - 11}{4} - 6 (\pm \frac{1}{2}) + 9$

Step 5

To write $- 6 (\pm \frac{1}{2})$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{16 {(\pm \frac{1}{2})}^{3} - 11}{4} - 6 (\pm \frac{1}{2}) \cdot \frac{4}{4} + 9$

Step 6

Combine $- 6 (\pm \frac{1}{2})$ and $\frac{4}{4}$ .

$\frac{16 {(\pm \frac{1}{2})}^{3} - 11}{4} + \frac{- 6 (\pm \frac{1}{2}) \cdot 4}{4} + 9$

Step 7

Simplify the expression.

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Step 7.1

Combine the numerators over the common denominator.

$\frac{16 {(\pm \frac{1}{2})}^{3} - 11 - 6 (\pm \frac{1}{2}) \cdot 4}{4} + 9$

Step 7.2

Multiply $4$ by $- 6$ .

$\frac{16 {(\pm \frac{1}{2})}^{3} - 11 - 24 (\pm \frac{1}{2})}{4} + 9$

Step 8

To write $9$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{16 {(\pm \frac{1}{2})}^{3} - 11 - 24 (\pm \frac{1}{2})}{4} + 9 \cdot \frac{4}{4}$

Step 9

Combine fractions.

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Step 9.1

Combine $9$ and $\frac{4}{4}$ .

$\frac{16 {(\pm \frac{1}{2})}^{3} - 11 - 24 (\pm \frac{1}{2})}{4} + \frac{9 \cdot 4}{4}$

Step 9.2

Combine the numerators over the common denominator.

$\frac{16 {(\pm \frac{1}{2})}^{3} - 11 - 24 (\pm \frac{1}{2}) + 9 \cdot 4}{4}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $9$ by $4$ .

$\frac{16 {(\pm \frac{1}{2})}^{3} - 11 - 24 (\pm \frac{1}{2}) + 36}{4}$

Step 10.2

Add $- 11$ and $36$ .

$\frac{16 {(\pm \frac{1}{2})}^{3} + 25 - 24 (\pm \frac{1}{2})}{4}$

Step 11

Simplify the numerator.

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Step 11.1

Apply the product rule to $\frac{1}{2}$ .

$\frac{16 \frac{1^{3}}{2^{3}} + 25 - 24 (\frac{1}{2})}{4}$

Step 11.2

One to any power is one.

$\frac{16 \frac{1}{2^{3}} + 25 - 24 (\frac{1}{2})}{4}$

Step 11.3

Raise $2$ to the power of $3$ .

$\frac{16 (\frac{1}{8}) + 25 - 24 (\frac{1}{2})}{4}$

Step 11.4

Cancel the common factor of $8$ .

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Step 11.4.1

Factor $8$ out of $16$ .

$\frac{8 (2) \frac{1}{8} + 25 - 24 (\frac{1}{2})}{4}$

Step 11.4.2

Cancel the common factor.

$\frac{8 \cdot 2 \frac{1}{8} + 25 - 24 (\frac{1}{2})}{4}$

Step 11.4.3

Rewrite the expression.

$\frac{2 + 25 - 24 (\frac{1}{2})}{4}$

Step 11.5

Cancel the common factor of $2$ .

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Step 11.5.1

Factor $2$ out of $- 24$ .

$\frac{2 + 25 + 2 (- 12) \frac{1}{2}}{4}$

Step 11.5.2

Cancel the common factor.

$\frac{2 + 25 + 2 \cdot - 12 \frac{1}{2}}{4}$

Step 11.5.3

Rewrite the expression.

$\frac{2 + 25 - 12}{4}$

Step 11.6

Add $2$ and $25$ .

$\frac{27 - 12}{4}$

Step 11.7

Subtract $12$ from $27$ .

$\frac{15}{4}$

Step 12

Simplify the numerator.

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Step 12.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 12.1.1

Apply the product rule to $- \frac{1}{2}$ .

$\frac{16 ({(- 1)}^{3} {(\frac{1}{2})}^{3}) + 25 - 24 (- \frac{1}{2})}{4}$

Step 12.1.2

Apply the product rule to $\frac{1}{2}$ .

$\frac{16 ({(- 1)}^{3} \frac{1^{3}}{2^{3}}) + 25 - 24 (- \frac{1}{2})}{4}$

Step 12.2

Raise $- 1$ to the power of $3$ .

$\frac{16 (- \frac{1^{3}}{2^{3}}) + 25 - 24 (- \frac{1}{2})}{4}$

Step 12.3

One to any power is one.

$\frac{16 (- \frac{1}{2^{3}}) + 25 - 24 (- \frac{1}{2})}{4}$

Step 12.4

Raise $2$ to the power of $3$ .

$\frac{16 (- \frac{1}{8}) + 25 - 24 (- \frac{1}{2})}{4}$

Step 12.5

Cancel the common factor of $8$ .

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Step 12.5.1

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$\frac{16 (\frac{- 1}{8}) + 25 - 24 (- \frac{1}{2})}{4}$

Step 12.5.2

Factor $8$ out of $16$ .

$\frac{8 (2) \frac{- 1}{8} + 25 - 24 (- \frac{1}{2})}{4}$

Step 12.5.3

Cancel the common factor.

$\frac{8 \cdot 2 \frac{- 1}{8} + 25 - 24 (- \frac{1}{2})}{4}$

Step 12.5.4

Rewrite the expression.

$\frac{2 \cdot - 1 + 25 - 24 (- \frac{1}{2})}{4}$

Step 12.6

Multiply $2$ by $- 1$ .

$\frac{- 2 + 25 - 24 (- \frac{1}{2})}{4}$

Step 12.7

Cancel the common factor of $2$ .

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Step 12.7.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 2 + 25 - 24 (\frac{- 1}{2})}{4}$

Step 12.7.2

Factor $2$ out of $- 24$ .

$\frac{- 2 + 25 + 2 (- 12) \frac{- 1}{2}}{4}$

Step 12.7.3

Cancel the common factor.

$\frac{- 2 + 25 + 2 \cdot - 12 \frac{- 1}{2}}{4}$

Step 12.7.4

Rewrite the expression.

$\frac{- 2 + 25 - 12 \cdot - 1}{4}$

Step 12.8

Multiply $- 12$ by $- 1$ .

$\frac{- 2 + 25 + 12}{4}$

Step 12.9

Add $- 2$ and $25$ .

$\frac{23 + 12}{4}$

Step 12.10

Add $23$ and $12$ .

$\frac{35}{4}$

Step 13

The complete solution is the result of both the positive and negative portions of the solution.

$\frac{15}{4}, \frac{35}{4}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{4}, \frac{35}{4}$

Decimal Form:

$3.75, 8.75$

Mixed Number Form:

$3 \frac{3}{4}, 8 \frac{3}{4}$