Algebra Examples

$4 - \sqrt{81} + 2 (4 + 3^{2}) \div \frac{1}{2}$

Step 1

Find the common denominator.

Tap for more steps...

Step 1.1

Write $4$ as a fraction with denominator $1$ .

$\frac{4}{1} - \sqrt{81} + 2 (4 + 3^{2}) \div \frac{1}{2}$

Step 1.2

Multiply $\frac{4}{1}$ by $\frac{\frac{1}{2}}{\frac{1}{2}}$ .

$\frac{4}{1} \cdot \frac{\frac{1}{2}}{\frac{1}{2}} - \sqrt{81} + 2 (4 + 3^{2}) \div \frac{1}{2}$

Step 1.3

Multiply $\frac{4}{1}$ by $\frac{\frac{1}{2}}{\frac{1}{2}}$ .

$\frac{4 (\frac{1}{2})}{\frac{1}{2}} - \sqrt{81} + 2 (4 + 3^{2}) \div \frac{1}{2}$

Step 1.4

Write $- \sqrt{81}$ as a fraction with denominator $1$ .

$\frac{4 (\frac{1}{2})}{\frac{1}{2}} + \frac{- \sqrt{81}}{1} + 2 (4 + 3^{2}) \div \frac{1}{2}$

Step 1.5

Multiply $\frac{- \sqrt{81}}{1}$ by $\frac{\frac{1}{2}}{\frac{1}{2}}$ .

$\frac{4 (\frac{1}{2})}{\frac{1}{2}} + \frac{- \sqrt{81}}{1} \cdot \frac{\frac{1}{2}}{\frac{1}{2}} + 2 (4 + 3^{2}) \div \frac{1}{2}$

Step 1.6

Multiply $\frac{- \sqrt{81}}{1}$ by $\frac{\frac{1}{2}}{\frac{1}{2}}$ .

$\frac{4 (\frac{1}{2})}{\frac{1}{2}} + \frac{- \sqrt{81} \frac{1}{2}}{\frac{1}{2}} + 2 (4 + 3^{2}) \div \frac{1}{2}$

Step 2

Combine the numerators over the common denominator.

$\frac{4 (\frac{1}{2}) - \sqrt{81} \frac{1}{2} + 2 (4 + 3^{2})}{\frac{1}{2}}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.1

Factor $2$ out of $4$ .

$\frac{2 (2) \frac{1}{2} - \sqrt{81} \frac{1}{2} + 2 (4 + 3^{2})}{\frac{1}{2}}$

Step 3.1.2

Cancel the common factor.

$\frac{2 \cdot 2 \frac{1}{2} - \sqrt{81} \frac{1}{2} + 2 (4 + 3^{2})}{\frac{1}{2}}$

Step 3.1.3

Rewrite the expression.

$\frac{2 - \sqrt{81} \frac{1}{2} + 2 (4 + 3^{2})}{\frac{1}{2}}$

Step 3.2

Rewrite $81$ as $9^{2}$ .

$\frac{2 - \sqrt{9^{2}} \frac{1}{2} + 2 (4 + 3^{2})}{\frac{1}{2}}$

Step 3.3

Pull terms out from under the radical, assuming positive real numbers.

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

Step 3.4

Multiply $- 1$ by $9$ .

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

Step 3.5

Combine $- 9$ and $\frac{1}{2}$ .

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

Step 3.6

Move the negative in front of the fraction.

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

Step 3.7

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

$\frac{2 - \frac{9}{2} + 2 (4 + 9)}{\frac{1}{2}}$

Step 3.8

Add $4$ and $9$ .

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

Step 3.9

Multiply $2$ by $13$ .

$\frac{2 - \frac{9}{2} + 26}{\frac{1}{2}}$

Step 4

Find the common denominator.

Tap for more steps...

Step 4.1

Write $2$ as a fraction with denominator $1$ .

$\frac{\frac{2}{1} - \frac{9}{2} + 26}{\frac{1}{2}}$

Step 4.2

Multiply $\frac{2}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{2}{1} \cdot \frac{2}{2} - \frac{9}{2} + 26}{\frac{1}{2}}$

Step 4.3

Multiply $\frac{2}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{2 \cdot 2}{2} - \frac{9}{2} + 26}{\frac{1}{2}}$

Step 4.4

Write $26$ as a fraction with denominator $1$ .

$\frac{\frac{2 \cdot 2}{2} - \frac{9}{2} + \frac{26}{1}}{\frac{1}{2}}$

Step 4.5

Multiply $\frac{26}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{2 \cdot 2}{2} - \frac{9}{2} + \frac{26}{1} \cdot \frac{2}{2}}{\frac{1}{2}}$

Step 4.6

Multiply $\frac{26}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{2 \cdot 2}{2} - \frac{9}{2} + \frac{26 \cdot 2}{2}}{\frac{1}{2}}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 2 - 9 + 26 \cdot 2}{2}}{\frac{1}{2}}$

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

Multiply $2$ by $2$ .

$\frac{\frac{4 - 9 + 26 \cdot 2}{2}}{\frac{1}{2}}$

Step 6.2

Multiply $26$ by $2$ .

$\frac{\frac{4 - 9 + 52}{2}}{\frac{1}{2}}$

Step 7

Simplify by adding and subtracting.

Tap for more steps...

Step 7.1

Subtract $9$ from $4$ .

$\frac{\frac{- 5 + 52}{2}}{\frac{1}{2}}$

Step 7.2

Add $- 5$ and $52$ .

$\frac{\frac{47}{2}}{\frac{1}{2}}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{47}{2} \cdot 2$

Step 9

Cancel the common factor of $2$ .

Tap for more steps...

Step 9.1

Cancel the common factor.

$\frac{47}{2} \cdot 2$

Step 9.2

Rewrite the expression.

$47$