Algebra Examples

$3 - \sqrt{49} + 2 (3 + 4^{2}) \div \frac{1}{2}$

Step 1

Find the common denominator.

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Step 1.1

Write $3$ as a fraction with denominator $1$ .

$\frac{3}{1} - \sqrt{49} + 2 (3 + 4^{2}) \div \frac{1}{2}$

Step 1.2

Multiply $\frac{3}{1}$ by $\frac{\frac{1}{2}}{\frac{1}{2}}$ .

$\frac{3}{1} \cdot \frac{\frac{1}{2}}{\frac{1}{2}} - \sqrt{49} + 2 (3 + 4^{2}) \div \frac{1}{2}$

Step 1.3

Multiply $\frac{3}{1}$ by $\frac{\frac{1}{2}}{\frac{1}{2}}$ .

$\frac{3 (\frac{1}{2})}{\frac{1}{2}} - \sqrt{49} + 2 (3 + 4^{2}) \div \frac{1}{2}$

Step 1.4

Write $- \sqrt{49}$ as a fraction with denominator $1$ .

$\frac{3 (\frac{1}{2})}{\frac{1}{2}} + \frac{- \sqrt{49}}{1} + 2 (3 + 4^{2}) \div \frac{1}{2}$

Step 1.5

Multiply $\frac{- \sqrt{49}}{1}$ by $\frac{\frac{1}{2}}{\frac{1}{2}}$ .

$\frac{3 (\frac{1}{2})}{\frac{1}{2}} + \frac{- \sqrt{49}}{1} \cdot \frac{\frac{1}{2}}{\frac{1}{2}} + 2 (3 + 4^{2}) \div \frac{1}{2}$

Step 1.6

Multiply $\frac{- \sqrt{49}}{1}$ by $\frac{\frac{1}{2}}{\frac{1}{2}}$ .

$\frac{3 (\frac{1}{2})}{\frac{1}{2}} + \frac{- \sqrt{49} \frac{1}{2}}{\frac{1}{2}} + 2 (3 + 4^{2}) \div \frac{1}{2}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 (\frac{1}{2}) - \sqrt{49} \frac{1}{2} + 2 (3 + 4^{2})}{\frac{1}{2}}$

Step 3

Simplify each term.

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Step 3.1

Combine $3$ and $\frac{1}{2}$ .

$\frac{\frac{3}{2} - \sqrt{49} \frac{1}{2} + 2 (3 + 4^{2})}{\frac{1}{2}}$

Step 3.2

Rewrite $49$ as $7^{2}$ .

$\frac{\frac{3}{2} - \sqrt{7^{2}} \frac{1}{2} + 2 (3 + 4^{2})}{\frac{1}{2}}$

Step 3.3

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

$\frac{\frac{3}{2} - 1 \cdot 7 \frac{1}{2} + 2 (3 + 4^{2})}{\frac{1}{2}}$

Step 3.4

Multiply $- 1$ by $7$ .

$\frac{\frac{3}{2} - 7 (\frac{1}{2}) + 2 (3 + 4^{2})}{\frac{1}{2}}$

Step 3.5

Combine $- 7$ and $\frac{1}{2}$ .

$\frac{\frac{3}{2} + \frac{- 7}{2} + 2 (3 + 4^{2})}{\frac{1}{2}}$

Step 3.6

Move the negative in front of the fraction.

$\frac{\frac{3}{2} - \frac{7}{2} + 2 (3 + 4^{2})}{\frac{1}{2}}$

Step 3.7

Raise $4$ to the power of $2$ .

$\frac{\frac{3}{2} - \frac{7}{2} + 2 (3 + 16)}{\frac{1}{2}}$

Step 3.8

Add $3$ and $16$ .

$\frac{\frac{3}{2} - \frac{7}{2} + 2 \cdot 19}{\frac{1}{2}}$

Step 3.9

Multiply $2$ by $19$ .

$\frac{\frac{3}{2} - \frac{7}{2} + 38}{\frac{1}{2}}$

Step 4

Combine fractions.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{38 + \frac{3 - 7}{2}}{\frac{1}{2}}$

Step 4.2

Simplify the expression.

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Step 4.2.1

Subtract $7$ from $3$ .

$\frac{38 + \frac{- 4}{2}}{\frac{1}{2}}$

Step 4.2.2

Divide $- 4$ by $2$ .

$\frac{38 - 2}{\frac{1}{2}}$

Step 4.2.3

Subtract $2$ from $38$ .

$\frac{36}{\frac{1}{2}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$36 \cdot 2$

Step 6

Multiply $36$ by $2$ .

$72$