Pre-Algebra Examples

$27 - 4^{2} \div 2 + (11 - 5)$

Step 1

Remove parentheses.

$27 - 4^{2} \div 2 + 11 - 5$

Step 2

Find the common denominator.

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Step 2.1

Write $27$ as a fraction with denominator $1$ .

$\frac{27}{1} - 4^{2} \div 2 + 11 - 5$

Step 2.2

Multiply $\frac{27}{1}$ by $\frac{2}{2}$ .

$\frac{27}{1} \cdot \frac{2}{2} - 4^{2} \div 2 + 11 - 5$

Step 2.3

Multiply $\frac{27}{1}$ by $\frac{2}{2}$ .

$\frac{27 \cdot 2}{2} - 4^{2} \div 2 + 11 - 5$

Step 2.4

Write $11$ as a fraction with denominator $1$ .

$\frac{27 \cdot 2}{2} - 4^{2} \div 2 + \frac{11}{1} - 5$

Step 2.5

Multiply $\frac{11}{1}$ by $\frac{2}{2}$ .

$\frac{27 \cdot 2}{2} - 4^{2} \div 2 + \frac{11}{1} \cdot \frac{2}{2} - 5$

Step 2.6

Multiply $\frac{11}{1}$ by $\frac{2}{2}$ .

$\frac{27 \cdot 2}{2} - 4^{2} \div 2 + \frac{11 \cdot 2}{2} - 5$

Step 2.7

Write $- 5$ as a fraction with denominator $1$ .

$\frac{27 \cdot 2}{2} - 4^{2} \div 2 + \frac{11 \cdot 2}{2} + \frac{- 5}{1}$

Step 2.8

Multiply $\frac{- 5}{1}$ by $\frac{2}{2}$ .

$\frac{27 \cdot 2}{2} - 4^{2} \div 2 + \frac{11 \cdot 2}{2} + \frac{- 5}{1} \cdot \frac{2}{2}$

Step 2.9

Multiply $\frac{- 5}{1}$ by $\frac{2}{2}$ .

$\frac{27 \cdot 2}{2} - 4^{2} \div 2 + \frac{11 \cdot 2}{2} + \frac{- 5 \cdot 2}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{27 \cdot 2 - 4^{2} + 11 \cdot 2 - 5 \cdot 2}{2}$

Step 4

Simplify each term.

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Step 4.1

Multiply $27$ by $2$ .

$\frac{54 - 4^{2} + 11 \cdot 2 - 5 \cdot 2}{2}$

Step 4.2

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

$\frac{54 - 1 \cdot 16 + 11 \cdot 2 - 5 \cdot 2}{2}$

Step 4.3

Multiply $- 1$ by $16$ .

$\frac{54 - 16 + 11 \cdot 2 - 5 \cdot 2}{2}$

Step 4.4

Multiply $11$ by $2$ .

$\frac{54 - 16 + 22 - 5 \cdot 2}{2}$

Step 4.5

Multiply $- 5$ by $2$ .

$\frac{54 - 16 + 22 - 10}{2}$

Step 5

Simplify the expression.

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Step 5.1

Subtract $16$ from $54$ .

$\frac{38 + 22 - 10}{2}$

Step 5.2

Add $38$ and $22$ .

$\frac{60 - 10}{2}$

Step 5.3

Subtract $10$ from $60$ .

$\frac{50}{2}$

Step 5.4

Divide $50$ by $2$ .

$25$