Pre-Algebra Examples

$7 + \frac{16 - 4}{2^{2} + 2} - 2$

Step 1

Subtract $4$ from $16$ .

$7 + \frac{12}{2^{2} + 2} - 2$

Step 2

Find the common denominator.

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Step 2.1

Write $7$ as a fraction with denominator $1$ .

$\frac{7}{1} + \frac{12}{2^{2} + 2} - 2$

Step 2.2

Multiply $\frac{7}{1}$ by $\frac{2^{2} + 2}{2^{2} + 2}$ .

$\frac{7}{1} \cdot \frac{2^{2} + 2}{2^{2} + 2} + \frac{12}{2^{2} + 2} - 2$

Step 2.3

Multiply $\frac{7}{1}$ by $\frac{2^{2} + 2}{2^{2} + 2}$ .

$\frac{7 (2^{2} + 2)}{2^{2} + 2} + \frac{12}{2^{2} + 2} - 2$

Step 2.4

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

$\frac{7 (2^{2} + 2)}{2^{2} + 2} + \frac{12}{2^{2} + 2} + \frac{- 2}{1}$

Step 2.5

Multiply $\frac{- 2}{1}$ by $\frac{2^{2} + 2}{2^{2} + 2}$ .

$\frac{7 (2^{2} + 2)}{2^{2} + 2} + \frac{12}{2^{2} + 2} + \frac{- 2}{1} \cdot \frac{2^{2} + 2}{2^{2} + 2}$

Step 2.6

Multiply $\frac{- 2}{1}$ by $\frac{2^{2} + 2}{2^{2} + 2}$ .

$\frac{7 (2^{2} + 2)}{2^{2} + 2} + \frac{12}{2^{2} + 2} + \frac{- 2 (2^{2} + 2)}{2^{2} + 2}$

Step 3

Combine the numerators over the common denominator.

$\frac{7 (2^{2} + 2) + 12 - 2 (2^{2} + 2)}{2^{2} + 2}$

Step 4

Simplify each term.

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Step 4.1

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

$\frac{7 (4 + 2) + 12 - 2 (2^{2} + 2)}{2^{2} + 2}$

Step 4.2

Add $4$ and $2$ .

$\frac{7 \cdot 6 + 12 - 2 (2^{2} + 2)}{2^{2} + 2}$

Step 4.3

Multiply $7$ by $6$ .

$\frac{42 + 12 - 2 (2^{2} + 2)}{2^{2} + 2}$

Step 4.4

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

$\frac{42 + 12 - 2 (4 + 2)}{2^{2} + 2}$

Step 4.5

Add $4$ and $2$ .

$\frac{42 + 12 - 2 \cdot 6}{2^{2} + 2}$

Step 4.6

Multiply $- 2$ by $6$ .

$\frac{42 + 12 - 12}{2^{2} + 2}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Add $42$ and $12$ .

$\frac{54 - 12}{2^{2} + 2}$

Step 5.2

Subtract $12$ from $54$ .

$\frac{42}{2^{2} + 2}$

Step 5.3

Cancel the common factor of $42$ and $2^{2} + 2$ .

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Step 5.3.1

Factor $2$ out of $42$ .

$\frac{2 \cdot 21}{2^{2} + 2}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $2$ out of $2^{2}$ .

$\frac{2 \cdot 21}{2 \cdot 2 + 2}$

Step 5.3.2.2

Factor $2$ out of $2$ .

$\frac{2 \cdot 21}{2 \cdot 2 + 2 (1)}$

Step 5.3.2.3

Factor $2$ out of $2 \cdot 2 + 2 (1)$ .

$\frac{2 \cdot 21}{2 \cdot (2 + 1)}$

Step 5.3.2.4

Cancel the common factor.

$\frac{2 \cdot 21}{2 \cdot (2 + 1)}$

Step 5.3.2.5

Rewrite the expression.

$\frac{21}{2 + 1}$

Step 5.4

Simplify the expression.

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Step 5.4.1

Add $2$ and $1$ .

$\frac{21}{3}$

Step 5.4.2

Divide $21$ by $3$ .

$7$