Algebra Examples

$8 + \frac{6 \cdot 3 - 20}{2^{2}}$

Step 1

Simplify the expression.

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Step 1.1

Multiply $6$ by $3$ .

$8 + \frac{18 - 20}{2^{2}}$

Step 1.2

Subtract $20$ from $18$ .

$8 + \frac{- 2}{2^{2}}$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Rewrite $- 2$ as $- 1 (2)$ .

$8 + \frac{- 1 (2)}{2^{2}}$

Step 2.1.2

Factor $2$ out of $- 1 (2)$ .

$8 + \frac{2 \cdot - 1}{2^{2}}$

Step 2.1.3

Cancel the common factors.

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Step 2.1.3.1

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

$8 + \frac{2 \cdot - 1}{2 \cdot 2}$

Step 2.1.3.2

Cancel the common factor.

$8 + \frac{2 \cdot - 1}{2 \cdot 2}$

Step 2.1.3.3

Rewrite the expression.

$8 + \frac{- 1}{2}$

Step 2.2

Move the negative in front of the fraction.

$8 - \frac{1}{2}$

Step 3

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$8 \cdot \frac{2}{2} - \frac{1}{2}$

Step 4

Combine $8$ and $\frac{2}{2}$ .

$\frac{8 \cdot 2}{2} - \frac{1}{2}$

Step 5

Combine the numerators over the common denominator.

$\frac{8 \cdot 2 - 1}{2}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $8$ by $2$ .

$\frac{16 - 1}{2}$

Step 6.2

Subtract $1$ from $16$ .

$\frac{15}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{2}$

Decimal Form:

$7.5$

Mixed Number Form:

$7 \frac{1}{2}$