Simplify (1/2)^2-6(2-2/3)

${(\frac{1}{2})}^{2} - 6 (2 - \frac{2}{3})$

Simplify each term.

Apply the product rule to $\frac{1}{2}$ .

$\frac{1^{2}}{2^{2}} - 6 (2 - \frac{2}{3})$

One to any power is one.

$\frac{1}{2^{2}} - 6 (2 - \frac{2}{3})$

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

$\frac{1}{4} - 6 (2 - \frac{2}{3})$

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{4} - 6 (2 \cdot \frac{3}{3} - \frac{2}{3})$

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

$\frac{1}{4} - 6 (\frac{2 \cdot 3}{3} - \frac{2}{3})$

Combine the numerators over the common denominator.

$\frac{1}{4} - 6 \frac{2 \cdot 3 - 2}{3}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{1}{4} - 6 \frac{6 - 2}{3}$

Subtract $2$ from $6$ .

$\frac{1}{4} - 6 (\frac{4}{3})$

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

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

Cancel the common factor.

$\frac{1}{4} + 3 \cdot - 2 \frac{4}{3}$

Rewrite the expression.

$\frac{1}{4} - 2 \cdot 4$

Multiply $- 2$ by $4$ .

$\frac{1}{4} - 8$

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{4} - 8 \cdot \frac{4}{4}$

Combine $- 8$ and $\frac{4}{4}$ .

$\frac{1}{4} + \frac{- 8 \cdot 4}{4}$

Combine the numerators over the common denominator.

$\frac{1 - 8 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 8$ by $4$ .

$\frac{1 - 32}{4}$

Subtract $32$ from $1$ .

$\frac{- 31}{4}$

Move the negative in front of the fraction.

$- \frac{31}{4}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{31}{4}$

Decimal Form:

$- 7.75$

Mixed Number Form:

$- 7 \frac{3}{4}$

Simplify (1/2)^2-6(2-2/3)

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