Evaluate 1/4(23/6)^2-23/1223/6-2/3

$\frac{1}{4} \cdot {(\frac{23}{6})}^{2} - \frac{23}{12} \cdot \frac{23}{6} - \frac{2}{3}$

Step 1

Simplify each term.

Apply the product rule to $\frac{23}{6}$ .

$\frac{1}{4} \cdot \frac{23^{2}}{6^{2}} - \frac{23}{12} \cdot \frac{23}{6} - \frac{2}{3}$

Combine.

$\frac{1 \cdot 23^{2}}{4 \cdot 6^{2}} - \frac{23}{12} \cdot \frac{23}{6} - \frac{2}{3}$

Multiply $23^{2}$ by $1$ .

$\frac{23^{2}}{4 \cdot 6^{2}} - \frac{23}{12} \cdot \frac{23}{6} - \frac{2}{3}$

Raise $6$ to the power of $2$ .

$\frac{23^{2}}{4 \cdot 36} - \frac{23}{12} \cdot \frac{23}{6} - \frac{2}{3}$

Raise $23$ to the power of $2$ .

$\frac{529}{4 \cdot 36} - \frac{23}{12} \cdot \frac{23}{6} - \frac{2}{3}$

Multiply $4$ by $36$ .

$\frac{529}{144} - \frac{23}{12} \cdot \frac{23}{6} - \frac{2}{3}$

Multiply $- \frac{23}{12} \cdot \frac{23}{6}$ .

Multiply $\frac{23}{6}$ by $\frac{23}{12}$ .

$\frac{529}{144} - \frac{23 \cdot 23}{6 \cdot 12} - \frac{2}{3}$

Multiply $23$ by $23$ .

$\frac{529}{144} - \frac{529}{6 \cdot 12} - \frac{2}{3}$

Multiply $6$ by $12$ .

$\frac{529}{144} - \frac{529}{72} - \frac{2}{3}$

Step 2

Find the common denominator.

Multiply $\frac{529}{72}$ by $\frac{2}{2}$ .

$\frac{529}{144} - (\frac{529}{72} \cdot \frac{2}{2}) - \frac{2}{3}$

Multiply $\frac{529}{72}$ by $\frac{2}{2}$ .

$\frac{529}{144} - \frac{529 \cdot 2}{72 \cdot 2} - \frac{2}{3}$

Multiply $\frac{2}{3}$ by $\frac{48}{48}$ .

$\frac{529}{144} - \frac{529 \cdot 2}{72 \cdot 2} - (\frac{2}{3} \cdot \frac{48}{48})$

Multiply $\frac{2}{3}$ by $\frac{48}{48}$ .

$\frac{529}{144} - \frac{529 \cdot 2}{72 \cdot 2} - \frac{2 \cdot 48}{3 \cdot 48}$

Reorder the factors of $72 \cdot 2$ .

$\frac{529}{144} - \frac{529 \cdot 2}{2 \cdot 72} - \frac{2 \cdot 48}{3 \cdot 48}$

Multiply $2$ by $72$ .

$\frac{529}{144} - \frac{529 \cdot 2}{144} - \frac{2 \cdot 48}{3 \cdot 48}$

Multiply $3$ by $48$ .

$\frac{529}{144} - \frac{529 \cdot 2}{144} - \frac{2 \cdot 48}{144}$

Step 3

Combine the numerators over the common denominator.

$\frac{529 - 529 \cdot 2 - 2 \cdot 48}{144}$

Step 4

Simplify each term.

Multiply $- 529$ by $2$ .

$\frac{529 - 1058 - 2 \cdot 48}{144}$

Multiply $- 2$ by $48$ .

$\frac{529 - 1058 - 96}{144}$

Step 5

Simplify the expression.

Subtract $1058$ from $529$ .

$\frac{- 529 - 96}{144}$

Subtract $96$ from $- 529$ .

$\frac{- 625}{144}$

Move the negative in front of the fraction.

$- \frac{625}{144}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{625}{144}$

Decimal Form:

$- 4.3402\overline{7}$

Mixed Number Form:

$- 4 \frac{49}{144}$

Evaluate 1/4*(23/6)^2-23/12*23/6-2/3

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Evaluate 1/4(23/6)^2-23/1223/6-2/3