Evaluate 1/4*(2/3)^2-4 2/3+8

$\frac{1}{4} \cdot {(\frac{2}{3})}^{2} - 4 \frac{2}{3} + 8$

Step 1

Convert $4 \frac{2}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{1}{4} \cdot {(\frac{2}{3})}^{2} - (4 + \frac{2}{3}) + 8$

Add $4$ and $\frac{2}{3}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{4} \cdot {(\frac{2}{3})}^{2} - (4 \cdot \frac{3}{3} + \frac{2}{3}) + 8$

Combine $4$ and $\frac{3}{3}$ .

$\frac{1}{4} \cdot {(\frac{2}{3})}^{2} - (\frac{4 \cdot 3}{3} + \frac{2}{3}) + 8$

Combine the numerators over the common denominator.

$\frac{1}{4} \cdot {(\frac{2}{3})}^{2} - \frac{4 \cdot 3 + 2}{3} + 8$

Simplify the numerator.

Multiply $4$ by $3$ .

$\frac{1}{4} \cdot {(\frac{2}{3})}^{2} - \frac{12 + 2}{3} + 8$

Add $12$ and $2$ .

$\frac{1}{4} \cdot {(\frac{2}{3})}^{2} - \frac{14}{3} + 8$

Step 2

Simplify each term.

Apply the product rule to $\frac{2}{3}$ .

$\frac{1}{4} \cdot \frac{2^{2}}{3^{2}} - \frac{14}{3} + 8$

Combine.

$\frac{1 \cdot 2^{2}}{4 \cdot 3^{2}} - \frac{14}{3} + 8$

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

$\frac{2^{2}}{4 \cdot 3^{2}} - \frac{14}{3} + 8$

Raise $3$ to the power of $2$ .

$\frac{2^{2}}{4 \cdot 9} - \frac{14}{3} + 8$

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

$\frac{4}{4 \cdot 9} - \frac{14}{3} + 8$

Multiply $4$ by $9$ .

$\frac{4}{36} - \frac{14}{3} + 8$

Cancel the common factor of $4$ and $36$ .

Factor $4$ out of $4$ .

$\frac{4 (1)}{36} - \frac{14}{3} + 8$

Cancel the common factors.

Factor $4$ out of $36$ .

$\frac{4 \cdot 1}{4 \cdot 9} - \frac{14}{3} + 8$

Cancel the common factor.

$\frac{4 \cdot 1}{4 \cdot 9} - \frac{14}{3} + 8$

Rewrite the expression.

$\frac{1}{9} - \frac{14}{3} + 8$

Step 3

Find the common denominator.

Multiply $\frac{14}{3}$ by $\frac{3}{3}$ .

$\frac{1}{9} - (\frac{14}{3} \cdot \frac{3}{3}) + 8$

Multiply $\frac{14}{3}$ by $\frac{3}{3}$ .

$\frac{1}{9} - \frac{14 \cdot 3}{3 \cdot 3} + 8$

Write $8$ as a fraction with denominator $1$ .

$\frac{1}{9} - \frac{14 \cdot 3}{3 \cdot 3} + \frac{8}{1}$

Multiply $\frac{8}{1}$ by $\frac{9}{9}$ .

$\frac{1}{9} - \frac{14 \cdot 3}{3 \cdot 3} + \frac{8}{1} \cdot \frac{9}{9}$

Multiply $\frac{8}{1}$ by $\frac{9}{9}$ .

$\frac{1}{9} - \frac{14 \cdot 3}{3 \cdot 3} + \frac{8 \cdot 9}{9}$

Multiply $3$ by $3$ .

$\frac{1}{9} - \frac{14 \cdot 3}{9} + \frac{8 \cdot 9}{9}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 - 14 \cdot 3 + 8 \cdot 9}{9}$

Step 5

Simplify each term.

Multiply $- 14$ by $3$ .

$\frac{1 - 42 + 8 \cdot 9}{9}$

Multiply $8$ by $9$ .

$\frac{1 - 42 + 72}{9}$

Step 6

Simplify by adding and subtracting.

Subtract $42$ from $1$ .

$\frac{- 41 + 72}{9}$

Add $- 41$ and $72$ .

$\frac{31}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{31}{9}$

Decimal Form:

$3.\overline{4}$

Mixed Number Form:

$3 \frac{4}{9}$

Evaluate 1/4*(2/3)^2-4 2/3+8

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