Evaluate (-3/2)^2-1/3*3 1/2

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

Convert $3 \frac{1}{2}$ to an improper fraction.

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

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

Add $3$ and $\frac{1}{2}$ .

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Multiply $3$ by $2$ .

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

Add $6$ and $1$ .

${(- \frac{3}{2})}^{2} - \frac{1}{3} \cdot \frac{7}{2}$

Simplify each term.

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Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

${(- 1)}^{2} {(\frac{3}{2})}^{2} - \frac{1}{3} \cdot \frac{7}{2}$

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

${(- 1)}^{2} \frac{3^{2}}{2^{2}} - \frac{1}{3} \cdot \frac{7}{2}$

Raise $- 1$ to the power of $2$ .

$1 \frac{3^{2}}{2^{2}} - \frac{1}{3} \cdot \frac{7}{2}$

Multiply $\frac{3^{2}}{2^{2}}$ by $1$ .

$\frac{3^{2}}{2^{2}} - \frac{1}{3} \cdot \frac{7}{2}$

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

$\frac{9}{2^{2}} - \frac{1}{3} \cdot \frac{7}{2}$

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

$\frac{9}{4} - \frac{1}{3} \cdot \frac{7}{2}$

Multiply $- \frac{1}{3} \cdot \frac{7}{2}$ .

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Multiply $\frac{7}{2}$ and $\frac{1}{3}$ .

$\frac{9}{4} - \frac{7}{2 \cdot 3}$

Multiply $2$ by $3$ .

$\frac{9}{4} - \frac{7}{6}$

To write $\frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9}{4} \cdot \frac{3}{3} - \frac{7}{6}$

To write $- \frac{7}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{4} \cdot \frac{3}{3} - \frac{7}{6} \cdot \frac{2}{2}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{9}{4}$ and $\frac{3}{3}$ .

$\frac{9 \cdot 3}{4 \cdot 3} - \frac{7}{6} \cdot \frac{2}{2}$

Multiply $4$ by $3$ .

$\frac{9 \cdot 3}{12} - \frac{7}{6} \cdot \frac{2}{2}$

Multiply $\frac{7}{6}$ and $\frac{2}{2}$ .

$\frac{9 \cdot 3}{12} - \frac{7 \cdot 2}{6 \cdot 2}$

Multiply $6$ by $2$ .

$\frac{9 \cdot 3}{12} - \frac{7 \cdot 2}{12}$

Combine the numerators over the common denominator.

$\frac{9 \cdot 3 - 7 \cdot 2}{12}$

Simplify the numerator.

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Multiply $9$ by $3$ .

$\frac{27 - 7 \cdot 2}{12}$

Multiply $- 7$ by $2$ .

$\frac{27 - 14}{12}$

Subtract $14$ from $27$ .

$\frac{13}{12}$

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{12}$

Decimal Form:

$1.08\overline{3}$

Mixed Number Form:

$1 \frac{1}{12}$

Evaluate (-3/2)^2-1/3*3 1/2

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