Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $2$ .

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

Step 1.2.4.2

Add $6$ and $1$ .

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

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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

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

Step 2.6

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

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Step 2.6.1

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

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

Step 2.6.2

Multiply $2$ by $3$ .

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

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Multiply $4$ by $3$ .

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

Step 5.3

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

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

Step 5.4

Multiply $6$ by $2$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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Step 7.1

Multiply $9$ by $3$ .

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

Step 7.2

Multiply $- 7$ by $2$ .

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

Step 7.3

Subtract $14$ from $27$ .

$\frac{13}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{12}$

Decimal Form:

$1.08\overline{3}$

Mixed Number Form:

$1 \frac{1}{12}$