Basic Math Examples

{(\frac{3}{2})}^{2} - 3 (\frac{3}{2})

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

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to

\frac{3}{2}

$\frac{3}{2}$ .

\frac{3^{2}}{2^{2}} - 3 (\frac{3}{2})

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

Step 1.2

Raise

3

$3$ to the power of

2

$2$ .

\frac{9}{2^{2}} - 3 (\frac{3}{2})

$\frac{9}{2^{2}} - 3 (\frac{3}{2})$

Step 1.3

Raise

2

$2$ to the power of

2

$2$ .

\frac{9}{4} - 3 (\frac{3}{2})

$\frac{9}{4} - 3 (\frac{3}{2})$

Step 1.4

Multiply

- 3 (\frac{3}{2})

$- 3 (\frac{3}{2})$ .

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Step 1.4.1

Combine

- 3

$- 3$ and

\frac{3}{2}

$\frac{3}{2}$ .

\frac{9}{4} + \frac{- 3 \cdot 3}{2}

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

Step 1.4.2

Multiply

- 3

$- 3$ by

3

$3$ .

\frac{9}{4} + \frac{- 9}{2}

$\frac{9}{4} + \frac{- 9}{2}$

\frac{9}{4} + \frac{- 9}{2}

$\frac{9}{4} + \frac{- 9}{2}$

Step 1.5

Move the negative in front of the fraction.

\frac{9}{4} - \frac{9}{2}

$\frac{9}{4} - \frac{9}{2}$

\frac{9}{4} - \frac{9}{2}

$\frac{9}{4} - \frac{9}{2}$

Step 2

To write

- \frac{9}{2}

$- \frac{9}{2}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{9}{4} - \frac{9}{2} \cdot \frac{2}{2}

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

Step 3

Write each expression with a common denominator of

4

$4$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{9}{2}

$\frac{9}{2}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{9}{4} - \frac{9 \cdot 2}{2 \cdot 2}

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

Step 3.2

Multiply

2

$2$ by

2

$2$ .

\frac{9}{4} - \frac{9 \cdot 2}{4}

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

\frac{9}{4} - \frac{9 \cdot 2}{4}

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

Step 4

Combine the numerators over the common denominator.

\frac{9 - 9 \cdot 2}{4}

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply

- 9

$- 9$ by

2

$2$ .

\frac{9 - 18}{4}

$\frac{9 - 18}{4}$

Step 5.2

Subtract

18

$18$ from

9

$9$ .

\frac{- 9}{4}

$\frac{- 9}{4}$

\frac{- 9}{4}

$\frac{- 9}{4}$

Step 6

Move the negative in front of the fraction.

- \frac{9}{4}

$- \frac{9}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

- \frac{9}{4}

$- \frac{9}{4}$

Decimal Form:

- 2.25

$- 2.25$

Mixed Number Form:

- 2 \frac{1}{4}

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