Basic Math Examples

$- (- 7 a^{2}) - \frac{16}{4} a^{2} + \frac{1}{2} a^{2} - \frac{9}{2} a^{2}$

Step 1

Simplify each term.

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Step 1.1

Multiply $- 7$ by $- 1$ .

$7 a^{2} - \frac{16}{4} a^{2} + \frac{1}{2} a^{2} - \frac{9}{2} a^{2}$

Step 1.2

Divide $16$ by $4$ .

$7 a^{2} - 1 \cdot 4 a^{2} + \frac{1}{2} a^{2} - \frac{9}{2} a^{2}$

Step 1.3

Multiply $- 1$ by $4$ .

$7 a^{2} - 4 a^{2} + \frac{1}{2} a^{2} - \frac{9}{2} a^{2}$

Step 1.4

Combine $\frac{1}{2}$ and $a^{2}$ .

$7 a^{2} - 4 a^{2} + \frac{a^{2}}{2} - \frac{9}{2} a^{2}$

Step 1.5

Combine $a^{2}$ and $\frac{9}{2}$ .

$7 a^{2} - 4 a^{2} + \frac{a^{2}}{2} - \frac{a^{2} \cdot 9}{2}$

Step 1.6

Move $9$ to the left of $a^{2}$ .

$7 a^{2} - 4 a^{2} + \frac{a^{2}}{2} - \frac{9 a^{2}}{2}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$7 a^{2} - 4 a^{2} + \frac{a^{2} - 9 a^{2}}{2}$

Step 2.2

Subtract $9 a^{2}$ from $a^{2}$ .

$7 a^{2} - 4 a^{2} + \frac{- 8 a^{2}}{2}$

Step 3

Find the common denominator.

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Step 3.1

Write $7 a^{2}$ as a fraction with denominator $1$ .

$\frac{7 a^{2}}{1} - 4 a^{2} + \frac{- 8 a^{2}}{2}$

Step 3.2

Multiply $\frac{7 a^{2}}{1}$ by $\frac{2}{2}$ .

$\frac{7 a^{2}}{1} \cdot \frac{2}{2} - 4 a^{2} + \frac{- 8 a^{2}}{2}$

Step 3.3

Multiply $\frac{7 a^{2}}{1}$ by $\frac{2}{2}$ .

$\frac{7 a^{2} \cdot 2}{2} - 4 a^{2} + \frac{- 8 a^{2}}{2}$

Step 3.4

Write $- 4 a^{2}$ as a fraction with denominator $1$ .

$\frac{7 a^{2} \cdot 2}{2} + \frac{- 4 a^{2}}{1} + \frac{- 8 a^{2}}{2}$

Step 3.5

Multiply $\frac{- 4 a^{2}}{1}$ by $\frac{2}{2}$ .

$\frac{7 a^{2} \cdot 2}{2} + \frac{- 4 a^{2}}{1} \cdot \frac{2}{2} + \frac{- 8 a^{2}}{2}$

Step 3.6

Multiply $\frac{- 4 a^{2}}{1}$ by $\frac{2}{2}$ .

$\frac{7 a^{2} \cdot 2}{2} + \frac{- 4 a^{2} \cdot 2}{2} + \frac{- 8 a^{2}}{2}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 a^{2} \cdot 2 - 4 a^{2} \cdot 2 - 8 a^{2}}{2}$

Step 5

Simplify each term.

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Step 5.1

Multiply $2$ by $7$ .

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

Step 5.2

Multiply $2$ by $- 4$ .

$\frac{14 a^{2} - 8 a^{2} - 8 a^{2}}{2}$

Step 6

Simplify terms.

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Step 6.1

Subtract $8 a^{2}$ from $14 a^{2}$ .

$\frac{6 a^{2} - 8 a^{2}}{2}$

Step 6.2

Subtract $8 a^{2}$ from $6 a^{2}$ .

$\frac{- 2 a^{2}}{2}$

Step 6.3

Cancel the common factor of $- 2$ and $2$ .

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Step 6.3.1

Factor $2$ out of $- 2 a^{2}$ .

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

Step 6.3.2

Cancel the common factors.

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Step 6.3.2.1

Factor $2$ out of $2$ .

$\frac{2 (- a^{2})}{2 (1)}$

Step 6.3.2.2

Cancel the common factor.

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

Step 6.3.2.3

Rewrite the expression.

$\frac{- a^{2}}{1}$

Step 6.3.2.4

Divide $- a^{2}$ by $1$ .

$- a^{2}$