Basic Math Examples

$\frac{- 32 {(100)}^{2}}{120^{2}} + 100$

Step 1

Simplify each term.

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Step 1.1

Raise $100$ to the power of $2$ .

$\frac{- 32 \cdot 10000}{120^{2}} + 100$

Step 1.2

Raise $120$ to the power of $2$ .

$\frac{- 32 \cdot 10000}{14400} + 100$

Step 1.3

Multiply $- 32$ by $10000$ .

$\frac{- 320000}{14400} + 100$

Step 1.4

Cancel the common factor of $- 320000$ and $14400$ .

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Step 1.4.1

Factor $1600$ out of $- 320000$ .

$\frac{1600 (- 200)}{14400} + 100$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $1600$ out of $14400$ .

$\frac{1600 \cdot - 200}{1600 \cdot 9} + 100$

Step 1.4.2.2

Cancel the common factor.

$\frac{1600 \cdot - 200}{1600 \cdot 9} + 100$

Step 1.4.2.3

Rewrite the expression.

$\frac{- 200}{9} + 100$

Step 1.5

Move the negative in front of the fraction.

$- \frac{200}{9} + 100$

Step 2

To write $100$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{200}{9} + 100 \cdot \frac{9}{9}$

Step 3

Combine $100$ and $\frac{9}{9}$ .

$- \frac{200}{9} + \frac{100 \cdot 9}{9}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 200 + 100 \cdot 9}{9}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $100$ by $9$ .

$\frac{- 200 + 900}{9}$

Step 5.2

Add $- 200$ and $900$ .

$\frac{700}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{700}{9}$

Decimal Form:

$77.\overline{7}$

Mixed Number Form:

$77 \frac{7}{9}$