Basic Math Examples

$- 8 - \frac{9}{10 + \frac{3}{10}}$

Step 1

Simplify each term.

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Step 1.1

Simplify the denominator.

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Step 1.1.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$- 8 - \frac{9}{10 \cdot \frac{10}{10} + \frac{3}{10}}$

Step 1.1.2

Combine $10$ and $\frac{10}{10}$ .

$- 8 - \frac{9}{\frac{10 \cdot 10}{10} + \frac{3}{10}}$

Step 1.1.3

Combine the numerators over the common denominator.

$- 8 - \frac{9}{\frac{10 \cdot 10 + 3}{10}}$

Step 1.1.4

Simplify the numerator.

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Step 1.1.4.1

Multiply $10$ by $10$ .

$- 8 - \frac{9}{\frac{100 + 3}{10}}$

Step 1.1.4.2

Add $100$ and $3$ .

$- 8 - \frac{9}{\frac{103}{10}}$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$- 8 - (9 (\frac{10}{103}))$

Step 1.3

Multiply $9 (\frac{10}{103})$ .

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Step 1.3.1

Combine $9$ and $\frac{10}{103}$ .

$- 8 - \frac{9 \cdot 10}{103}$

Step 1.3.2

Multiply $9$ by $10$ .

$- 8 - \frac{90}{103}$

Step 2

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{103}{103}$ .

$- 8 \cdot \frac{103}{103} - \frac{90}{103}$

Step 3

Combine $- 8$ and $\frac{103}{103}$ .

$\frac{- 8 \cdot 103}{103} - \frac{90}{103}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 8 \cdot 103 - 90}{103}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 8$ by $103$ .

$\frac{- 824 - 90}{103}$

Step 5.2

Subtract $90$ from $- 824$ .

$\frac{- 914}{103}$

Step 6

Move the negative in front of the fraction.

$- \frac{914}{103}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{914}{103}$

Decimal Form:

$- 8.87378640 \dots$

Mixed Number Form:

$- 8 \frac{90}{103}$