Basic Math Examples

$(\frac{19}{8} - \frac{9}{2}) \div (\frac{9}{8} - \frac{9}{4})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{19}{8} - \frac{9}{2}}{\frac{9}{8} - \frac{9}{4}}$

Step 2

Multiply the numerator and denominator of the fraction by $8$ .

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Step 2.1

Multiply $\frac{\frac{19}{8} - \frac{9}{2}}{\frac{9}{8} - \frac{9}{4}}$ by $\frac{8}{8}$ .

$\frac{8}{8} \cdot \frac{\frac{19}{8} - \frac{9}{2}}{\frac{9}{8} - \frac{9}{4}}$

Step 2.2

Combine.

$\frac{8 (\frac{19}{8} - \frac{9}{2})}{8 (\frac{9}{8} - \frac{9}{4})}$

Step 3

Apply the distributive property.

$\frac{8 (\frac{19}{8}) + 8 (- \frac{9}{2})}{8 (\frac{9}{8}) + 8 (- \frac{9}{4})}$

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $8$ .

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Step 4.1.1

Cancel the common factor.

$\frac{8 (\frac{19}{8}) + 8 (- \frac{9}{2})}{8 (\frac{9}{8}) + 8 (- \frac{9}{4})}$

Step 4.1.2

Rewrite the expression.

$\frac{19 + 8 (- \frac{9}{2})}{8 (\frac{9}{8}) + 8 (- \frac{9}{4})}$

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$\frac{19 + 8 (\frac{- 9}{2})}{8 (\frac{9}{8}) + 8 (- \frac{9}{4})}$

Step 4.2.2

Factor $2$ out of $8$ .

$\frac{19 + 2 (4) \frac{- 9}{2}}{8 (\frac{9}{8}) + 8 (- \frac{9}{4})}$

Step 4.2.3

Cancel the common factor.

$\frac{19 + 2 \cdot 4 \frac{- 9}{2}}{8 (\frac{9}{8}) + 8 (- \frac{9}{4})}$

Step 4.2.4

Rewrite the expression.

$\frac{19 + 4 \cdot - 9}{8 (\frac{9}{8}) + 8 (- \frac{9}{4})}$

Step 4.3

Multiply $4$ by $- 9$ .

$\frac{19 - 36}{8 (\frac{9}{8}) + 8 (- \frac{9}{4})}$

Step 4.4

Cancel the common factor of $8$ .

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Step 4.4.1

Cancel the common factor.

$\frac{19 - 36}{8 (\frac{9}{8}) + 8 (- \frac{9}{4})}$

Step 4.4.2

Rewrite the expression.

$\frac{19 - 36}{9 + 8 (- \frac{9}{4})}$

Step 4.5

Cancel the common factor of $4$ .

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Step 4.5.1

Move the leading negative in $- \frac{9}{4}$ into the numerator.

$\frac{19 - 36}{9 + 8 (\frac{- 9}{4})}$

Step 4.5.2

Factor $4$ out of $8$ .

$\frac{19 - 36}{9 + 4 (2) \frac{- 9}{4}}$

Step 4.5.3

Cancel the common factor.

$\frac{19 - 36}{9 + 4 \cdot 2 \frac{- 9}{4}}$

Step 4.5.4

Rewrite the expression.

$\frac{19 - 36}{9 + 2 \cdot - 9}$

Step 4.6

Multiply $2$ by $- 9$ .

$\frac{19 - 36}{9 - 18}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Subtract $36$ from $19$ .

$\frac{- 17}{9 - 18}$

Step 5.2

Subtract $18$ from $9$ .

$\frac{- 17}{- 9}$

Step 5.3

Dividing two negative values results in a positive value.

$\frac{17}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{9}$

Decimal Form:

$1.\overline{8}$

Mixed Number Form:

$1 \frac{8}{9}$