Basic Math Examples

$\frac{\frac{5}{7}}{2 - \frac{9}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{7} \cdot \frac{1}{2 - \frac{9}{2}}$

Step 2

Simplify the denominator.

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Step 2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{7} \cdot \frac{1}{2 \cdot \frac{2}{2} - \frac{9}{2}}$

Step 2.2

Combine $2$ and $\frac{2}{2}$ .

$\frac{5}{7} \cdot \frac{1}{\frac{2 \cdot 2}{2} - \frac{9}{2}}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{5}{7} \cdot \frac{1}{\frac{2 \cdot 2 - 9}{2}}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $2$ by $2$ .

$\frac{5}{7} \cdot \frac{1}{\frac{4 - 9}{2}}$

Step 2.4.2

Subtract $9$ from $4$ .

$\frac{5}{7} \cdot \frac{1}{\frac{- 5}{2}}$

Step 2.5

Move the negative in front of the fraction.

$\frac{5}{7} \cdot \frac{1}{- \frac{5}{2}}$

Step 3

Cancel the common factor of $1$ and $- 1$ .

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Step 3.1

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{5}{7} \cdot \frac{- 1 (- 1)}{- \frac{5}{2}}$

Step 3.2

Move the negative in front of the fraction.

$\frac{5}{7} (- \frac{1}{\frac{5}{2}})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{7} (- (1 (\frac{2}{5})))$

Step 5

Multiply $\frac{2}{5}$ by $1$ .

$\frac{5}{7} (- \frac{2}{5})$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{5}{7} \cdot \frac{- 2}{5}$

Step 6.2

Cancel the common factor.

$\frac{5}{7} \cdot \frac{- 2}{5}$

Step 6.3

Rewrite the expression.

$\frac{1}{7} \cdot - 2$

Step 7

Combine $\frac{1}{7}$ and $- 2$ .

$\frac{- 2}{7}$

Step 8

Move the negative in front of the fraction.

$- \frac{2}{7}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{7}$

Decimal Form:

$- 0.\overline{285714}$