Basic Math Examples

$\frac{\frac{4}{5}}{\frac{2}{25} - \frac{5}{16}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{5} \cdot \frac{1}{\frac{2}{25} - \frac{5}{16}}$

Step 2

Simplify the denominator.

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Step 2.1

To write $\frac{2}{25}$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\frac{4}{5} \cdot \frac{1}{\frac{2}{25} \cdot \frac{16}{16} - \frac{5}{16}}$

Step 2.2

To write $- \frac{5}{16}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{4}{5} \cdot \frac{1}{\frac{2}{25} \cdot \frac{16}{16} - \frac{5}{16} \cdot \frac{25}{25}}$

Step 2.3

Write each expression with a common denominator of $400$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{2}{25}$ by $\frac{16}{16}$ .

$\frac{4}{5} \cdot \frac{1}{\frac{2 \cdot 16}{25 \cdot 16} - \frac{5}{16} \cdot \frac{25}{25}}$

Step 2.3.2

Multiply $25$ by $16$ .

$\frac{4}{5} \cdot \frac{1}{\frac{2 \cdot 16}{400} - \frac{5}{16} \cdot \frac{25}{25}}$

Step 2.3.3

Multiply $\frac{5}{16}$ by $\frac{25}{25}$ .

$\frac{4}{5} \cdot \frac{1}{\frac{2 \cdot 16}{400} - \frac{5 \cdot 25}{16 \cdot 25}}$

Step 2.3.4

Multiply $16$ by $25$ .

$\frac{4}{5} \cdot \frac{1}{\frac{2 \cdot 16}{400} - \frac{5 \cdot 25}{400}}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{4}{5} \cdot \frac{1}{\frac{2 \cdot 16 - 5 \cdot 25}{400}}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $16$ .

$\frac{4}{5} \cdot \frac{1}{\frac{32 - 5 \cdot 25}{400}}$

Step 2.5.2

Multiply $- 5$ by $25$ .

$\frac{4}{5} \cdot \frac{1}{\frac{32 - 125}{400}}$

Step 2.5.3

Subtract $125$ from $32$ .

$\frac{4}{5} \cdot \frac{1}{\frac{- 93}{400}}$

Step 2.6

Move the negative in front of the fraction.

$\frac{4}{5} \cdot \frac{1}{- \frac{93}{400}}$

Step 3

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

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Step 3.1

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

$\frac{4}{5} \cdot \frac{- 1 (- 1)}{- \frac{93}{400}}$

Step 3.2

Move the negative in front of the fraction.

$\frac{4}{5} (- \frac{1}{\frac{93}{400}})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{5} (- (1 (\frac{400}{93})))$

Step 5

Multiply $\frac{400}{93}$ by $1$ .

$\frac{4}{5} (- \frac{400}{93})$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Move the leading negative in $- \frac{400}{93}$ into the numerator.

$\frac{4}{5} \cdot \frac{- 400}{93}$

Step 6.2

Factor $5$ out of $- 400$ .

$\frac{4}{5} \cdot \frac{5 (- 80)}{93}$

Step 6.3

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 \cdot - 80}{93}$

Step 6.4

Rewrite the expression.

$4 (\frac{- 80}{93})$

Step 7

Combine $4$ and $\frac{- 80}{93}$ .

$\frac{4 \cdot - 80}{93}$

Step 8

Simplify the expression.

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Step 8.1

Multiply $4$ by $- 80$ .

$\frac{- 320}{93}$

Step 8.2

Move the negative in front of the fraction.

$- \frac{320}{93}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{320}{93}$

Decimal Form:

$- 3.44086021 \dots$

Mixed Number Form:

$- 3 \frac{41}{93}$