Basic Math Examples

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

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

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

Step 2

Simplify the denominator.

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Step 2.1

To write

\frac{2}{25}

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

\frac{16}{16}

$\frac{16}{16}$ .

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

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

\frac{25}{25}

$\frac{25}{25}$ .

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

$400$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 2.3.1

Multiply

\frac{2}{25}

$\frac{2}{25}$ by

\frac{16}{16}

$\frac{16}{16}$ .

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

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

Step 2.3.2

Multiply

25

$25$ by

16

$16$ .

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

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

Step 2.3.3

Multiply

\frac{5}{16}

$\frac{5}{16}$ by

\frac{25}{25}

$\frac{25}{25}$ .

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

$16$ by

25

$25$ .

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

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

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

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

Step 2.4

Combine the numerators over the common denominator.

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

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply

2

$2$ by

16

$16$ .

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

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

Step 2.5.2

Multiply

- 5

$- 5$ by

25

$25$ .

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

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

Step 2.5.3

Subtract

125

$125$ from

32

$32$ .

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

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

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

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

Step 2.6

Move the negative in front of the fraction.

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

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

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

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

Step 3

Cancel the common factor of

1

$1$ and

- 1

$- 1$ .

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Step 3.1

Rewrite

1

$1$ as

- 1 (- 1)

$- 1 (- 1)$ .

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

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

Step 3.2

Move the negative in front of the fraction.

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

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

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

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

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

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

Step 5

Multiply

\frac{400}{93}

$\frac{400}{93}$ by

1

$1$ .

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

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

Step 6

Cancel the common factor of

5

$5$ .

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Step 6.1

Move the leading negative in

- \frac{400}{93}

$- \frac{400}{93}$ into the numerator.

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

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

Step 6.2

Factor

5

$5$ out of

- 400

$- 400$ .

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

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

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:

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