Basic Math Examples

\frac{\frac{5}{9}}{4 \frac{1}{5}}

$\frac{\frac{5}{9}}{4 \frac{1}{5}}$

Step 1

Convert

4 \frac{1}{5}

$4 \frac{1}{5}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

\frac{\frac{5}{9}}{4 + \frac{1}{5}}

$\frac{\frac{5}{9}}{4 + \frac{1}{5}}$

Step 1.2

Add

4

$4$ and

\frac{1}{5}

$\frac{1}{5}$ .

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Step 1.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{\frac{5}{9}}{4 \cdot \frac{5}{5} + \frac{1}{5}}

$\frac{\frac{5}{9}}{4 \cdot \frac{5}{5} + \frac{1}{5}}$

Step 1.2.2

Combine

4

$4$ and

\frac{5}{5}

$\frac{5}{5}$ .

\frac{\frac{5}{9}}{\frac{4 \cdot 5}{5} + \frac{1}{5}}

$\frac{\frac{5}{9}}{\frac{4 \cdot 5}{5} + \frac{1}{5}}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{\frac{5}{9}}{\frac{4 \cdot 5 + 1}{5}}

$\frac{\frac{5}{9}}{\frac{4 \cdot 5 + 1}{5}}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

4

$4$ by

5

$5$ .

\frac{\frac{5}{9}}{\frac{20 + 1}{5}}

$\frac{\frac{5}{9}}{\frac{20 + 1}{5}}$

Step 1.2.4.2

Add

20

$20$ and

1

$1$ .

\frac{\frac{5}{9}}{\frac{21}{5}}

$\frac{\frac{5}{9}}{\frac{21}{5}}$

\frac{\frac{5}{9}}{\frac{21}{5}}

$\frac{\frac{5}{9}}{\frac{21}{5}}$

\frac{\frac{5}{9}}{\frac{21}{5}}

$\frac{\frac{5}{9}}{\frac{21}{5}}$

\frac{\frac{5}{9}}{\frac{21}{5}}

$\frac{\frac{5}{9}}{\frac{21}{5}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

\frac{5}{9} \cdot \frac{5}{21}

$\frac{5}{9} \cdot \frac{5}{21}$

Step 3

Multiply

\frac{5}{9} \cdot \frac{5}{21}

$\frac{5}{9} \cdot \frac{5}{21}$ .

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Step 3.1

Multiply

\frac{5}{9}

$\frac{5}{9}$ by

\frac{5}{21}

$\frac{5}{21}$ .

\frac{5 \cdot 5}{9 \cdot 21}

$\frac{5 \cdot 5}{9 \cdot 21}$

Step 3.2

Multiply

5

$5$ by

5

$5$ .

\frac{25}{9 \cdot 21}

$\frac{25}{9 \cdot 21}$

Step 3.3

Multiply

9

$9$ by

21

$21$ .

\frac{25}{189}

$\frac{25}{189}$

\frac{25}{189}

$\frac{25}{189}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{25}{189}

$\frac{25}{189}$

Decimal Form:

0. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 132275

$0.\overline{132275}$