Basic Math Examples

\frac{13}{5} \div 4 \frac{3}{5}

$\frac{13}{5} \div 4 \frac{3}{5}$

Step 1

Convert

4 \frac{3}{5}

$4 \frac{3}{5}$ to an improper fraction.

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Step 1.1

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

\frac{13}{5} \div (4 + \frac{3}{5})

$\frac{13}{5} \div (4 + \frac{3}{5})$

Step 1.2

Add

4

$4$ and

\frac{3}{5}

$\frac{3}{5}$ .

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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{13}{5} \div (4 \cdot \frac{5}{5} + \frac{3}{5})

$\frac{13}{5} \div (4 \cdot \frac{5}{5} + \frac{3}{5})$

Step 1.2.2

Combine

4

$4$ and

\frac{5}{5}

$\frac{5}{5}$ .

\frac{13}{5} \div (\frac{4 \cdot 5}{5} + \frac{3}{5})

$\frac{13}{5} \div (\frac{4 \cdot 5}{5} + \frac{3}{5})$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{13}{5} \div \frac{4 \cdot 5 + 3}{5}

$\frac{13}{5} \div \frac{4 \cdot 5 + 3}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

4

$4$ by

5

$5$ .

\frac{13}{5} \div \frac{20 + 3}{5}

$\frac{13}{5} \div \frac{20 + 3}{5}$

Step 1.2.4.2

Add

20

$20$ and

3

$3$ .

\frac{13}{5} \div \frac{23}{5}

$\frac{13}{5} \div \frac{23}{5}$

\frac{13}{5} \div \frac{23}{5}

$\frac{13}{5} \div \frac{23}{5}$

\frac{13}{5} \div \frac{23}{5}

$\frac{13}{5} \div \frac{23}{5}$

\frac{13}{5} \div \frac{23}{5}

$\frac{13}{5} \div \frac{23}{5}$

Step 2

To divide by a fraction, multiply by its reciprocal.

\frac{13}{5} \cdot \frac{5}{23}

$\frac{13}{5} \cdot \frac{5}{23}$

Step 3

Cancel the common factor of

5

$5$ .

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Step 3.1

Cancel the common factor.

$\frac{13}{5} \cdot \frac{5}{23}$

Step 3.2

Rewrite the expression.

$13 (\frac{1}{23})$

Step 4

Combine

$13$ and

$\frac{1}{23}$ .

$\frac{13}{23}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{23}$

Decimal Form:

$0.56521739 \dots$