Basic Math Examples

\frac{8}{5} \div 4 \frac{3}{2}

$\frac{8}{5} \div 4 \frac{3}{2}$

Step 1

Convert

4 \frac{3}{2}

$4 \frac{3}{2}$ to an improper fraction.

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Step 1.1

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

\frac{8}{5} \div (4 + \frac{3}{2})

$\frac{8}{5} \div (4 + \frac{3}{2})$

Step 1.2

Add

4

$4$ and

\frac{3}{2}

$\frac{3}{2}$ .

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Step 1.2.1

To write

4

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{8}{5} \div (4 \cdot \frac{2}{2} + \frac{3}{2})

$\frac{8}{5} \div (4 \cdot \frac{2}{2} + \frac{3}{2})$

Step 1.2.2

Combine

4

$4$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{8}{5} \div (\frac{4 \cdot 2}{2} + \frac{3}{2})

$\frac{8}{5} \div (\frac{4 \cdot 2}{2} + \frac{3}{2})$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{8}{5} \div \frac{4 \cdot 2 + 3}{2}

$\frac{8}{5} \div \frac{4 \cdot 2 + 3}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

4

$4$ by

2

$2$ .

\frac{8}{5} \div \frac{8 + 3}{2}

$\frac{8}{5} \div \frac{8 + 3}{2}$

Step 1.2.4.2

Add

8

$8$ and

3

$3$ .

\frac{8}{5} \div \frac{11}{2}

$\frac{8}{5} \div \frac{11}{2}$

\frac{8}{5} \div \frac{11}{2}

$\frac{8}{5} \div \frac{11}{2}$

\frac{8}{5} \div \frac{11}{2}

$\frac{8}{5} \div \frac{11}{2}$

\frac{8}{5} \div \frac{11}{2}

$\frac{8}{5} \div \frac{11}{2}$

Step 2

To divide by a fraction, multiply by its reciprocal.

\frac{8}{5} \cdot \frac{2}{11}

$\frac{8}{5} \cdot \frac{2}{11}$

Step 3

Multiply

\frac{8}{5} \cdot \frac{2}{11}

$\frac{8}{5} \cdot \frac{2}{11}$ .

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Step 3.1

Multiply

\frac{8}{5}

$\frac{8}{5}$ by

\frac{2}{11}

$\frac{2}{11}$ .

\frac{8 \cdot 2}{5 \cdot 11}

$\frac{8 \cdot 2}{5 \cdot 11}$

Step 3.2

Multiply

8

$8$ by

2

$2$ .

\frac{16}{5 \cdot 11}

$\frac{16}{5 \cdot 11}$

Step 3.3

Multiply

5

$5$ by

11

$11$ .

\frac{16}{55}

$\frac{16}{55}$

\frac{16}{55}

$\frac{16}{55}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{16}{55}

$\frac{16}{55}$

Decimal Form:

0.2 ¯ ¯¯ ¯ 90

$0.2\overline{90}$