Basic Math Examples

1 \frac{1}{3} \cdot \frac{2}{3}

$1 \frac{1}{3} \cdot \frac{2}{3}$

Step 1

Convert

1 \frac{1}{3}

$1 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

(1 + \frac{1}{3}) \cdot \frac{2}{3}

$(1 + \frac{1}{3}) \cdot \frac{2}{3}$

Step 1.2

Add

1

$1$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

(\frac{3}{3} + \frac{1}{3}) \cdot \frac{2}{3}

$(\frac{3}{3} + \frac{1}{3}) \cdot \frac{2}{3}$

Step 1.2.2

Combine the numerators over the common denominator.

\frac{3 + 1}{3} \cdot \frac{2}{3}

$\frac{3 + 1}{3} \cdot \frac{2}{3}$

Step 1.2.3

Add

3

$3$ and

1

$1$ .

\frac{4}{3} \cdot \frac{2}{3}

$\frac{4}{3} \cdot \frac{2}{3}$

\frac{4}{3} \cdot \frac{2}{3}

$\frac{4}{3} \cdot \frac{2}{3}$

\frac{4}{3} \cdot \frac{2}{3}

$\frac{4}{3} \cdot \frac{2}{3}$

Step 2

Multiply

\frac{4}{3} \cdot \frac{2}{3}

$\frac{4}{3} \cdot \frac{2}{3}$ .

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Step 2.1

Multiply

\frac{4}{3}

$\frac{4}{3}$ by

\frac{2}{3}

$\frac{2}{3}$ .

\frac{4 \cdot 2}{3 \cdot 3}

$\frac{4 \cdot 2}{3 \cdot 3}$

Step 2.2

Multiply

4

$4$ by

2

$2$ .

\frac{8}{3 \cdot 3}

$\frac{8}{3 \cdot 3}$

Step 2.3

Multiply

3

$3$ by

3

$3$ .

\frac{8}{9}

$\frac{8}{9}$

\frac{8}{9}

$\frac{8}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\frac{8}{9}

$\frac{8}{9}$

Decimal Form:

0. ¯ 8

$0.\overline{8}$