Basic Math Examples

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

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

Step 1

Convert

2 \frac{1}{2}

$2 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

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

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

Step 1.2

Add

2

$2$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

2

$2$ .

\frac{4 + 1}{2} (3 \frac{1}{3})

$\frac{4 + 1}{2} (3 \frac{1}{3})$

Step 1.2.4.2

Add

4

$4$ and

1

$1$ .

\frac{5}{2} (3 \frac{1}{3})

$\frac{5}{2} (3 \frac{1}{3})$

\frac{5}{2} (3 \frac{1}{3})

$\frac{5}{2} (3 \frac{1}{3})$

\frac{5}{2} (3 \frac{1}{3})

$\frac{5}{2} (3 \frac{1}{3})$

\frac{5}{2} (3 \frac{1}{3})

$\frac{5}{2} (3 \frac{1}{3})$

Step 2

Convert

3 \frac{1}{3}

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

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Step 2.1

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

\frac{5}{2} (3 + \frac{1}{3})

$\frac{5}{2} (3 + \frac{1}{3})$

Step 2.2

Add

3

$3$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 2.2.1

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{5}{2} (3 \cdot \frac{3}{3} + \frac{1}{3})

$\frac{5}{2} (3 \cdot \frac{3}{3} + \frac{1}{3})$

Step 2.2.2

Combine

3

$3$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{5}{2} (\frac{3 \cdot 3}{3} + \frac{1}{3})

$\frac{5}{2} (\frac{3 \cdot 3}{3} + \frac{1}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{5}{2} \cdot \frac{3 \cdot 3 + 1}{3}

$\frac{5}{2} \cdot \frac{3 \cdot 3 + 1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

3

$3$ .

\frac{5}{2} \cdot \frac{9 + 1}{3}

$\frac{5}{2} \cdot \frac{9 + 1}{3}$

Step 2.2.4.2

Add

9

$9$ and

1

$1$ .

\frac{5}{2} \cdot \frac{10}{3}

$\frac{5}{2} \cdot \frac{10}{3}$

\frac{5}{2} \cdot \frac{10}{3}

$\frac{5}{2} \cdot \frac{10}{3}$

\frac{5}{2} \cdot \frac{10}{3}

$\frac{5}{2} \cdot \frac{10}{3}$

\frac{5}{2} \cdot \frac{10}{3}

$\frac{5}{2} \cdot \frac{10}{3}$

Step 3

Cancel the common factor of

2

$2$ .

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Step 3.1

Factor

2

$2$ out of

10

$10$ .

$\frac{5}{2} \cdot \frac{2 (5)}{3}$

Step 3.2

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 \cdot 5}{3}$

Step 3.3

Rewrite the expression.

$5 (\frac{5}{3})$

Step 4

Combine

$5$ and

$\frac{5}{3}$ .

$\frac{5 \cdot 5}{3}$

Step 5

Multiply

$5$ by

$5$ .

$\frac{25}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{3}$

Decimal Form:

$8.\overline{3}$

Mixed Number Form:

$8 \frac{1}{3}$