Basic Math Examples

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

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

Step 1

Convert

2 \frac{1}{3}

$2 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

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

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

Step 1.2

Add

2

$2$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 1.2.1

To write

2

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

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

3

$3$ .

\frac{6 + 1}{3} \cdot 5 \frac{1}{3}

$\frac{6 + 1}{3} \cdot 5 \frac{1}{3}$

Step 1.2.4.2

Add

6

$6$ and

1

$1$ .

\frac{7}{3} \cdot 5 \frac{1}{3}

$\frac{7}{3} \cdot 5 \frac{1}{3}$

\frac{7}{3} \cdot 5 \frac{1}{3}

$\frac{7}{3} \cdot 5 \frac{1}{3}$

\frac{7}{3} \cdot 5 \frac{1}{3}

$\frac{7}{3} \cdot 5 \frac{1}{3}$

\frac{7}{3} \cdot 5 \frac{1}{3}

$\frac{7}{3} \cdot 5 \frac{1}{3}$

Step 2

Convert

5 \frac{1}{3}

$5 \frac{1}{3}$ to an improper fraction.

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Step 2.1

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

\frac{7}{3} \cdot (5 + \frac{1}{3})

$\frac{7}{3} \cdot (5 + \frac{1}{3})$

Step 2.2

Add

5

$5$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 2.2.1

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{7}{3} \cdot (5 \cdot \frac{3}{3} + \frac{1}{3})

$\frac{7}{3} \cdot (5 \cdot \frac{3}{3} + \frac{1}{3})$

Step 2.2.2

Combine

5

$5$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{7}{3} \cdot (\frac{5 \cdot 3}{3} + \frac{1}{3})

$\frac{7}{3} \cdot (\frac{5 \cdot 3}{3} + \frac{1}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{7}{3} \cdot \frac{5 \cdot 3 + 1}{3}

$\frac{7}{3} \cdot \frac{5 \cdot 3 + 1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

5

$5$ by

3

$3$ .

\frac{7}{3} \cdot \frac{15 + 1}{3}

$\frac{7}{3} \cdot \frac{15 + 1}{3}$

Step 2.2.4.2

Add

15

$15$ and

1

$1$ .

\frac{7}{3} \cdot \frac{16}{3}

$\frac{7}{3} \cdot \frac{16}{3}$

\frac{7}{3} \cdot \frac{16}{3}

$\frac{7}{3} \cdot \frac{16}{3}$

\frac{7}{3} \cdot \frac{16}{3}

$\frac{7}{3} \cdot \frac{16}{3}$

\frac{7}{3} \cdot \frac{16}{3}

$\frac{7}{3} \cdot \frac{16}{3}$

Step 3

Multiply

\frac{7}{3} \cdot \frac{16}{3}

$\frac{7}{3} \cdot \frac{16}{3}$ .

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Step 3.1

Multiply

\frac{7}{3}

$\frac{7}{3}$ by

\frac{16}{3}

$\frac{16}{3}$ .

\frac{7 \cdot 16}{3 \cdot 3}

$\frac{7 \cdot 16}{3 \cdot 3}$

Step 3.2

Multiply

$7$ by

$16$ .

$\frac{112}{3 \cdot 3}$

Step 3.3

Multiply

$3$ by

$3$ .

$\frac{112}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{112}{9}$

Decimal Form:

$12.\overline{4}$

Mixed Number Form:

$12 \frac{4}{9}$