Basic Math Examples

10 \frac{1}{2} \cdot 10 \frac{1}{2}

$10 \frac{1}{2} \cdot 10 \frac{1}{2}$

Step 1

Convert

10 \frac{1}{2}

$10 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

(10 + \frac{1}{2}) \cdot 10 \frac{1}{2}

$(10 + \frac{1}{2}) \cdot 10 \frac{1}{2}$

Step 1.2

Add

10

$10$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

10

$10$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

(10 \cdot \frac{2}{2} + \frac{1}{2}) \cdot 10 \frac{1}{2}

$(10 \cdot \frac{2}{2} + \frac{1}{2}) \cdot 10 \frac{1}{2}$

Step 1.2.2

Combine

10

$10$ and

\frac{2}{2}

$\frac{2}{2}$ .

(\frac{10 \cdot 2}{2} + \frac{1}{2}) \cdot 10 \frac{1}{2}

$(\frac{10 \cdot 2}{2} + \frac{1}{2}) \cdot 10 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{10 \cdot 2 + 1}{2} \cdot 10 \frac{1}{2}

$\frac{10 \cdot 2 + 1}{2} \cdot 10 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

10

$10$ by

2

$2$ .

\frac{20 + 1}{2} \cdot 10 \frac{1}{2}

$\frac{20 + 1}{2} \cdot 10 \frac{1}{2}$

Step 1.2.4.2

Add

20

$20$ and

1

$1$ .

\frac{21}{2} \cdot 10 \frac{1}{2}

$\frac{21}{2} \cdot 10 \frac{1}{2}$

\frac{21}{2} \cdot 10 \frac{1}{2}

$\frac{21}{2} \cdot 10 \frac{1}{2}$

\frac{21}{2} \cdot 10 \frac{1}{2}

$\frac{21}{2} \cdot 10 \frac{1}{2}$

\frac{21}{2} \cdot 10 \frac{1}{2}

$\frac{21}{2} \cdot 10 \frac{1}{2}$

Step 2

Convert

10 \frac{1}{2}

$10 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

\frac{21}{2} \cdot (10 + \frac{1}{2})

$\frac{21}{2} \cdot (10 + \frac{1}{2})$

Step 2.2

Add

10

$10$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.2.1

To write

10

$10$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{21}{2} \cdot (10 \cdot \frac{2}{2} + \frac{1}{2})

$\frac{21}{2} \cdot (10 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine

10

$10$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{21}{2} \cdot (\frac{10 \cdot 2}{2} + \frac{1}{2})

$\frac{21}{2} \cdot (\frac{10 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{21}{2} \cdot \frac{10 \cdot 2 + 1}{2}

$\frac{21}{2} \cdot \frac{10 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

10

$10$ by

2

$2$ .

\frac{21}{2} \cdot \frac{20 + 1}{2}

$\frac{21}{2} \cdot \frac{20 + 1}{2}$

Step 2.2.4.2

Add

20

$20$ and

1

$1$ .

\frac{21}{2} \cdot \frac{21}{2}

$\frac{21}{2} \cdot \frac{21}{2}$

\frac{21}{2} \cdot \frac{21}{2}

$\frac{21}{2} \cdot \frac{21}{2}$

\frac{21}{2} \cdot \frac{21}{2}

$\frac{21}{2} \cdot \frac{21}{2}$

\frac{21}{2} \cdot \frac{21}{2}

$\frac{21}{2} \cdot \frac{21}{2}$

Step 3

Multiply

\frac{21}{2} \cdot \frac{21}{2}

$\frac{21}{2} \cdot \frac{21}{2}$ .

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Step 3.1

Multiply

\frac{21}{2}

$\frac{21}{2}$ by

\frac{21}{2}

$\frac{21}{2}$ .

\frac{21 \cdot 21}{2 \cdot 2}

$\frac{21 \cdot 21}{2 \cdot 2}$

Step 3.2

Multiply

21

$21$ by

21

$21$ .

\frac{441}{2 \cdot 2}

$\frac{441}{2 \cdot 2}$

Step 3.3

Multiply

2

$2$ by

2

$2$ .

\frac{441}{4}

$\frac{441}{4}$

\frac{441}{4}

$\frac{441}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{441}{4}

$\frac{441}{4}$

Decimal Form:

110.25

$110.25$

Mixed Number Form:

110 \frac{1}{4}

$110 \frac{1}{4}$