Basic Math Examples

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

$66 \cdot 5 \frac{1}{2}$

Step 1

Convert

5 \frac{1}{2}

$5 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

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

$66 \cdot (5 + \frac{1}{2})$

Step 1.2

Add

5

$5$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

5

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

\frac{2}{2}

$\frac{2}{2}$ .

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

$66 \cdot (5 \cdot \frac{2}{2} + \frac{1}{2})$

Step 1.2.2

Combine

5

$5$ and

\frac{2}{2}

$\frac{2}{2}$ .

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

$66 \cdot (\frac{5 \cdot 2}{2} + \frac{1}{2})$

Step 1.2.3

Combine the numerators over the common denominator.

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

$66 \cdot \frac{5 \cdot 2 + 1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

2

$2$ .

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

$66 \cdot \frac{10 + 1}{2}$

Step 1.2.4.2

Add

10

$10$ and

1

$1$ .

66 \cdot \frac{11}{2}

$66 \cdot \frac{11}{2}$

66 \cdot \frac{11}{2}

$66 \cdot \frac{11}{2}$

66 \cdot \frac{11}{2}

$66 \cdot \frac{11}{2}$

66 \cdot \frac{11}{2}

$66 \cdot \frac{11}{2}$

Step 2

Cancel the common factor of

2

$2$ .

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Step 2.1

Factor

2

$2$ out of

66

$66$ .

2 (33) \cdot \frac{11}{2}

$2 (33) \cdot \frac{11}{2}$

Step 2.2

Cancel the common factor.

2 \cdot 33 \cdot \frac{11}{2}

$2 \cdot 33 \cdot \frac{11}{2}$

Step 2.3

Rewrite the expression.

33 \cdot 11

$33 \cdot 11$

33 \cdot 11

$33 \cdot 11$

Step 3

Multiply

33

$33$ by

11

$11$ .

363

$363$