Basic Math Examples

2 \frac{1}{2} \cdot 12

$2 \frac{1}{2} \cdot 12$

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}) \cdot 12

$(2 + \frac{1}{2}) \cdot 12$

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}) \cdot 12

$(2 \cdot \frac{2}{2} + \frac{1}{2}) \cdot 12$

Step 1.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

(\frac{2 \cdot 2}{2} + \frac{1}{2}) \cdot 12

$(\frac{2 \cdot 2}{2} + \frac{1}{2}) \cdot 12$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 2 + 1}{2} \cdot 12

$\frac{2 \cdot 2 + 1}{2} \cdot 12$

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} \cdot 12

$\frac{4 + 1}{2} \cdot 12$

Step 1.2.4.2

Add

4

$4$ and

1

$1$ .

\frac{5}{2} \cdot 12

$\frac{5}{2} \cdot 12$

\frac{5}{2} \cdot 12

$\frac{5}{2} \cdot 12$

\frac{5}{2} \cdot 12

$\frac{5}{2} \cdot 12$

\frac{5}{2} \cdot 12

$\frac{5}{2} \cdot 12$

Step 2

Cancel the common factor of

2

$2$ .

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Step 2.1

Factor

2

$2$ out of

12

$12$ .

\frac{5}{2} \cdot (2 (6))

$\frac{5}{2} \cdot (2 (6))$

Step 2.2

Cancel the common factor.

$\frac{5}{2} \cdot (2 \cdot 6)$

Step 2.3

Rewrite the expression.

$5 \cdot 6$

Step 3

Multiply

$5$ by

$6$ .

$30$