Basic Math Examples

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

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

Step 1

Convert

3 \frac{1}{2}

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

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Step 1.1

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

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

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

Step 1.2

Add

3

$3$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

3

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

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.2

Combine

3

$3$ and

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

3

$3$ by

2

$2$ .

5 \cdot \frac{6 + 1}{2}

$5 \cdot \frac{6 + 1}{2}$

Step 1.2.4.2

Add

6

$6$ and

1

$1$ .

5 \cdot \frac{7}{2}

$5 \cdot \frac{7}{2}$

5 \cdot \frac{7}{2}

$5 \cdot \frac{7}{2}$

5 \cdot \frac{7}{2}

$5 \cdot \frac{7}{2}$

5 \cdot \frac{7}{2}

$5 \cdot \frac{7}{2}$

Step 2

Multiply

5 (\frac{7}{2})

$5 (\frac{7}{2})$ .

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Step 2.1

Combine

5

$5$ and

\frac{7}{2}

$\frac{7}{2}$ .

\frac{5 \cdot 7}{2}

$\frac{5 \cdot 7}{2}$

Step 2.2

Multiply

5

$5$ by

7

$7$ .

\frac{35}{2}

$\frac{35}{2}$

\frac{35}{2}

$\frac{35}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\frac{35}{2}

$\frac{35}{2}$

Decimal Form:

17.5

$17.5$

Mixed Number Form:

17 \frac{1}{2}

$17 \frac{1}{2}$