Basic Math Examples

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

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

Step 1

Convert

3 \frac{1}{2}

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

Tap for more steps...

Step 1.1

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

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

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

Step 1.2

Add

3

$3$ and

\frac{1}{2}

$\frac{1}{2}$ .

Tap for more steps...

Step 1.2.1

To write

3

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

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.2

Combine

3

$3$ and

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply

3

$3$ by

2

$2$ .

\frac{6 + 1}{2} \cdot 3 \frac{1}{2}

$\frac{6 + 1}{2} \cdot 3 \frac{1}{2}$

Step 1.2.4.2

Add

6

$6$ and

1

$1$ .

\frac{7}{2} \cdot 3 \frac{1}{2}

$\frac{7}{2} \cdot 3 \frac{1}{2}$

\frac{7}{2} \cdot 3 \frac{1}{2}

$\frac{7}{2} \cdot 3 \frac{1}{2}$

\frac{7}{2} \cdot 3 \frac{1}{2}

$\frac{7}{2} \cdot 3 \frac{1}{2}$

\frac{7}{2} \cdot 3 \frac{1}{2}

$\frac{7}{2} \cdot 3 \frac{1}{2}$

Step 2

Convert

3 \frac{1}{2}

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

Tap for more steps...

Step 2.1

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

\frac{7}{2} \cdot (3 + \frac{1}{2})

$\frac{7}{2} \cdot (3 + \frac{1}{2})$

Step 2.2

Add

3

$3$ and

\frac{1}{2}

$\frac{1}{2}$ .

Tap for more steps...

Step 2.2.1

To write

3

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{7}{2} \cdot (3 \cdot \frac{2}{2} + \frac{1}{2})

$\frac{7}{2} \cdot (3 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine

3

$3$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{7}{2} \cdot (\frac{3 \cdot 2}{2} + \frac{1}{2})

$\frac{7}{2} \cdot (\frac{3 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{7}{2} \cdot \frac{3 \cdot 2 + 1}{2}

$\frac{7}{2} \cdot \frac{3 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply

3

$3$ by

2

$2$ .

\frac{7}{2} \cdot \frac{6 + 1}{2}

$\frac{7}{2} \cdot \frac{6 + 1}{2}$

Step 2.2.4.2

Add

6

$6$ and

1

$1$ .

\frac{7}{2} \cdot \frac{7}{2}

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

\frac{7}{2} \cdot \frac{7}{2}

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

\frac{7}{2} \cdot \frac{7}{2}

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

\frac{7}{2} \cdot \frac{7}{2}

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

Step 3

Multiply

\frac{7}{2} \cdot \frac{7}{2}

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

Tap for more steps...

Step 3.1

Multiply

$\frac{7}{2}$ by

$\frac{7}{2}$ .

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

Step 3.2

Multiply

$7$ by

$7$ .

$\frac{49}{2 \cdot 2}$

Step 3.3

Multiply

$2$ by

$2$ .

$\frac{49}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{49}{4}$

Decimal Form:

$12.25$

Mixed Number Form:

$12 \frac{1}{4}$