Basic Math Examples

3 \frac{1}{2} \cdot \frac{3}{4}

$3 \frac{1}{2} \cdot \frac{3}{4}$

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.

(3 + \frac{1}{2}) \cdot \frac{3}{4}

$(3 + \frac{1}{2}) \cdot \frac{3}{4}$

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}

$\frac{2}{2}$ .

(3 \cdot \frac{2}{2} + \frac{1}{2}) \cdot \frac{3}{4}

$(3 \cdot \frac{2}{2} + \frac{1}{2}) \cdot \frac{3}{4}$

Step 1.2.2

Combine

3

$3$ and

\frac{2}{2}

$\frac{2}{2}$ .

(\frac{3 \cdot 2}{2} + \frac{1}{2}) \cdot \frac{3}{4}

$(\frac{3 \cdot 2}{2} + \frac{1}{2}) \cdot \frac{3}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{3 \cdot 2 + 1}{2} \cdot \frac{3}{4}

$\frac{3 \cdot 2 + 1}{2} \cdot \frac{3}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

3

$3$ by

2

$2$ .

\frac{6 + 1}{2} \cdot \frac{3}{4}

$\frac{6 + 1}{2} \cdot \frac{3}{4}$

Step 1.2.4.2

Add

6

$6$ and

1

$1$ .

\frac{7}{2} \cdot \frac{3}{4}

$\frac{7}{2} \cdot \frac{3}{4}$

\frac{7}{2} \cdot \frac{3}{4}

$\frac{7}{2} \cdot \frac{3}{4}$

\frac{7}{2} \cdot \frac{3}{4}

$\frac{7}{2} \cdot \frac{3}{4}$

\frac{7}{2} \cdot \frac{3}{4}

$\frac{7}{2} \cdot \frac{3}{4}$

Step 2

Multiply

\frac{7}{2} \cdot \frac{3}{4}

$\frac{7}{2} \cdot \frac{3}{4}$ .

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Step 2.1

Multiply

\frac{7}{2}

$\frac{7}{2}$ by

\frac{3}{4}

$\frac{3}{4}$ .

\frac{7 \cdot 3}{2 \cdot 4}

$\frac{7 \cdot 3}{2 \cdot 4}$

Step 2.2

Multiply

7

$7$ by

3

$3$ .

\frac{21}{2 \cdot 4}

$\frac{21}{2 \cdot 4}$

Step 2.3

Multiply

2

$2$ by

4

$4$ .

\frac{21}{8}

$\frac{21}{8}$

\frac{21}{8}

$\frac{21}{8}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\frac{21}{8}

$\frac{21}{8}$

Decimal Form:

2.625

$2.625$

Mixed Number Form:

2 \frac{5}{8}

$2 \frac{5}{8}$