Basic Math Examples

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

Step 1

Convert

$2 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add

$2$ and

$\frac{1}{4}$ .

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Step 1.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

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

Step 1.2.2

Combine

$2$ and

$\frac{4}{4}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$4$ .

$\frac{8 + 1}{4} \cdot 2 \frac{1}{2}$

Step 1.2.4.2

Add

$8$ and

$1$ .

$\frac{9}{4} \cdot 2 \frac{1}{2}$

Step 2

Convert

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

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Step 2.1

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

$\frac{9}{4} \cdot (2 + \frac{1}{2})$

Step 2.2

Add

$2$ and

$\frac{1}{2}$ .

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Step 2.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{9}{4} \cdot (2 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine

$2$ and

$\frac{2}{2}$ .

$\frac{9}{4} \cdot (\frac{2 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{9}{4} \cdot \frac{2 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$2$ by

$2$ .

$\frac{9}{4} \cdot \frac{4 + 1}{2}$

Step 2.2.4.2

Add

$4$ and

$1$ .

$\frac{9}{4} \cdot \frac{5}{2}$

Step 3

Multiply

$\frac{9}{4} \cdot \frac{5}{2}$ .

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Step 3.1

Multiply

$\frac{9}{4}$ by

$\frac{5}{2}$ .

$\frac{9 \cdot 5}{4 \cdot 2}$

Step 3.2

Multiply

$9$ by

$5$ .

$\frac{45}{4 \cdot 2}$

Step 3.3

Multiply

$4$ by

$2$ .

$\frac{45}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{45}{8}$

Decimal Form:

$5.625$

Mixed Number Form:

$5 \frac{5}{8}$