Basic Math Examples

$2 \frac{2}{5} \cdot 5 \frac{11}{12}$

Step 1

Convert

$2 \frac{2}{5}$ to an improper fraction.

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Step 1.1

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

$(2 + \frac{2}{5}) \cdot 5 \frac{11}{12}$

Step 1.2

Add

$2$ and

$\frac{2}{5}$ .

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Step 1.2.1

To write

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

$\frac{5}{5}$ .

$(2 \cdot \frac{5}{5} + \frac{2}{5}) \cdot 5 \frac{11}{12}$

Step 1.2.2

Combine

$2$ and

$\frac{5}{5}$ .

$(\frac{2 \cdot 5}{5} + \frac{2}{5}) \cdot 5 \frac{11}{12}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 + 2}{5} \cdot 5 \frac{11}{12}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$5$ .

$\frac{10 + 2}{5} \cdot 5 \frac{11}{12}$

Step 1.2.4.2

Add

$10$ and

$2$ .

$\frac{12}{5} \cdot 5 \frac{11}{12}$

Step 2

Convert

$5 \frac{11}{12}$ to an improper fraction.

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Step 2.1

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

$\frac{12}{5} \cdot (5 + \frac{11}{12})$

Step 2.2

Add

$5$ and

$\frac{11}{12}$ .

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Step 2.2.1

To write

$5$ as a fraction with a common denominator, multiply by

$\frac{12}{12}$ .

$\frac{12}{5} \cdot (5 \cdot \frac{12}{12} + \frac{11}{12})$

Step 2.2.2

Combine

$5$ and

$\frac{12}{12}$ .

$\frac{12}{5} \cdot (\frac{5 \cdot 12}{12} + \frac{11}{12})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{12}{5} \cdot \frac{5 \cdot 12 + 11}{12}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$5$ by

$12$ .

$\frac{12}{5} \cdot \frac{60 + 11}{12}$

Step 2.2.4.2

Add

$60$ and

$11$ .

$\frac{12}{5} \cdot \frac{71}{12}$

Step 3

Cancel the common factor of

$12$ .

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Step 3.1

Cancel the common factor.

$\frac{12}{5} \cdot \frac{71}{12}$

Step 3.2

Rewrite the expression.

$\frac{1}{5} \cdot 71$

Step 4

Combine

$\frac{1}{5}$ and

$71$ .

$\frac{71}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{71}{5}$

Decimal Form:

$14.2$

Mixed Number Form:

$14 \frac{1}{5}$