Basic Math Examples

3 \frac{2}{5} \cdot 3 \frac{1}{4}

$3 \frac{2}{5} \cdot 3 \frac{1}{4}$

Step 1

Convert

3 \frac{2}{5}

$3 \frac{2}{5}$ to an improper fraction.

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Step 1.1

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

(3 + \frac{2}{5}) \cdot 3 \frac{1}{4}

$(3 + \frac{2}{5}) \cdot 3 \frac{1}{4}$

Step 1.2

Add

3

$3$ and

\frac{2}{5}

$\frac{2}{5}$ .

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Step 1.2.1

To write

3

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

\frac{5}{5}

$\frac{5}{5}$ .

(3 \cdot \frac{5}{5} + \frac{2}{5}) \cdot 3 \frac{1}{4}

$(3 \cdot \frac{5}{5} + \frac{2}{5}) \cdot 3 \frac{1}{4}$

Step 1.2.2

Combine

3

$3$ and

\frac{5}{5}

$\frac{5}{5}$ .

(\frac{3 \cdot 5}{5} + \frac{2}{5}) \cdot 3 \frac{1}{4}

$(\frac{3 \cdot 5}{5} + \frac{2}{5}) \cdot 3 \frac{1}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{3 \cdot 5 + 2}{5} \cdot 3 \frac{1}{4}

$\frac{3 \cdot 5 + 2}{5} \cdot 3 \frac{1}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

3

$3$ by

5

$5$ .

\frac{15 + 2}{5} \cdot 3 \frac{1}{4}

$\frac{15 + 2}{5} \cdot 3 \frac{1}{4}$

Step 1.2.4.2

Add

15

$15$ and

2

$2$ .

\frac{17}{5} \cdot 3 \frac{1}{4}

$\frac{17}{5} \cdot 3 \frac{1}{4}$

Step 2

Convert

$3 \frac{1}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{17}{5} \cdot (3 + \frac{1}{4})$

Step 2.2

Add

$3$ and

$\frac{1}{4}$ .

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Step 2.2.1

To write

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

$\frac{4}{4}$ .

$\frac{17}{5} \cdot (3 \cdot \frac{4}{4} + \frac{1}{4})$

Step 2.2.2

Combine

$3$ and

$\frac{4}{4}$ .

$\frac{17}{5} \cdot (\frac{3 \cdot 4}{4} + \frac{1}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{17}{5} \cdot \frac{3 \cdot 4 + 1}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$3$ by

$4$ .

$\frac{17}{5} \cdot \frac{12 + 1}{4}$

Step 2.2.4.2

Add

$12$ and

$1$ .

$\frac{17}{5} \cdot \frac{13}{4}$

Step 3

Multiply

$\frac{17}{5} \cdot \frac{13}{4}$ .

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Step 3.1

Multiply

$\frac{17}{5}$ by

$\frac{13}{4}$ .

$\frac{17 \cdot 13}{5 \cdot 4}$

Step 3.2

Multiply

$17$ by

$13$ .

$\frac{221}{5 \cdot 4}$

Step 3.3

Multiply

$5$ by

$4$ .

$\frac{221}{20}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{221}{20}$

Decimal Form:

$11.05$

Mixed Number Form:

$11 \frac{1}{20}$