Basic Math Examples

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

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

Step 1

Convert

3 \frac{3}{4}

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

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

Step 1.2

Add

3

$3$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 1.2.1

To write

3

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

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.2

Combine

3

$3$ and

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

3

$3$ by

4

$4$ .

\frac{12 + 3}{4} \cdot 2 \frac{1}{5}

$\frac{12 + 3}{4} \cdot 2 \frac{1}{5}$

Step 1.2.4.2

Add

12

$12$ and

3

$3$ .

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

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

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

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

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

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

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

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

Step 2

Convert

2 \frac{1}{5}

$2 \frac{1}{5}$ to an improper fraction.

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Step 2.1

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

\frac{15}{4} \cdot (2 + \frac{1}{5})

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

Step 2.2

Add

2

$2$ and

\frac{1}{5}

$\frac{1}{5}$ .

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Step 2.2.1

To write

2

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

\frac{5}{5}

$\frac{5}{5}$ .

\frac{15}{4} \cdot (2 \cdot \frac{5}{5} + \frac{1}{5})

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

Step 2.2.2

Combine

2

$2$ and

\frac{5}{5}

$\frac{5}{5}$ .

\frac{15}{4} \cdot (\frac{2 \cdot 5}{5} + \frac{1}{5})

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

Step 2.2.3

Combine the numerators over the common denominator.

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

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

5

$5$ .

\frac{15}{4} \cdot \frac{10 + 1}{5}

$\frac{15}{4} \cdot \frac{10 + 1}{5}$

Step 2.2.4.2

Add

10

$10$ and

1

$1$ .

\frac{15}{4} \cdot \frac{11}{5}

$\frac{15}{4} \cdot \frac{11}{5}$

\frac{15}{4} \cdot \frac{11}{5}

$\frac{15}{4} \cdot \frac{11}{5}$

\frac{15}{4} \cdot \frac{11}{5}

$\frac{15}{4} \cdot \frac{11}{5}$

\frac{15}{4} \cdot \frac{11}{5}

$\frac{15}{4} \cdot \frac{11}{5}$

Step 3

Cancel the common factor of

5

$5$ .

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Step 3.1

Factor

5

$5$ out of

15

$15$ .

\frac{5 (3)}{4} \cdot \frac{11}{5}

$\frac{5 (3)}{4} \cdot \frac{11}{5}$

Step 3.2

Cancel the common factor.

$\frac{5 \cdot 3}{4} \cdot \frac{11}{5}$

Step 3.3

Rewrite the expression.

$\frac{3}{4} \cdot 11$

Step 4

Combine

$\frac{3}{4}$ and

$11$ .

$\frac{3 \cdot 11}{4}$

Step 5

Multiply

$3$ by

$11$ .

$\frac{33}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{33}{4}$

Decimal Form:

$8.25$

Mixed Number Form:

$8 \frac{1}{4}$