Basic Math Examples

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

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

Step 1

Convert

2 \frac{1}{5}

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

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

Step 1.2

Add

2

$2$ and

\frac{1}{5}

$\frac{1}{5}$ .

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Step 1.2.1

To write

2

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

\frac{5}{5}

$\frac{5}{5}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{5}{5}

$\frac{5}{5}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

5

$5$ .

\frac{10 + 1}{5} \cdot 1 \frac{2}{3}

$\frac{10 + 1}{5} \cdot 1 \frac{2}{3}$

Step 1.2.4.2

Add

10

$10$ and

1

$1$ .

\frac{11}{5} \cdot 1 \frac{2}{3}

$\frac{11}{5} \cdot 1 \frac{2}{3}$

\frac{11}{5} \cdot 1 \frac{2}{3}

$\frac{11}{5} \cdot 1 \frac{2}{3}$

\frac{11}{5} \cdot 1 \frac{2}{3}

$\frac{11}{5} \cdot 1 \frac{2}{3}$

\frac{11}{5} \cdot 1 \frac{2}{3}

$\frac{11}{5} \cdot 1 \frac{2}{3}$

Step 2

Convert

1 \frac{2}{3}

$1 \frac{2}{3}$ to an improper fraction.

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Step 2.1

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

\frac{11}{5} \cdot (1 + \frac{2}{3})

$\frac{11}{5} \cdot (1 + \frac{2}{3})$

Step 2.2

Add

1

$1$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 2.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{11}{5} \cdot (\frac{3}{3} + \frac{2}{3})

$\frac{11}{5} \cdot (\frac{3}{3} + \frac{2}{3})$

Step 2.2.2

Combine the numerators over the common denominator.

\frac{11}{5} \cdot \frac{3 + 2}{3}

$\frac{11}{5} \cdot \frac{3 + 2}{3}$

Step 2.2.3

Add

3

$3$ and

2

$2$ .

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

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

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

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

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

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

Step 3

Cancel the common factor of

5

$5$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$11 \cdot \frac{1}{3}$

Step 4

Combine

$11$ and

$\frac{1}{3}$ .

$\frac{11}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{3}$

Decimal Form:

$3.\overline{6}$

Mixed Number Form:

$3 \frac{2}{3}$