Basic Math Examples

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

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

Step 1

Convert

1 \frac{1}{3}

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

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Step 1.1

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

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

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

Step 1.2

Add

1

$1$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

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

Step 1.2.3

Add

3

$3$ and

1

$1$ .

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

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

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

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

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

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

Step 2

Convert

1 \frac{1}{2}

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

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Step 2.1

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

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

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

Step 2.2

Add

1

$1$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.2.1

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 2.2.2

Combine the numerators over the common denominator.

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

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

Step 2.2.3

Add

2

$2$ and

1

$1$ .

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

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

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

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

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

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

Step 3

Cancel the common factor of

2

$2$ .

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Step 3.1

Factor

2

$2$ out of

4

$4$ .

\frac{2 (2)}{3} \cdot \frac{3}{2}

$\frac{2 (2)}{3} \cdot \frac{3}{2}$

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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

Step 4

Cancel the common factor of

$3$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$2$