Basic Math Examples

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

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

Step 1

Convert

4 \frac{1}{2}

$4 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

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

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

Step 1.2

Add

4

$4$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.2

Combine

4

$4$ and

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

4

$4$ by

2

$2$ .

\frac{8 + 1}{2} \cdot \frac{2}{3}

$\frac{8 + 1}{2} \cdot \frac{2}{3}$

Step 1.2.4.2

Add

8

$8$ and

1

$1$ .

\frac{9}{2} \cdot \frac{2}{3}

$\frac{9}{2} \cdot \frac{2}{3}$

\frac{9}{2} \cdot \frac{2}{3}

$\frac{9}{2} \cdot \frac{2}{3}$

\frac{9}{2} \cdot \frac{2}{3}

$\frac{9}{2} \cdot \frac{2}{3}$

\frac{9}{2} \cdot \frac{2}{3}

$\frac{9}{2} \cdot \frac{2}{3}$

Step 2

Cancel the common factor of

3

$3$ .

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Step 2.1

Factor

3

$3$ out of

9

$9$ .

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

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of

$2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$3$