Basic Math Examples

4 \frac{1}{2} \div 6

$4 \frac{1}{2} \div 6$

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}) \div 6

$(4 + \frac{1}{2}) \div 6$

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}) \div 6

$(4 \cdot \frac{2}{2} + \frac{1}{2}) \div 6$

Step 1.2.2

Combine

4

$4$ and

\frac{2}{2}

$\frac{2}{2}$ .

(\frac{4 \cdot 2}{2} + \frac{1}{2}) \div 6

$(\frac{4 \cdot 2}{2} + \frac{1}{2}) \div 6$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{4 \cdot 2 + 1}{2} \div 6

$\frac{4 \cdot 2 + 1}{2} \div 6$

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} \div 6

$\frac{8 + 1}{2} \div 6$

Step 1.2.4.2

Add

8

$8$ and

1

$1$ .

\frac{9}{2} \div 6

$\frac{9}{2} \div 6$

\frac{9}{2} \div 6

$\frac{9}{2} \div 6$

\frac{9}{2} \div 6

$\frac{9}{2} \div 6$

\frac{9}{2} \div 6

$\frac{9}{2} \div 6$

Step 2

Rewrite the division as a fraction.

\frac{\frac{9}{2}}{6}

$\frac{\frac{9}{2}}{6}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

\frac{9}{2} \cdot \frac{1}{6}

$\frac{9}{2} \cdot \frac{1}{6}$

Step 4

Cancel the common factor of

3

$3$ .

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Step 4.1

Factor

3

$3$ out of

9

$9$ .

\frac{3 (3)}{2} \cdot \frac{1}{6}

$\frac{3 (3)}{2} \cdot \frac{1}{6}$

Step 4.2

Factor

3

$3$ out of

6

$6$ .

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

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

Step 4.3

Cancel the common factor.

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

Step 4.4

Rewrite the expression.

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

Step 5

Multiply

$\frac{3}{2}$ by

$\frac{1}{2}$ .

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

Step 6

Multiply

$2$ by

$2$ .

$\frac{3}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$