Basic Math Examples

3 \frac{1}{3} \div 2

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

Step 1

Convert

3 \frac{1}{3}

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

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Step 1.1

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

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

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

Step 1.2

Add

3

$3$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 1.2.1

To write

3

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

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.2

Combine

3

$3$ and

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

3

$3$ by

3

$3$ .

\frac{9 + 1}{3} \div 2

$\frac{9 + 1}{3} \div 2$

Step 1.2.4.2

Add

9

$9$ and

1

$1$ .

\frac{10}{3} \div 2

$\frac{10}{3} \div 2$

\frac{10}{3} \div 2

$\frac{10}{3} \div 2$

\frac{10}{3} \div 2

$\frac{10}{3} \div 2$

\frac{10}{3} \div 2

$\frac{10}{3} \div 2$

Step 2

Rewrite the division as a fraction.

\frac{\frac{10}{3}}{2}

$\frac{\frac{10}{3}}{2}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

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

Step 4

Cancel the common factor of

2

$2$ .

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Step 4.1

Factor

2

$2$ out of

10

$10$ .

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

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

$\frac{5}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{3}$

Decimal Form:

$1.\overline{6}$

Mixed Number Form:

$1 \frac{2}{3}$