Basic Math Examples

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

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

Step 1

Convert

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

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Step 1.1

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

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

Step 1.2

Add

$3$ and

$\frac{1}{3}$ .

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Step 1.2.1

To write

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

$\frac{3}{3}$ .

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

Step 1.2.2

Combine

$3$ and

$\frac{3}{3}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$3$ by

$3$ .

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

Step 1.2.4.2

Add

$9$ and

$1$ .

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

Step 2

Convert

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

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Step 2.1

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

$\frac{10}{3} \div (2 + \frac{1}{2})$

Step 2.2

Add

$2$ and

$\frac{1}{2}$ .

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Step 2.2.1

To write

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

$\frac{2}{2}$ .

$\frac{10}{3} \div (2 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine

$2$ and

$\frac{2}{2}$ .

$\frac{10}{3} \div (\frac{2 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$2$ by

$2$ .

$\frac{10}{3} \div \frac{4 + 1}{2}$

Step 2.2.4.2

Add

$4$ and

$1$ .

$\frac{10}{3} \div \frac{5}{2}$

Step 3

To divide by a fraction, multiply by its reciprocal.

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

Step 4

Cancel the common factor of

$5$ .

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Step 4.1

Factor

$5$ out of

$10$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

Combine

$\frac{2}{3}$ and

$2$ .

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

Step 6

Multiply

$2$ by

$2$ .

$\frac{4}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$