Basic Math Examples

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

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

Step 1

Convert

2 \frac{1}{3}

$2 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

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

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

Step 1.2

Add

2

$2$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 1.2.1

To write

2

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

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

3

$3$ .

\frac{6 + 1}{3} \div 2 \frac{1}{2}

$\frac{6 + 1}{3} \div 2 \frac{1}{2}$

Step 1.2.4.2

Add

6

$6$ and

1

$1$ .

\frac{7}{3} \div 2 \frac{1}{2}

$\frac{7}{3} \div 2 \frac{1}{2}$

\frac{7}{3} \div 2 \frac{1}{2}

$\frac{7}{3} \div 2 \frac{1}{2}$

\frac{7}{3} \div 2 \frac{1}{2}

$\frac{7}{3} \div 2 \frac{1}{2}$

\frac{7}{3} \div 2 \frac{1}{2}

$\frac{7}{3} \div 2 \frac{1}{2}$

Step 2

Convert

2 \frac{1}{2}

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

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Step 2.1

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

\frac{7}{3} \div (2 + \frac{1}{2})

$\frac{7}{3} \div (2 + \frac{1}{2})$

Step 2.2

Add

2

$2$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.2.1

To write

2

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{7}{3} \div (2 \cdot \frac{2}{2} + \frac{1}{2})

$\frac{7}{3} \div (2 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{7}{3} \div (\frac{2 \cdot 2}{2} + \frac{1}{2})

$\frac{7}{3} \div (\frac{2 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{7}{3} \div \frac{2 \cdot 2 + 1}{2}

$\frac{7}{3} \div \frac{2 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

2

$2$ .

\frac{7}{3} \div \frac{4 + 1}{2}

$\frac{7}{3} \div \frac{4 + 1}{2}$

Step 2.2.4.2

Add

4

$4$ and

1

$1$ .

\frac{7}{3} \div \frac{5}{2}

$\frac{7}{3} \div \frac{5}{2}$

\frac{7}{3} \div \frac{5}{2}

$\frac{7}{3} \div \frac{5}{2}$

\frac{7}{3} \div \frac{5}{2}

$\frac{7}{3} \div \frac{5}{2}$

\frac{7}{3} \div \frac{5}{2}

$\frac{7}{3} \div \frac{5}{2}$

Step 3

To divide by a fraction, multiply by its reciprocal.

\frac{7}{3} \cdot \frac{2}{5}

$\frac{7}{3} \cdot \frac{2}{5}$

Step 4

Multiply

\frac{7}{3} \cdot \frac{2}{5}

$\frac{7}{3} \cdot \frac{2}{5}$ .

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Step 4.1

Multiply

\frac{7}{3}

$\frac{7}{3}$ by

\frac{2}{5}

$\frac{2}{5}$ .

\frac{7 \cdot 2}{3 \cdot 5}

$\frac{7 \cdot 2}{3 \cdot 5}$

Step 4.2

Multiply

7

$7$ by

2

$2$ .

\frac{14}{3 \cdot 5}

$\frac{14}{3 \cdot 5}$

Step 4.3

Multiply

3

$3$ by

5

$5$ .

\frac{14}{15}

$\frac{14}{15}$

\frac{14}{15}

$\frac{14}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

\frac{14}{15}

$\frac{14}{15}$

Decimal Form:

0.9 ¯ 3

$0.9\overline{3}$