Basic Math Examples

- 2 \frac{1}{2} \div \frac{2}{5}

$- 2 \frac{1}{2} \div \frac{2}{5}$

Step 1

Convert

2 \frac{1}{2}

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

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Step 1.1

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

- (2 + \frac{1}{2}) \div \frac{2}{5}

$- (2 + \frac{1}{2}) \div \frac{2}{5}$

Step 1.2

Add

2

$2$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

2

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

\frac{2}{2}

$\frac{2}{2}$ .

- (2 \cdot \frac{2}{2} + \frac{1}{2}) \div \frac{2}{5}

$- (2 \cdot \frac{2}{2} + \frac{1}{2}) \div \frac{2}{5}$

Step 1.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

- (\frac{2 \cdot 2}{2} + \frac{1}{2}) \div \frac{2}{5}

$- (\frac{2 \cdot 2}{2} + \frac{1}{2}) \div \frac{2}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

- \frac{2 \cdot 2 + 1}{2} \div \frac{2}{5}

$- \frac{2 \cdot 2 + 1}{2} \div \frac{2}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

2

$2$ .

- \frac{4 + 1}{2} \div \frac{2}{5}

$- \frac{4 + 1}{2} \div \frac{2}{5}$

Step 1.2.4.2

Add

4

$4$ and

1

$1$ .

- \frac{5}{2} \div \frac{2}{5}

$- \frac{5}{2} \div \frac{2}{5}$

- \frac{5}{2} \div \frac{2}{5}

$- \frac{5}{2} \div \frac{2}{5}$

- \frac{5}{2} \div \frac{2}{5}

$- \frac{5}{2} \div \frac{2}{5}$

- \frac{5}{2} \div \frac{2}{5}

$- \frac{5}{2} \div \frac{2}{5}$

Step 2

To divide by a fraction, multiply by its reciprocal.

- \frac{5}{2} \cdot \frac{5}{2}

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

Step 3

Multiply

- \frac{5}{2} \cdot \frac{5}{2}

$- \frac{5}{2} \cdot \frac{5}{2}$ .

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Step 3.1

Multiply

\frac{5}{2}

$\frac{5}{2}$ by

\frac{5}{2}

$\frac{5}{2}$ .

- \frac{5 \cdot 5}{2 \cdot 2}

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

Step 3.2

Multiply

5

$5$ by

5

$5$ .

- \frac{25}{2 \cdot 2}

$- \frac{25}{2 \cdot 2}$

Step 3.3

Multiply

2

$2$ by

2

$2$ .

- \frac{25}{4}

$- \frac{25}{4}$

- \frac{25}{4}

$- \frac{25}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

- \frac{25}{4}

$- \frac{25}{4}$

Decimal Form:

- 6.25

$- 6.25$

Mixed Number Form:

- 6 \frac{1}{4}

$- 6 \frac{1}{4}$