Basic Math Examples

- 2 \frac{1}{8} \div \frac{1}{5}

$- 2 \frac{1}{8} \div \frac{1}{5}$

Step 1

Convert

2 \frac{1}{8}

$2 \frac{1}{8}$ 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}{8}) \div \frac{1}{5}

$- (2 + \frac{1}{8}) \div \frac{1}{5}$

Step 1.2

Add

2

$2$ and

\frac{1}{8}

$\frac{1}{8}$ .

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Step 1.2.1

To write

2

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

\frac{8}{8}

$\frac{8}{8}$ .

- (2 \cdot \frac{8}{8} + \frac{1}{8}) \div \frac{1}{5}

$- (2 \cdot \frac{8}{8} + \frac{1}{8}) \div \frac{1}{5}$

Step 1.2.2

Combine

2

$2$ and

\frac{8}{8}

$\frac{8}{8}$ .

- (\frac{2 \cdot 8}{8} + \frac{1}{8}) \div \frac{1}{5}

$- (\frac{2 \cdot 8}{8} + \frac{1}{8}) \div \frac{1}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

- \frac{2 \cdot 8 + 1}{8} \div \frac{1}{5}

$- \frac{2 \cdot 8 + 1}{8} \div \frac{1}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

8

$8$ .

- \frac{16 + 1}{8} \div \frac{1}{5}

$- \frac{16 + 1}{8} \div \frac{1}{5}$

Step 1.2.4.2

Add

16

$16$ and

1

$1$ .

- \frac{17}{8} \div \frac{1}{5}

$- \frac{17}{8} \div \frac{1}{5}$

- \frac{17}{8} \div \frac{1}{5}

$- \frac{17}{8} \div \frac{1}{5}$

- \frac{17}{8} \div \frac{1}{5}

$- \frac{17}{8} \div \frac{1}{5}$

- \frac{17}{8} \div \frac{1}{5}

$- \frac{17}{8} \div \frac{1}{5}$

Step 2

To divide by a fraction, multiply by its reciprocal.

- \frac{17}{8} \cdot 5

$- \frac{17}{8} \cdot 5$

Step 3

Multiply

- \frac{17}{8} \cdot 5

$- \frac{17}{8} \cdot 5$ .

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Step 3.1

Multiply

5

$5$ by

- 1

$- 1$ .

- 5 (\frac{17}{8})

$- 5 (\frac{17}{8})$

Step 3.2

Combine

- 5

$- 5$ and

\frac{17}{8}

$\frac{17}{8}$ .

\frac{- 5 \cdot 17}{8}

$\frac{- 5 \cdot 17}{8}$

Step 3.3

Multiply

- 5

$- 5$ by

17

$17$ .

\frac{- 85}{8}

$\frac{- 85}{8}$

\frac{- 85}{8}

$\frac{- 85}{8}$

Step 4

Move the negative in front of the fraction.

- \frac{85}{8}

$- \frac{85}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

- \frac{85}{8}

$- \frac{85}{8}$

Decimal Form:

- 10.625

$- 10.625$

Mixed Number Form:

- 10 \frac{5}{8}

$- 10 \frac{5}{8}$