Basic Math Examples

- 4 \frac{4}{9} \div \frac{4}{9}

$- 4 \frac{4}{9} \div \frac{4}{9}$

Step 1

Convert

4 \frac{4}{9}

$4 \frac{4}{9}$ to an improper fraction.

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Step 1.1

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

- (4 + \frac{4}{9}) \div \frac{4}{9}

$- (4 + \frac{4}{9}) \div \frac{4}{9}$

Step 1.2

Add

4

$4$ and

\frac{4}{9}

$\frac{4}{9}$ .

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Step 1.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{9}{9}

$\frac{9}{9}$ .

- (4 \cdot \frac{9}{9} + \frac{4}{9}) \div \frac{4}{9}

$- (4 \cdot \frac{9}{9} + \frac{4}{9}) \div \frac{4}{9}$

Step 1.2.2

Combine

4

$4$ and

\frac{9}{9}

$\frac{9}{9}$ .

- (\frac{4 \cdot 9}{9} + \frac{4}{9}) \div \frac{4}{9}

$- (\frac{4 \cdot 9}{9} + \frac{4}{9}) \div \frac{4}{9}$

Step 1.2.3

Combine the numerators over the common denominator.

- \frac{4 \cdot 9 + 4}{9} \div \frac{4}{9}

$- \frac{4 \cdot 9 + 4}{9} \div \frac{4}{9}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

4

$4$ by

9

$9$ .

- \frac{36 + 4}{9} \div \frac{4}{9}

$- \frac{36 + 4}{9} \div \frac{4}{9}$

Step 1.2.4.2

Add

36

$36$ and

4

$4$ .

- \frac{40}{9} \div \frac{4}{9}

$- \frac{40}{9} \div \frac{4}{9}$

- \frac{40}{9} \div \frac{4}{9}

$- \frac{40}{9} \div \frac{4}{9}$

- \frac{40}{9} \div \frac{4}{9}

$- \frac{40}{9} \div \frac{4}{9}$

- \frac{40}{9} \div \frac{4}{9}

$- \frac{40}{9} \div \frac{4}{9}$

Step 2

To divide by a fraction, multiply by its reciprocal.

- \frac{40}{9} \cdot \frac{9}{4}

$- \frac{40}{9} \cdot \frac{9}{4}$

Step 3

Cancel the common factor of

4

$4$ .

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Step 3.1

Move the leading negative in

- \frac{40}{9}

$- \frac{40}{9}$ into the numerator.

\frac{- 40}{9} \cdot \frac{9}{4}

$\frac{- 40}{9} \cdot \frac{9}{4}$

Step 3.2

Factor

4

$4$ out of

- 40

$- 40$ .

\frac{4 (- 10)}{9} \cdot \frac{9}{4}

$\frac{4 (- 10)}{9} \cdot \frac{9}{4}$

Step 3.3

Cancel the common factor.

$\frac{4 \cdot - 10}{9} \cdot \frac{9}{4}$

Step 3.4

Rewrite the expression.

$\frac{- 10}{9} \cdot 9$

Step 4

Cancel the common factor of

$9$ .

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Step 4.1

Cancel the common factor.

$\frac{- 10}{9} \cdot 9$

Step 4.2

Rewrite the expression.

$- 10$