Basic Math Examples

- \frac{5}{9} - \frac{1}{2}

$- \frac{5}{9} - \frac{1}{2}$

Step 1

To write

- \frac{5}{9}

$- \frac{5}{9}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

- \frac{5}{9} \cdot \frac{2}{2} - \frac{1}{2}

$- \frac{5}{9} \cdot \frac{2}{2} - \frac{1}{2}$

Step 2

To write

- \frac{1}{2}

$- \frac{1}{2}$ as a fraction with a common denominator, multiply by

\frac{9}{9}

$\frac{9}{9}$ .

- \frac{5}{9} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{9}{9}

$- \frac{5}{9} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{9}{9}$

Step 3

Write each expression with a common denominator of

18

$18$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{5}{9}

$\frac{5}{9}$ by

\frac{2}{2}

$\frac{2}{2}$ .

- \frac{5 \cdot 2}{9 \cdot 2} - \frac{1}{2} \cdot \frac{9}{9}

$- \frac{5 \cdot 2}{9 \cdot 2} - \frac{1}{2} \cdot \frac{9}{9}$

Step 3.2

Multiply

9

$9$ by

2

$2$ .

- \frac{5 \cdot 2}{18} - \frac{1}{2} \cdot \frac{9}{9}

$- \frac{5 \cdot 2}{18} - \frac{1}{2} \cdot \frac{9}{9}$

Step 3.3

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{9}{9}

$\frac{9}{9}$ .

- \frac{5 \cdot 2}{18} - \frac{9}{2 \cdot 9}

$- \frac{5 \cdot 2}{18} - \frac{9}{2 \cdot 9}$

Step 3.4

Multiply

2

$2$ by

9

$9$ .

- \frac{5 \cdot 2}{18} - \frac{9}{18}

$- \frac{5 \cdot 2}{18} - \frac{9}{18}$

- \frac{5 \cdot 2}{18} - \frac{9}{18}

$- \frac{5 \cdot 2}{18} - \frac{9}{18}$

Step 4

Combine the numerators over the common denominator.

\frac{- 5 \cdot 2 - 9}{18}

$\frac{- 5 \cdot 2 - 9}{18}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

- 5

$- 5$ by

2

$2$ .

\frac{- 10 - 9}{18}

$\frac{- 10 - 9}{18}$

Step 5.2

Subtract

9

$9$ from

- 10

$- 10$ .

\frac{- 19}{18}

$\frac{- 19}{18}$

\frac{- 19}{18}

$\frac{- 19}{18}$

Step 6

Move the negative in front of the fraction.

- \frac{19}{18}

$- \frac{19}{18}$

Step 7

The result can be shown in multiple forms.

Exact Form:

- \frac{19}{18}

$- \frac{19}{18}$

Decimal Form:

- 1.0 ¯ 5

$- 1.0\overline{5}$

Mixed Number Form:

- 1 \frac{1}{18}

$- 1 \frac{1}{18}$