Basic Math Examples

$\frac{\frac{1}{3} - 2 \frac{1}{9} + \frac{5}{3}}{\frac{2}{3} - \frac{1}{6}}$

Step 1

Convert $2 \frac{1}{9}$ to an improper fraction.

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Step 1.1

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

$\frac{\frac{1}{3} - (2 + \frac{1}{9}) + \frac{5}{3}}{\frac{2}{3} - \frac{1}{6}}$

Step 1.2

Add $2$ and $\frac{1}{9}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{\frac{1}{3} - (2 \cdot \frac{9}{9} + \frac{1}{9}) + \frac{5}{3}}{\frac{2}{3} - \frac{1}{6}}$

Step 1.2.2

Combine $2$ and $\frac{9}{9}$ .

$\frac{\frac{1}{3} - (\frac{2 \cdot 9}{9} + \frac{1}{9}) + \frac{5}{3}}{\frac{2}{3} - \frac{1}{6}}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{\frac{1}{3} - \frac{2 \cdot 9 + 1}{9} + \frac{5}{3}}{\frac{2}{3} - \frac{1}{6}}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $9$ .

$\frac{\frac{1}{3} - \frac{18 + 1}{9} + \frac{5}{3}}{\frac{2}{3} - \frac{1}{6}}$

Step 1.2.4.2

Add $18$ and $1$ .

$\frac{\frac{1}{3} - \frac{19}{9} + \frac{5}{3}}{\frac{2}{3} - \frac{1}{6}}$

Step 2

Multiply the numerator and denominator of the fraction by $18$ .

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Step 2.1

Multiply $\frac{\frac{1}{3} - \frac{19}{9} + \frac{5}{3}}{\frac{2}{3} - \frac{1}{6}}$ by $\frac{18}{18}$ .

$\frac{18}{18} \cdot \frac{\frac{1}{3} - \frac{19}{9} + \frac{5}{3}}{\frac{2}{3} - \frac{1}{6}}$

Step 2.2

Combine.

$\frac{18 (\frac{1}{3} - \frac{19}{9} + \frac{5}{3})}{18 (\frac{2}{3} - \frac{1}{6})}$

Step 3

Apply the distributive property.

$\frac{18 (\frac{1}{3}) + 18 (- \frac{19}{9}) + 18 (\frac{5}{3})}{18 (\frac{2}{3}) + 18 (- \frac{1}{6})}$

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $3$ .

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Step 4.1.1

Factor $3$ out of $18$ .

$\frac{3 (6) \frac{1}{3} + 18 (- \frac{19}{9}) + 18 (\frac{5}{3})}{18 (\frac{2}{3}) + 18 (- \frac{1}{6})}$

Step 4.1.2

Cancel the common factor.

$\frac{3 \cdot 6 \frac{1}{3} + 18 (- \frac{19}{9}) + 18 (\frac{5}{3})}{18 (\frac{2}{3}) + 18 (- \frac{1}{6})}$

Step 4.1.3

Rewrite the expression.

$\frac{6 + 18 (- \frac{19}{9}) + 18 (\frac{5}{3})}{18 (\frac{2}{3}) + 18 (- \frac{1}{6})}$

Step 4.2

Cancel the common factor of $9$ .

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Step 4.2.1

Move the leading negative in $- \frac{19}{9}$ into the numerator.

$\frac{6 + 18 (\frac{- 19}{9}) + 18 (\frac{5}{3})}{18 (\frac{2}{3}) + 18 (- \frac{1}{6})}$

Step 4.2.2

Factor $9$ out of $18$ .

$\frac{6 + 9 (2) \frac{- 19}{9} + 18 (\frac{5}{3})}{18 (\frac{2}{3}) + 18 (- \frac{1}{6})}$

Step 4.2.3

Cancel the common factor.

$\frac{6 + 9 \cdot 2 \frac{- 19}{9} + 18 (\frac{5}{3})}{18 (\frac{2}{3}) + 18 (- \frac{1}{6})}$

Step 4.2.4

Rewrite the expression.

$\frac{6 + 2 \cdot - 19 + 18 (\frac{5}{3})}{18 (\frac{2}{3}) + 18 (- \frac{1}{6})}$

Step 4.3

Multiply $2$ by $- 19$ .

$\frac{6 - 38 + 18 (\frac{5}{3})}{18 (\frac{2}{3}) + 18 (- \frac{1}{6})}$

Step 4.4

Cancel the common factor of $3$ .

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Step 4.4.1

Factor $3$ out of $18$ .

$\frac{6 - 38 + 3 (6) \frac{5}{3}}{18 (\frac{2}{3}) + 18 (- \frac{1}{6})}$

Step 4.4.2

Cancel the common factor.

$\frac{6 - 38 + 3 \cdot 6 \frac{5}{3}}{18 (\frac{2}{3}) + 18 (- \frac{1}{6})}$

Step 4.4.3

Rewrite the expression.

$\frac{6 - 38 + 6 \cdot 5}{18 (\frac{2}{3}) + 18 (- \frac{1}{6})}$

Step 4.5

Multiply $6$ by $5$ .

$\frac{6 - 38 + 30}{18 (\frac{2}{3}) + 18 (- \frac{1}{6})}$

Step 4.6

Cancel the common factor of $3$ .

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Step 4.6.1

Factor $3$ out of $18$ .

$\frac{6 - 38 + 30}{3 (6) \frac{2}{3} + 18 (- \frac{1}{6})}$

Step 4.6.2

Cancel the common factor.

$\frac{6 - 38 + 30}{3 \cdot 6 \frac{2}{3} + 18 (- \frac{1}{6})}$

Step 4.6.3

Rewrite the expression.

$\frac{6 - 38 + 30}{6 \cdot 2 + 18 (- \frac{1}{6})}$

Step 4.7

Multiply $6$ by $2$ .

$\frac{6 - 38 + 30}{12 + 18 (- \frac{1}{6})}$

Step 4.8

Cancel the common factor of $6$ .

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Step 4.8.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$\frac{6 - 38 + 30}{12 + 18 (\frac{- 1}{6})}$

Step 4.8.2

Factor $6$ out of $18$ .

$\frac{6 - 38 + 30}{12 + 6 (3) \frac{- 1}{6}}$

Step 4.8.3

Cancel the common factor.

$\frac{6 - 38 + 30}{12 + 6 \cdot 3 \frac{- 1}{6}}$

Step 4.8.4

Rewrite the expression.

$\frac{6 - 38 + 30}{12 + 3 \cdot - 1}$

Step 4.9

Multiply $3$ by $- 1$ .

$\frac{6 - 38 + 30}{12 - 3}$

Step 5

Simplify the numerator.

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Step 5.1

Subtract $38$ from $6$ .

$\frac{- 32 + 30}{12 - 3}$

Step 5.2

Add $- 32$ and $30$ .

$\frac{- 2}{12 - 3}$

Step 6

Simplify the expression.

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Step 6.1

Subtract $3$ from $12$ .

$\frac{- 2}{9}$

Step 6.2

Move the negative in front of the fraction.

$- \frac{2}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{9}$

Decimal Form:

$- 0.\overline{2}$