Basic Math Examples

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

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{2}$ by $\frac{\frac{3 \cdot 5}{9}}{\frac{3 \cdot 5}{9}}$ .

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

Step 1.2

Multiply $\frac{1}{2}$ by $\frac{\frac{3 \cdot 5}{9}}{\frac{3 \cdot 5}{9}}$ .

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

Step 1.3

Multiply $\frac{2}{3} \div \frac{5}{9}$ by $\frac{6}{6}$ .

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

Step 1.4

Multiply $\frac{2}{3} \div \frac{5}{9}$ by $\frac{6}{6}$ .

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

Step 1.5

Multiply $\frac{5}{6}$ by $\frac{\frac{5}{9}}{\frac{5}{9}}$ .

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

Step 1.6

Multiply $\frac{5}{6}$ by $\frac{\frac{5}{9}}{\frac{5}{9}}$ .

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

Step 1.7

Multiply $3$ by $5$ .

$\frac{\frac{3 \cdot 5}{9}}{2 (\frac{15}{9})} - \frac{\frac{2}{3} \cdot 6}{\frac{5}{9} \cdot 6} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 1.8

Combine $2$ and $\frac{15}{9}$ .

$\frac{\frac{3 \cdot 5}{9}}{\frac{2 \cdot 15}{9}} - \frac{\frac{2}{3} \cdot 6}{\frac{5}{9} \cdot 6} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 1.9

Multiply $2$ by $15$ .

$\frac{\frac{3 \cdot 5}{9}}{\frac{30}{9}} - \frac{\frac{2}{3} \cdot 6}{\frac{5}{9} \cdot 6} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 1.10

Reorder the factors of $\frac{5}{9} \cdot 6$ .

$\frac{\frac{3 \cdot 5}{9}}{\frac{30}{9}} - \frac{\frac{2}{3} \cdot 6}{6 (\frac{5}{9})} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 1.11

Combine $6$ and $\frac{5}{9}$ .

$\frac{\frac{3 \cdot 5}{9}}{\frac{30}{9}} - \frac{\frac{2}{3} \cdot 6}{\frac{6 \cdot 5}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 1.12

Multiply $6$ by $5$ .

$\frac{\frac{3 \cdot 5}{9}}{\frac{30}{9}} - \frac{\frac{2}{3} \cdot 6}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{\frac{3 \cdot 5}{9} - \frac{2}{3} \cdot 6}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 2.2

Multiply $3$ by $5$ .

$\frac{\frac{15}{9} - \frac{2}{3} \cdot 6}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $15$ and $9$ .

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Step 3.1.1

Factor $3$ out of $15$ .

$\frac{\frac{3 (5)}{9} - \frac{2}{3} \cdot 6}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $3$ out of $9$ .

$\frac{\frac{3 \cdot 5}{3 \cdot 3} - \frac{2}{3} \cdot 6}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{\frac{3 \cdot 5}{3 \cdot 3} - \frac{2}{3} \cdot 6}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 3.1.2.3

Rewrite the expression.

$\frac{\frac{5}{3} - \frac{2}{3} \cdot 6}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 3.2

Cancel the common factor of $3$ .

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Step 3.2.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{\frac{5}{3} + \frac{- 2}{3} \cdot 6}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 3.2.2

Factor $3$ out of $6$ .

$\frac{\frac{5}{3} + \frac{- 2}{3} \cdot (3 (2))}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 3.2.3

Cancel the common factor.

$\frac{\frac{5}{3} + \frac{- 2}{3} \cdot (3 \cdot 2)}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 3.2.4

Rewrite the expression.

$\frac{\frac{5}{3} - 2 \cdot 2}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 3.3

Multiply $- 2$ by $2$ .

$\frac{\frac{5}{3} - 4}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 4

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{5}{3} - 4 \cdot \frac{3}{3}}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 5

Combine $- 4$ and $\frac{3}{3}$ .

$\frac{\frac{5}{3} + \frac{- 4 \cdot 3}{3}}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 6

Combine the numerators over the common denominator.

$\frac{\frac{5 - 4 \cdot 3}{3}}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 4$ by $3$ .

$\frac{\frac{5 - 12}{3}}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 7.2

Subtract $12$ from $5$ .

$\frac{\frac{- 7}{3}}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 8

Move the negative in front of the fraction.

$\frac{- \frac{7}{3}}{\frac{30}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 9

Simplify each term.

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Step 9.1

Cancel the common factor of $30$ and $9$ .

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Step 9.1.1

Factor $3$ out of $30$ .

$\frac{- \frac{7}{3}}{\frac{3 (10)}{9}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 9.1.2

Cancel the common factors.

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Step 9.1.2.1

Factor $3$ out of $9$ .

$\frac{- \frac{7}{3}}{\frac{3 \cdot 10}{3 \cdot 3}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 9.1.2.2

Cancel the common factor.

$\frac{- \frac{7}{3}}{\frac{3 \cdot 10}{3 \cdot 3}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 9.1.2.3

Rewrite the expression.

$\frac{- \frac{7}{3}}{\frac{10}{3}} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 9.2

Multiply the numerator by the reciprocal of the denominator.

$- \frac{7}{3} \cdot \frac{3}{10} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 9.3

Cancel the common factor of $3$ .

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Step 9.3.1

Move the leading negative in $- \frac{7}{3}$ into the numerator.

$\frac{- 7}{3} \cdot \frac{3}{10} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 9.3.2

Cancel the common factor.

$\frac{- 7}{3} \cdot \frac{3}{10} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 9.3.3

Rewrite the expression.

$- 7 (\frac{1}{10}) + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 9.4

Combine $- 7$ and $\frac{1}{10}$ .

$\frac{- 7}{10} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 9.5

Move the negative in front of the fraction.

$- \frac{7}{10} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 9.6

Cancel the common factor of $\frac{5}{9}$ .

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Step 9.6.1

Cancel the common factor.

$- \frac{7}{10} + \frac{5 (\frac{5}{9})}{6 (\frac{5}{9})}$

Step 9.6.2

Rewrite the expression.

$- \frac{7}{10} + \frac{5}{6}$

Step 10

To write $- \frac{7}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{7}{10} \cdot \frac{3}{3} + \frac{5}{6}$

Step 11

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{7}{10} \cdot \frac{3}{3} + \frac{5}{6} \cdot \frac{5}{5}$

Step 12

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 12.1

Multiply $\frac{7}{10}$ by $\frac{3}{3}$ .

$- \frac{7 \cdot 3}{10 \cdot 3} + \frac{5}{6} \cdot \frac{5}{5}$

Step 12.2

Multiply $10$ by $3$ .

$- \frac{7 \cdot 3}{30} + \frac{5}{6} \cdot \frac{5}{5}$

Step 12.3

Multiply $\frac{5}{6}$ by $\frac{5}{5}$ .

$- \frac{7 \cdot 3}{30} + \frac{5 \cdot 5}{6 \cdot 5}$

Step 12.4

Multiply $6$ by $5$ .

$- \frac{7 \cdot 3}{30} + \frac{5 \cdot 5}{30}$

Step 13

Combine the numerators over the common denominator.

$\frac{- 7 \cdot 3 + 5 \cdot 5}{30}$

Step 14

Simplify the numerator.

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Step 14.1

Multiply $- 7$ by $3$ .

$\frac{- 21 + 5 \cdot 5}{30}$

Step 14.2

Multiply $5$ by $5$ .

$\frac{- 21 + 25}{30}$

Step 14.3

Add $- 21$ and $25$ .

$\frac{4}{30}$

Step 15

Cancel the common factor of $4$ and $30$ .

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Step 15.1

Factor $2$ out of $4$ .

$\frac{2 (2)}{30}$

Step 15.2

Cancel the common factors.

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Step 15.2.1

Factor $2$ out of $30$ .

$\frac{2 \cdot 2}{2 \cdot 15}$

Step 15.2.2

Cancel the common factor.

$\frac{2 \cdot 2}{2 \cdot 15}$

Step 15.2.3

Rewrite the expression.

$\frac{2}{15}$

Step 16

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{15}$

Decimal Form:

$0.1\overline{3}$