Basic Math Examples

$\frac{1}{3} - \frac{1}{4} \div \frac{1}{4} + \frac{1}{9}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{3}$ by $\frac{\frac{3}{4}}{\frac{3}{4}}$ .

$\frac{1}{3} \cdot \frac{\frac{3}{4}}{\frac{3}{4}} - \frac{1}{4} \div \frac{1}{4} + \frac{1}{9}$

Step 1.2

Multiply $\frac{1}{3}$ by $\frac{\frac{3}{4}}{\frac{3}{4}}$ .

$\frac{\frac{3}{4}}{3 (\frac{3}{4})} - \frac{1}{4} \div \frac{1}{4} + \frac{1}{9}$

Step 1.3

Multiply $\frac{1}{4} \div \frac{1}{4}$ by $\frac{9}{9}$ .

$\frac{\frac{3}{4}}{3 (\frac{3}{4})} - (\frac{1}{4} \div \frac{1}{4} \cdot \frac{9}{9}) + \frac{1}{9}$

Step 1.4

Multiply $\frac{1}{4} \div \frac{1}{4}$ by $\frac{9}{9}$ .

$\frac{\frac{3}{4}}{3 (\frac{3}{4})} - \frac{\frac{1}{4} \cdot 9}{\frac{1}{4} \cdot 9} + \frac{1}{9}$

Step 1.5

Multiply $\frac{1}{9}$ by $\frac{\frac{1}{4}}{\frac{1}{4}}$ .

$\frac{\frac{3}{4}}{3 (\frac{3}{4})} - \frac{\frac{1}{4} \cdot 9}{\frac{1}{4} \cdot 9} + \frac{1}{9} \cdot \frac{\frac{1}{4}}{\frac{1}{4}}$

Step 1.6

Multiply $\frac{1}{9}$ by $\frac{\frac{1}{4}}{\frac{1}{4}}$ .

$\frac{\frac{3}{4}}{3 (\frac{3}{4})} - \frac{\frac{1}{4} \cdot 9}{\frac{1}{4} \cdot 9} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 1.7

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

$\frac{\frac{3}{4}}{\frac{3 \cdot 3}{4}} - \frac{\frac{1}{4} \cdot 9}{\frac{1}{4} \cdot 9} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 1.8

Multiply $3$ by $3$ .

$\frac{\frac{3}{4}}{\frac{9}{4}} - \frac{\frac{1}{4} \cdot 9}{\frac{1}{4} \cdot 9} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 1.9

Reorder the factors of $\frac{1}{4} \cdot 9$ .

$\frac{\frac{3}{4}}{\frac{9}{4}} - \frac{\frac{1}{4} \cdot 9}{9 (\frac{1}{4})} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 1.10

Combine $9$ and $\frac{1}{4}$ .

$\frac{\frac{3}{4}}{\frac{9}{4}} - \frac{\frac{1}{4} \cdot 9}{\frac{9}{4}} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 2

Combine the numerators over the common denominator.

$\frac{\frac{3}{4} - \frac{1}{4} \cdot 9}{\frac{9}{4}} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- \frac{1}{4} \cdot 9$ .

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Step 3.1.1

Multiply $9$ by $- 1$ .

$\frac{\frac{3}{4} - 9 (\frac{1}{4})}{\frac{9}{4}} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 3.1.2

Combine $- 9$ and $\frac{1}{4}$ .

$\frac{\frac{3}{4} + \frac{- 9}{4}}{\frac{9}{4}} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 3.2

Move the negative in front of the fraction.

$\frac{\frac{3}{4} - \frac{9}{4}}{\frac{9}{4}} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 4

Simplify terms.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{\frac{3 - 9}{4}}{\frac{9}{4}} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 4.2

Subtract $9$ from $3$ .

$\frac{\frac{- 6}{4}}{\frac{9}{4}} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 4.3

Cancel the common factor of $- 6$ and $4$ .

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Step 4.3.1

Factor $2$ out of $- 6$ .

$\frac{\frac{2 (- 3)}{4}}{\frac{9}{4}} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $2$ out of $4$ .

$\frac{\frac{2 \cdot - 3}{2 \cdot 2}}{\frac{9}{4}} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 4.3.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot - 3}{2 \cdot 2}}{\frac{9}{4}} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 4.3.2.3

Rewrite the expression.

$\frac{\frac{- 3}{2}}{\frac{9}{4}} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 4.4

Move the negative in front of the fraction.

$\frac{- \frac{3}{2}}{\frac{9}{4}} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 5

Simplify each term.

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Step 5.1

Multiply the numerator by the reciprocal of the denominator.

$- \frac{3}{2} \cdot \frac{4}{9} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 5.2

Cancel the common factor of $3$ .

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Step 5.2.1

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

$\frac{- 3}{2} \cdot \frac{4}{9} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 5.2.2

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{2} \cdot \frac{4}{9} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 5.2.3

Factor $3$ out of $9$ .

$\frac{3 \cdot - 1}{2} \cdot \frac{4}{3 \cdot 3} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 5.2.4

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{4}{3 \cdot 3} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 5.2.5

Rewrite the expression.

$\frac{- 1}{2} \cdot \frac{4}{3} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 5.3

Cancel the common factor of $2$ .

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Step 5.3.1

Factor $2$ out of $4$ .

$\frac{- 1}{2} \cdot \frac{2 (2)}{3} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 5.3.2

Cancel the common factor.

$\frac{- 1}{2} \cdot \frac{2 \cdot 2}{3} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 5.3.3

Rewrite the expression.

$- \frac{2}{3} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 5.4

Cancel the common factor of $\frac{1}{4}$ .

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Step 5.4.1

Cancel the common factor.

$- \frac{2}{3} + \frac{\frac{1}{4}}{9 (\frac{1}{4})}$

Step 5.4.2

Rewrite the expression.

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

Step 6

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 7

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{2}{3}$ by $\frac{3}{3}$ .

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

Step 7.2

Multiply $3$ by $3$ .

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

Step 8

Combine the numerators over the common denominator.

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

Step 9

Simplify the numerator.

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Step 9.1

Multiply $- 2$ by $3$ .

$\frac{- 6 + 1}{9}$

Step 9.2

Add $- 6$ and $1$ .

$\frac{- 5}{9}$

Step 10

Move the negative in front of the fraction.

$- \frac{5}{9}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{9}$

Decimal Form:

$- 0.\overline{5}$