Algebra Examples

$z - \frac{4}{9} - \frac{1}{3} = \frac{5}{9}$

Step 1

Simplify $z - \frac{4}{9} - \frac{1}{3}$ .

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Step 1.1

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$z - \frac{4}{9} - \frac{1}{3} \cdot \frac{3}{3} = \frac{5}{9}$

Step 1.2

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

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Step 1.2.1

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

$z - \frac{4}{9} - \frac{3}{3 \cdot 3} = \frac{5}{9}$

Step 1.2.2

Multiply $3$ by $3$ .

$z - \frac{4}{9} - \frac{3}{9} = \frac{5}{9}$

Step 1.3

Combine the numerators over the common denominator.

$z + \frac{- 4 - 3}{9} = \frac{5}{9}$

Step 1.4

Subtract $3$ from $- 4$ .

$z + \frac{- 7}{9} = \frac{5}{9}$

Step 1.5

Move the negative in front of the fraction.

$z - \frac{7}{9} = \frac{5}{9}$

Step 2

Move all terms not containing $z$ to the right side of the equation.

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Step 2.1

Add $\frac{7}{9}$ to both sides of the equation.

$z = \frac{5}{9} + \frac{7}{9}$

Step 2.2

Combine the numerators over the common denominator.

$z = \frac{5 + 7}{9}$

Step 2.3

Add $5$ and $7$ .

$z = \frac{12}{9}$

Step 2.4

Cancel the common factor of $12$ and $9$ .

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Step 2.4.1

Factor $3$ out of $12$ .

$z = \frac{3 (4)}{9}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $3$ out of $9$ .

$z = \frac{3 \cdot 4}{3 \cdot 3}$

Step 2.4.2.2

Cancel the common factor.

$z = \frac{3 \cdot 4}{3 \cdot 3}$

Step 2.4.2.3

Rewrite the expression.

$z = \frac{4}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$z = \frac{4}{3}$

Decimal Form:

$z = 1.\overline{3}$

Mixed Number Form:

$z = 1 \frac{1}{3}$