Basic Math Examples

$- \frac{1}{9} = z - \frac{5}{6}$

Step 1

Rewrite the equation as $z - \frac{5}{6} = - \frac{1}{9}$ .

$z - \frac{5}{6} = - \frac{1}{9}$

Step 2

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

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Step 2.1

Add $\frac{5}{6}$ to both sides of the equation.

$z = - \frac{1}{9} + \frac{5}{6}$

Step 2.2

To write $- \frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.3

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2.4

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{1}{9}$ by $\frac{2}{2}$ .

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

Step 2.4.2

Multiply $9$ by $2$ .

$z = - \frac{2}{18} + \frac{5}{6} \cdot \frac{3}{3}$

Step 2.4.3

Multiply $\frac{5}{6}$ by $\frac{3}{3}$ .

$z = - \frac{2}{18} + \frac{5 \cdot 3}{6 \cdot 3}$

Step 2.4.4

Multiply $6$ by $3$ .

$z = - \frac{2}{18} + \frac{5 \cdot 3}{18}$

Step 2.5

Combine the numerators over the common denominator.

$z = \frac{- 2 + 5 \cdot 3}{18}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $5$ by $3$ .

$z = \frac{- 2 + 15}{18}$

Step 2.6.2

Add $- 2$ and $15$ .

$z = \frac{13}{18}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$z = \frac{13}{18}$

Decimal Form:

$z = 0.7\overline{2}$