Basic Math Examples

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

Step 1

Move the negative in front of the fraction.

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

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.

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

Step 2.2

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

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

Step 2.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

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

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

Step 2.3.2

Multiply $3$ by $2$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $2$ .

$z = \frac{4 + 5}{6}$

Step 2.5.2

Add $4$ and $5$ .

$z = \frac{9}{6}$

Step 2.6

Cancel the common factor of $9$ and $6$ .

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Step 2.6.1

Factor $3$ out of $9$ .

$z = \frac{3 (3)}{6}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $3$ out of $6$ .

$z = \frac{3 \cdot 3}{3 \cdot 2}$

Step 2.6.2.2

Cancel the common factor.

$z = \frac{3 \cdot 3}{3 \cdot 2}$

Step 2.6.2.3

Rewrite the expression.

$z = \frac{3}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$z = \frac{3}{2}$

Decimal Form:

$z = 1.5$

Mixed Number Form:

$z = 1 \frac{1}{2}$