Basic Math Examples

$\frac{z}{2} + \frac{z}{9} = \frac{5}{2}$

Step 1

Simplify $\frac{z}{2} + \frac{z}{9}$ .

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $9$ .

$\frac{z \cdot 9}{18} + \frac{z}{9} \cdot \frac{2}{2} = \frac{5}{2}$

Step 1.3.3

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

$\frac{z \cdot 9}{18} + \frac{z \cdot 2}{9 \cdot 2} = \frac{5}{2}$

Step 1.3.4

Multiply $9$ by $2$ .

$\frac{z \cdot 9}{18} + \frac{z \cdot 2}{18} = \frac{5}{2}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{z \cdot 9 + z \cdot 2}{18} = \frac{5}{2}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Move $9$ to the left of $z$ .

$\frac{9 \cdot z + z \cdot 2}{18} = \frac{5}{2}$

Step 1.5.2

Move $2$ to the left of $z$ .

$\frac{9 z + 2 \cdot z}{18} = \frac{5}{2}$

Step 1.5.3

Add $9 z$ and $2 z$ .

$\frac{11 z}{18} = \frac{5}{2}$

Step 2

Multiply both sides of the equation by $\frac{18}{11}$ .

$\frac{18}{11} \cdot \frac{11 z}{18} = \frac{18}{11} \cdot \frac{5}{2}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{18}{11} \cdot \frac{11 z}{18}$ .

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Step 3.1.1.1

Cancel the common factor of $18$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{18}{11} \cdot \frac{11 z}{18} = \frac{18}{11} \cdot \frac{5}{2}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{11} (11 z) = \frac{18}{11} \cdot \frac{5}{2}$

Step 3.1.1.2

Cancel the common factor of $11$ .

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Step 3.1.1.2.1

Factor $11$ out of $11 z$ .

$\frac{1}{11} (11 (z)) = \frac{18}{11} \cdot \frac{5}{2}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{11} (11 z) = \frac{18}{11} \cdot \frac{5}{2}$

Step 3.1.1.2.3

Rewrite the expression.

$z = \frac{18}{11} \cdot \frac{5}{2}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{18}{11} \cdot \frac{5}{2}$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Factor $2$ out of $18$ .

$z = \frac{2 (9)}{11} \cdot \frac{5}{2}$

Step 3.2.1.1.2

Cancel the common factor.

$z = \frac{2 \cdot 9}{11} \cdot \frac{5}{2}$

Step 3.2.1.1.3

Rewrite the expression.

$z = \frac{9}{11} \cdot 5$

Step 3.2.1.2

Combine $\frac{9}{11}$ and $5$ .

$z = \frac{9 \cdot 5}{11}$

Step 3.2.1.3

Multiply $9$ by $5$ .

$z = \frac{45}{11}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = \frac{45}{11}$

Decimal Form:

$z = 4.\overline{09}$

Mixed Number Form:

$z = 4 \frac{1}{11}$