Basic Math Examples

$3 k + \frac{4}{9} = \frac{1}{2} k + \frac{22}{9}$

Step 1

Combine $\frac{1}{2}$ and $k$ .

$3 k + \frac{4}{9} = \frac{k}{2} + \frac{22}{9}$

Step 2

Move all terms containing $k$ to the left side of the equation.

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Step 2.1

Subtract $\frac{k}{2}$ from both sides of the equation.

$3 k + \frac{4}{9} - \frac{k}{2} = \frac{22}{9}$

Step 2.2

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

$3 k \cdot \frac{2}{2} - \frac{k}{2} + \frac{4}{9} = \frac{22}{9}$

Step 2.3

Combine $3 k$ and $\frac{2}{2}$ .

$\frac{3 k \cdot 2}{2} - \frac{k}{2} + \frac{4}{9} = \frac{22}{9}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 k \cdot 2 - k}{2} + \frac{4}{9} = \frac{22}{9}$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $k$ out of $3 k \cdot 2 - k$ .

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Step 2.5.1.1.1

Factor $k$ out of $3 k \cdot 2$ .

$\frac{k (3 \cdot 2) - k}{2} + \frac{4}{9} = \frac{22}{9}$

Step 2.5.1.1.2

Factor $k$ out of $- k$ .

$\frac{k (3 \cdot 2) + k \cdot - 1}{2} + \frac{4}{9} = \frac{22}{9}$

Step 2.5.1.1.3

Factor $k$ out of $k (3 \cdot 2) + k \cdot - 1$ .

$\frac{k (3 \cdot 2 - 1)}{2} + \frac{4}{9} = \frac{22}{9}$

Step 2.5.1.2

Multiply $3$ by $2$ .

$\frac{k (6 - 1)}{2} + \frac{4}{9} = \frac{22}{9}$

Step 2.5.1.3

Subtract $1$ from $6$ .

$\frac{k \cdot 5}{2} + \frac{4}{9} = \frac{22}{9}$

Step 2.5.2

Move $5$ to the left of $k$ .

$\frac{5 k}{2} + \frac{4}{9} = \frac{22}{9}$

Step 3

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

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Step 3.1

Subtract $\frac{4}{9}$ from both sides of the equation.

$\frac{5 k}{2} = \frac{22}{9} - \frac{4}{9}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{5 k}{2} = \frac{22 - 4}{9}$

Step 3.3

Subtract $4$ from $22$ .

$\frac{5 k}{2} = \frac{18}{9}$

Step 3.4

Divide $18$ by $9$ .

$\frac{5 k}{2} = 2$

Step 4

Multiply both sides of the equation by $\frac{2}{5}$ .

$\frac{2}{5} \cdot \frac{5 k}{2} = \frac{2}{5} \cdot 2$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{2}{5} \cdot \frac{5 k}{2}$ .

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 k}{2} = \frac{2}{5} \cdot 2$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 k) = \frac{2}{5} \cdot 2$

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $5 k$ .

$\frac{1}{5} (5 (k)) = \frac{2}{5} \cdot 2$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 k) = \frac{2}{5} \cdot 2$

Step 5.1.1.2.3

Rewrite the expression.

$k = \frac{2}{5} \cdot 2$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{2}{5} \cdot 2$ .

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Step 5.2.1.1

Combine $\frac{2}{5}$ and $2$ .

$k = \frac{2 \cdot 2}{5}$

Step 5.2.1.2

Multiply $2$ by $2$ .

$k = \frac{4}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$k = \frac{4}{5}$

Decimal Form:

$k = 0.8$