Basic Math Examples

$\frac{k}{3} = \frac{k}{6} + \frac{1}{2}$

Step 1

Multiply both sides by $3$ .

$\frac{k}{3} \cdot 3 = (\frac{k}{6} + \frac{1}{2}) \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{k}{3} \cdot 3 = (\frac{k}{6} + \frac{1}{2}) \cdot 3$

Step 2.1.1.2

Rewrite the expression.

$k = (\frac{k}{6} + \frac{1}{2}) \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{k}{6} + \frac{1}{2}) \cdot 3$ .

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Step 2.2.1.1

Apply the distributive property.

$k = \frac{k}{6} \cdot 3 + \frac{1}{2} \cdot 3$

Step 2.2.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.2.1

Factor $3$ out of $6$ .

$k = \frac{k}{3 (2)} \cdot 3 + \frac{1}{2} \cdot 3$

Step 2.2.1.2.2

Cancel the common factor.

$k = \frac{k}{3 \cdot 2} \cdot 3 + \frac{1}{2} \cdot 3$

Step 2.2.1.2.3

Rewrite the expression.

$k = \frac{k}{2} + \frac{1}{2} \cdot 3$

Step 2.2.1.3

Combine $\frac{1}{2}$ and $3$ .

$k = \frac{k}{2} + \frac{3}{2}$

Step 3

Solve for $k$ .

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Step 3.1

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

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Step 3.1.1

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

$k - \frac{k}{2} = \frac{3}{2}$

Step 3.1.2

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

$k \cdot \frac{2}{2} - \frac{k}{2} = \frac{3}{2}$

Step 3.1.3

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

$\frac{k \cdot 2}{2} - \frac{k}{2} = \frac{3}{2}$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{k \cdot 2 - k}{2} = \frac{3}{2}$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

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

$\frac{2 \cdot k - k}{2} = \frac{3}{2}$

Step 3.1.5.2

Subtract $k$ from $2 k$ .

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

Step 3.2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$k = 3$