Algebra Examples

$\frac{3}{4} k + \frac{3}{8} k = \frac{1}{2}$

Step 1

Simplify $\frac{3}{4} k + \frac{3}{8} k$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{3}{4}$ and $k$ .

$\frac{3 k}{4} + \frac{3}{8} k = \frac{1}{2}$

Step 1.1.2

Combine $\frac{3}{8}$ and $k$ .

$\frac{3 k}{4} + \frac{3 k}{8} = \frac{1}{2}$

Step 1.2

To write $\frac{3 k}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 k}{4} \cdot \frac{2}{2} + \frac{3 k}{8} = \frac{1}{2}$

Step 1.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{3 k}{4}$ by $\frac{2}{2}$ .

$\frac{3 k \cdot 2}{4 \cdot 2} + \frac{3 k}{8} = \frac{1}{2}$

Step 1.3.2

Multiply $4$ by $2$ .

$\frac{3 k \cdot 2}{8} + \frac{3 k}{8} = \frac{1}{2}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 k \cdot 2 + 3 k}{8} = \frac{1}{2}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

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

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Step 1.5.1.1

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

$\frac{3 k (2) + 3 k}{8} = \frac{1}{2}$

Step 1.5.1.2

Factor $3 k$ out of $3 k$ .

$\frac{3 k (2) + 3 k (1)}{8} = \frac{1}{2}$

Step 1.5.1.3

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

$\frac{3 k (2 + 1)}{8} = \frac{1}{2}$

Step 1.5.2

Add $2$ and $1$ .

$\frac{3 k \cdot 3}{8} = \frac{1}{2}$

Step 1.5.3

Multiply $3$ by $3$ .

$\frac{9 k}{8} = \frac{1}{2}$

Step 2

Multiply both sides of the equation by $\frac{8}{9}$ .

$\frac{8}{9} \cdot \frac{9 k}{8} = \frac{8}{9} \cdot \frac{1}{2}$

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 $\frac{8}{9} \cdot \frac{9 k}{8}$ .

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Step 3.1.1.1

Cancel the common factor of $8$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{8}{9} \cdot \frac{9 k}{8} = \frac{8}{9} \cdot \frac{1}{2}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 k) = \frac{8}{9} \cdot \frac{1}{2}$

Step 3.1.1.2

Cancel the common factor of $9$ .

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Step 3.1.1.2.1

Factor $9$ out of $9 k$ .

$\frac{1}{9} (9 (k)) = \frac{8}{9} \cdot \frac{1}{2}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 k) = \frac{8}{9} \cdot \frac{1}{2}$

Step 3.1.1.2.3

Rewrite the expression.

$k = \frac{8}{9} \cdot \frac{1}{2}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Factor $2$ out of $8$ .

$k = \frac{2 (4)}{9} \cdot \frac{1}{2}$

Step 3.2.1.2

Cancel the common factor.

$k = \frac{2 \cdot 4}{9} \cdot \frac{1}{2}$

Step 3.2.1.3

Rewrite the expression.

$k = \frac{4}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$k = \frac{4}{9}$

Decimal Form:

$k = 0.\overline{4}$