Pre-Algebra Examples

$\frac{5 + 5 k}{4} + \frac{1 + k}{8}$

Step 1

Factor $5$ out of $5 + 5 k$ .

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Step 1.1

Factor $5$ out of $5$ .

$\frac{5 \cdot 1 + 5 k}{4} + \frac{1 + k}{8}$

Step 1.2

Factor $5$ out of $5 \cdot 1 + 5 k$ .

$\frac{5 (1 + k)}{4} + \frac{1 + k}{8}$

Step 2

To write $\frac{5 (1 + k)}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 (1 + k)}{4} \cdot \frac{2}{2} + \frac{1 + k}{8}$

Step 3

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

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Step 3.1

Multiply $\frac{5 (1 + k)}{4}$ by $\frac{2}{2}$ .

$\frac{5 (1 + k) \cdot 2}{4 \cdot 2} + \frac{1 + k}{8}$

Step 3.2

Multiply $4$ by $2$ .

$\frac{5 (1 + k) \cdot 2}{8} + \frac{1 + k}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 (1 + k) \cdot 2 + 1 + k}{8}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{(5 \cdot 1 + 5 k) \cdot 2 + 1 + k}{8}$

Step 5.2

Multiply $5$ by $1$ .

$\frac{(5 + 5 k) \cdot 2 + 1 + k}{8}$

Step 5.3

Apply the distributive property.

$\frac{5 \cdot 2 + 5 k \cdot 2 + 1 + k}{8}$

Step 5.4

Multiply $5$ by $2$ .

$\frac{10 + 5 k \cdot 2 + 1 + k}{8}$

Step 5.5

Multiply $2$ by $5$ .

$\frac{10 + 10 k + 1 + k}{8}$

Step 5.6

Add $10$ and $1$ .

$\frac{10 k + 11 + k}{8}$

Step 5.7

Add $10 k$ and $k$ .

$\frac{11 k + 11}{8}$

Step 5.8

Factor $11$ out of $11 k + 11$ .

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Step 5.8.1

Factor $11$ out of $11 k$ .

$\frac{11 (k) + 11}{8}$

Step 5.8.2

Factor $11$ out of $11$ .

$\frac{11 (k) + 11 (1)}{8}$

Step 5.8.3

Factor $11$ out of $11 (k) + 11 (1)$ .

$\frac{11 (k + 1)}{8}$