Basic Math Examples

$\frac{7 + 7 k}{4} + \frac{1 + k}{8}$

Step 1

Factor $7$ out of $7 + 7 k$ .

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Step 1.1

Factor $7$ out of $7$ .

$\frac{7 \cdot 1 + 7 k}{4} + \frac{1 + k}{8}$

Step 1.2

Factor $7$ out of $7 \cdot 1 + 7 k$ .

$\frac{7 (1 + k)}{4} + \frac{1 + k}{8}$

Step 2

To write $\frac{7 (1 + k)}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 (1 + k)}{4} \cdot \frac{2}{2} + \frac{1 + k}{8}$

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 $\frac{7 (1 + k)}{4}$ by $\frac{2}{2}$ .

$\frac{7 (1 + k) \cdot 2}{4 \cdot 2} + \frac{1 + k}{8}$

Step 3.2

Multiply $4$ by $2$ .

$\frac{7 (1 + k) \cdot 2}{8} + \frac{1 + k}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 (1 + k) \cdot 2 + 1 + k}{8}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{(7 \cdot 1 + 7 k) \cdot 2 + 1 + k}{8}$

Step 5.2

Multiply $7$ by $1$ .

$\frac{(7 + 7 k) \cdot 2 + 1 + k}{8}$

Step 5.3

Apply the distributive property.

$\frac{7 \cdot 2 + 7 k \cdot 2 + 1 + k}{8}$

Step 5.4

Multiply $7$ by $2$ .

$\frac{14 + 7 k \cdot 2 + 1 + k}{8}$

Step 5.5

Multiply $2$ by $7$ .

$\frac{14 + 14 k + 1 + k}{8}$

Step 5.6

Add $14$ and $1$ .

$\frac{14 k + 15 + k}{8}$

Step 5.7

Add $14 k$ and $k$ .

$\frac{15 k + 15}{8}$

Step 5.8

Factor $15$ out of $15 k + 15$ .

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Step 5.8.1

Factor $15$ out of $15 k$ .

$\frac{15 (k) + 15}{8}$

Step 5.8.2

Factor $15$ out of $15$ .

$\frac{15 (k) + 15 (1)}{8}$

Step 5.8.3

Factor $15$ out of $15 (k) + 15 (1)$ .

$\frac{15 (k + 1)}{8}$