Algebra Examples

$8 + \frac{2}{3} k - \frac{4}{15} k - \frac{1}{4}$

Step 1

Simplify each term.

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Step 1.1

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

$8 + \frac{2 k}{3} - \frac{4}{15} k - \frac{1}{4}$

Step 1.2

Combine $k$ and $\frac{4}{15}$ .

$8 + \frac{2 k}{3} - \frac{k \cdot 4}{15} - \frac{1}{4}$

Step 1.3

Move $4$ to the left of $k$ .

$8 + \frac{2 k}{3} - \frac{4 k}{15} - \frac{1}{4}$

Step 2

To write $8$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{2 k}{3} - \frac{4 k}{15} + 8 \cdot \frac{4}{4} - \frac{1}{4}$

Step 3

Combine $8$ and $\frac{4}{4}$ .

$\frac{2 k}{3} - \frac{4 k}{15} + \frac{8 \cdot 4}{4} - \frac{1}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 k}{3} - \frac{4 k}{15} + \frac{8 \cdot 4 - 1}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $8$ by $4$ .

$\frac{2 k}{3} - \frac{4 k}{15} + \frac{32 - 1}{4}$

Step 5.2

Subtract $1$ from $32$ .

$\frac{2 k}{3} - \frac{4 k}{15} + \frac{31}{4}$

Step 6

To write $\frac{2 k}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 k}{3} \cdot \frac{5}{5} - \frac{4 k}{15} + \frac{31}{4}$

Step 7

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{2 k}{3}$ by $\frac{5}{5}$ .

$\frac{2 k \cdot 5}{3 \cdot 5} - \frac{4 k}{15} + \frac{31}{4}$

Step 7.2

Multiply $3$ by $5$ .

$\frac{2 k \cdot 5}{15} - \frac{4 k}{15} + \frac{31}{4}$

Step 8

Combine the numerators over the common denominator.

$\frac{2 k \cdot 5 - 4 k}{15} + \frac{31}{4}$

Step 9

Simplify each term.

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Step 9.1

Simplify the numerator.

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Step 9.1.1

Factor $2 k$ out of $2 k \cdot 5 - 4 k$ .

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Step 9.1.1.1

Factor $2 k$ out of $2 k \cdot 5$ .

$\frac{2 k (5) - 4 k}{15} + \frac{31}{4}$

Step 9.1.1.2

Factor $2 k$ out of $- 4 k$ .

$\frac{2 k (5) + 2 k (- 2)}{15} + \frac{31}{4}$

Step 9.1.1.3

Factor $2 k$ out of $2 k (5) + 2 k (- 2)$ .

$\frac{2 k (5 - 2)}{15} + \frac{31}{4}$

Step 9.1.2

Subtract $2$ from $5$ .

$\frac{2 k \cdot 3}{15} + \frac{31}{4}$

Step 9.1.3

Multiply $3$ by $2$ .

$\frac{6 k}{15} + \frac{31}{4}$

Step 9.2

Cancel the common factor of $6$ and $15$ .

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Step 9.2.1

Factor $3$ out of $6 k$ .

$\frac{3 (2 k)}{15} + \frac{31}{4}$

Step 9.2.2

Cancel the common factors.

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Step 9.2.2.1

Factor $3$ out of $15$ .

$\frac{3 (2 k)}{3 (5)} + \frac{31}{4}$

Step 9.2.2.2

Cancel the common factor.

$\frac{3 (2 k)}{3 \cdot 5} + \frac{31}{4}$

Step 9.2.2.3

Rewrite the expression.

$\frac{2 k}{5} + \frac{31}{4}$