Pre-Algebra Examples

$\frac{6}{5} k + \frac{8}{5} - 2 k + \frac{2}{5} + \frac{2}{5} k - 6$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{6}{5} k - 2 k + \frac{2}{5} k - 6 + \frac{8 + 2}{5}$

Step 1.2

Add $8$ and $2$ .

$\frac{6}{5} k - 2 k + \frac{2}{5} k - 6 + \frac{10}{5}$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{6}{5}$ and $k$ .

$\frac{6 k}{5} - 2 k + \frac{2}{5} k - 6 + \frac{10}{5}$

Step 2.2

Combine $\frac{2}{5}$ and $k$ .

$\frac{6 k}{5} - 2 k + \frac{2 k}{5} - 6 + \frac{10}{5}$

Step 2.3

Divide $10$ by $5$ .

$\frac{6 k}{5} - 2 k + \frac{2 k}{5} - 6 + 2$

Step 3

Simplify terms.

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Step 3.1

Combine the numerators over the common denominator.

$- 2 k - 6 + 2 + \frac{6 k + 2 k}{5}$

Step 3.2

Add $6 k$ and $2 k$ .

$- 2 k - 6 + 2 + \frac{8 k}{5}$

Step 4

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

$- 2 k \cdot \frac{5}{5} + \frac{8 k}{5} - 6 + 2$

Step 5

Combine $- 2 k$ and $\frac{5}{5}$ .

$\frac{- 2 k \cdot 5}{5} + \frac{8 k}{5} - 6 + 2$

Step 6

Combine the numerators over the common denominator.

$\frac{- 2 k \cdot 5 + 8 k}{5} - 6 + 2$

Step 7

Find the common denominator.

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Step 7.1

Write $- 6$ as a fraction with denominator $1$ .

$\frac{- 2 k \cdot 5 + 8 k}{5} + \frac{- 6}{1} + 2$

Step 7.2

Multiply $\frac{- 6}{1}$ by $\frac{5}{5}$ .

$\frac{- 2 k \cdot 5 + 8 k}{5} + \frac{- 6}{1} \cdot \frac{5}{5} + 2$

Step 7.3

Multiply $\frac{- 6}{1}$ by $\frac{5}{5}$ .

$\frac{- 2 k \cdot 5 + 8 k}{5} + \frac{- 6 \cdot 5}{5} + 2$

Step 7.4

Write $2$ as a fraction with denominator $1$ .

$\frac{- 2 k \cdot 5 + 8 k}{5} + \frac{- 6 \cdot 5}{5} + \frac{2}{1}$

Step 7.5

Multiply $\frac{2}{1}$ by $\frac{5}{5}$ .

$\frac{- 2 k \cdot 5 + 8 k}{5} + \frac{- 6 \cdot 5}{5} + \frac{2}{1} \cdot \frac{5}{5}$

Step 7.6

Multiply $\frac{2}{1}$ by $\frac{5}{5}$ .

$\frac{- 2 k \cdot 5 + 8 k}{5} + \frac{- 6 \cdot 5}{5} + \frac{2 \cdot 5}{5}$

Step 8

Combine the numerators over the common denominator.

$\frac{- 2 k \cdot 5 + 8 k - 6 \cdot 5 + 2 \cdot 5}{5}$

Step 9

Simplify each term.

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Step 9.1

Multiply $5$ by $- 2$ .

$\frac{- 10 k + 8 k - 6 \cdot 5 + 2 \cdot 5}{5}$

Step 9.2

Multiply $- 6$ by $5$ .

$\frac{- 10 k + 8 k - 30 + 2 \cdot 5}{5}$

Step 9.3

Multiply $2$ by $5$ .

$\frac{- 10 k + 8 k - 30 + 10}{5}$

Step 10

Simplify terms.

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Step 10.1

Add $- 10 k$ and $8 k$ .

$\frac{- 2 k - 30 + 10}{5}$

Step 10.2

Add $- 30$ and $10$ .

$\frac{- 2 k - 20}{5}$

Step 10.3

Factor $2$ out of $- 2 k - 20$ .

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Step 10.3.1

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

$\frac{2 (- k) - 20}{5}$

Step 10.3.2

Factor $2$ out of $- 20$ .

$\frac{2 (- k) + 2 (- 10)}{5}$

Step 10.3.3

Factor $2$ out of $2 (- k) + 2 (- 10)$ .

$\frac{2 (- k - 10)}{5}$

Step 10.4

Factor $- 1$ out of $- k$ .

$\frac{2 (- (k) - 10)}{5}$

Step 10.5

Rewrite $- 10$ as $- 1 (10)$ .

$\frac{2 (- (k) - 1 (10))}{5}$

Step 10.6

Factor $- 1$ out of $- (k) - 1 (10)$ .

$\frac{2 (- (k + 10))}{5}$

Step 10.7

Simplify the expression.

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Step 10.7.1

Rewrite $- (k + 10)$ as $- 1 (k + 10)$ .

$\frac{2 (- 1 (k + 10))}{5}$

Step 10.7.2

Move the negative in front of the fraction.

$- \frac{2 (k + 10)}{5}$