Basic Math Examples

$\frac{6}{5} k + \frac{9}{5} - 2 k + \frac{2}{5} + \frac{2}{5} k - 6$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{6}{5} k - 2 k + \frac{2}{5} k - 6 + \frac{9 + 2}{5}$

Step 1.2

Add $9$ and $2$ .

$\frac{6}{5} k - 2 k + \frac{2}{5} k - 6 + \frac{11}{5}$

Step 2

Simplify each term.

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Step 2.1

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

$\frac{6 k}{5} - 2 k + \frac{2}{5} k - 6 + \frac{11}{5}$

Step 2.2

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

$\frac{6 k}{5} - 2 k + \frac{2 k}{5} - 6 + \frac{11}{5}$

Step 3

Simplify terms.

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Step 3.1

Combine the numerators over the common denominator.

$- 2 k - 6 + \frac{6 k + 2 k + 11}{5}$

Step 3.2

Add $6 k$ and $2 k$ .

$- 2 k - 6 + \frac{8 k + 11}{5}$

Step 4

Find the common denominator.

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Step 4.1

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

$\frac{- 2 k}{1} - 6 + \frac{8 k + 11}{5}$

Step 4.2

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

$\frac{- 2 k}{1} \cdot \frac{5}{5} - 6 + \frac{8 k + 11}{5}$

Step 4.3

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

$\frac{- 2 k \cdot 5}{5} - 6 + \frac{8 k + 11}{5}$

Step 4.4

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

$\frac{- 2 k \cdot 5}{5} + \frac{- 6}{1} + \frac{8 k + 11}{5}$

Step 4.5

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

$\frac{- 2 k \cdot 5}{5} + \frac{- 6}{1} \cdot \frac{5}{5} + \frac{8 k + 11}{5}$

Step 4.6

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

$\frac{- 2 k \cdot 5}{5} + \frac{- 6 \cdot 5}{5} + \frac{8 k + 11}{5}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 2 k \cdot 5 - 6 \cdot 5 + 8 k + 11}{5}$

Step 6

Simplify each term.

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Step 6.1

Multiply $5$ by $- 2$ .

$\frac{- 10 k - 6 \cdot 5 + 8 k + 11}{5}$

Step 6.2

Multiply $- 6$ by $5$ .

$\frac{- 10 k - 30 + 8 k + 11}{5}$

Step 7

Simplify terms.

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Step 7.1

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

$\frac{- 2 k - 30 + 11}{5}$

Step 7.2

Add $- 30$ and $11$ .

$\frac{- 2 k - 19}{5}$

Step 7.3

Factor $- 1$ out of $- 2 k$ .

$\frac{- (2 k) - 19}{5}$

Step 7.4

Rewrite $- 19$ as $- 1 (19)$ .

$\frac{- (2 k) - 1 (19)}{5}$

Step 7.5

Factor $- 1$ out of $- (2 k) - 1 (19)$ .

$\frac{- (2 k + 19)}{5}$

Step 7.6

Simplify the expression.

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Step 7.6.1

Rewrite $- (2 k + 19)$ as $- 1 (2 k + 19)$ .

$\frac{- 1 (2 k + 19)}{5}$

Step 7.6.2

Move the negative in front of the fraction.

$- \frac{2 k + 19}{5}$