Algebra Examples

$\frac{14}{9} k + \frac{13}{9} - 2 k + \frac{2}{9} + \frac{2}{9} k - 6$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{14}{9} k - 2 k + \frac{2}{9} k - 6 + \frac{13 + 2}{9}$

Step 1.2

Add $13$ and $2$ .

$\frac{14}{9} k - 2 k + \frac{2}{9} k - 6 + \frac{15}{9}$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{14}{9}$ and $k$ .

$\frac{14 k}{9} - 2 k + \frac{2}{9} k - 6 + \frac{15}{9}$

Step 2.2

Combine $\frac{2}{9}$ and $k$ .

$\frac{14 k}{9} - 2 k + \frac{2 k}{9} - 6 + \frac{15}{9}$

Step 2.3

Cancel the common factor of $15$ and $9$ .

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Step 2.3.1

Factor $3$ out of $15$ .

$\frac{14 k}{9} - 2 k + \frac{2 k}{9} - 6 + \frac{3 (5)}{9}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $3$ out of $9$ .

$\frac{14 k}{9} - 2 k + \frac{2 k}{9} - 6 + \frac{3 \cdot 5}{3 \cdot 3}$

Step 2.3.2.2

Cancel the common factor.

$\frac{14 k}{9} - 2 k + \frac{2 k}{9} - 6 + \frac{3 \cdot 5}{3 \cdot 3}$

Step 2.3.2.3

Rewrite the expression.

$\frac{14 k}{9} - 2 k + \frac{2 k}{9} - 6 + \frac{5}{3}$

Step 3

Simplify terms.

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Step 3.1

Combine the numerators over the common denominator.

$- 2 k - 6 + \frac{14 k + 2 k}{9} + \frac{5}{3}$

Step 3.2

Add $14 k$ and $2 k$ .

$- 2 k - 6 + \frac{16 k}{9} + \frac{5}{3}$

Step 4

Find the common denominator.

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Step 4.1

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

$\frac{- 2 k}{1} - 6 + \frac{16 k}{9} + \frac{5}{3}$

Step 4.2

Multiply $\frac{- 2 k}{1}$ by $\frac{9}{9}$ .

$\frac{- 2 k}{1} \cdot \frac{9}{9} - 6 + \frac{16 k}{9} + \frac{5}{3}$

Step 4.3

Multiply $\frac{- 2 k}{1}$ by $\frac{9}{9}$ .

$\frac{- 2 k \cdot 9}{9} - 6 + \frac{16 k}{9} + \frac{5}{3}$

Step 4.4

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

$\frac{- 2 k \cdot 9}{9} + \frac{- 6}{1} + \frac{16 k}{9} + \frac{5}{3}$

Step 4.5

Multiply $\frac{- 6}{1}$ by $\frac{9}{9}$ .

$\frac{- 2 k \cdot 9}{9} + \frac{- 6}{1} \cdot \frac{9}{9} + \frac{16 k}{9} + \frac{5}{3}$

Step 4.6

Multiply $\frac{- 6}{1}$ by $\frac{9}{9}$ .

$\frac{- 2 k \cdot 9}{9} + \frac{- 6 \cdot 9}{9} + \frac{16 k}{9} + \frac{5}{3}$

Step 4.7

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

$\frac{- 2 k \cdot 9}{9} + \frac{- 6 \cdot 9}{9} + \frac{16 k}{9} + \frac{5}{3} \cdot \frac{3}{3}$

Step 4.8

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

$\frac{- 2 k \cdot 9}{9} + \frac{- 6 \cdot 9}{9} + \frac{16 k}{9} + \frac{5 \cdot 3}{3 \cdot 3}$

Step 4.9

Multiply $3$ by $3$ .

$\frac{- 2 k \cdot 9}{9} + \frac{- 6 \cdot 9}{9} + \frac{16 k}{9} + \frac{5 \cdot 3}{9}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 2 k \cdot 9 - 6 \cdot 9 + 16 k + 5 \cdot 3}{9}$

Step 6

Simplify each term.

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Step 6.1

Multiply $9$ by $- 2$ .

$\frac{- 18 k - 6 \cdot 9 + 16 k + 5 \cdot 3}{9}$

Step 6.2

Multiply $- 6$ by $9$ .

$\frac{- 18 k - 54 + 16 k + 5 \cdot 3}{9}$

Step 6.3

Multiply $5$ by $3$ .

$\frac{- 18 k - 54 + 16 k + 15}{9}$

Step 7

Simplify terms.

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Step 7.1

Add $- 18 k$ and $16 k$ .

$\frac{- 2 k - 54 + 15}{9}$

Step 7.2

Add $- 54$ and $15$ .

$\frac{- 2 k - 39}{9}$

Step 7.3

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

$\frac{- (2 k) - 39}{9}$

Step 7.4

Rewrite $- 39$ as $- 1 (39)$ .

$\frac{- (2 k) - 1 (39)}{9}$

Step 7.5

Factor $- 1$ out of $- (2 k) - 1 (39)$ .

$\frac{- (2 k + 39)}{9}$

Step 7.6

Simplify the expression.

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Step 7.6.1

Rewrite $- (2 k + 39)$ as $- 1 (2 k + 39)$ .

$\frac{- 1 (2 k + 39)}{9}$

Step 7.6.2

Move the negative in front of the fraction.

$- \frac{2 k + 39}{9}$