Basic Math Examples

$\frac{- 5}{3} k + 3 - 2 k + \frac{7}{3} + \frac{2}{3} k - \frac{2}{3}$

Step 1

Regroup terms.

$\frac{- 5}{3} k + 3 - 2 k + \frac{7}{3} + \frac{2}{3} k - \frac{2}{3}$

Step 2

Factor $\frac{1}{3}$ out of each term.

$\frac{1}{3} (- 5 k + 9 - 6 k) + \frac{7}{3} + \frac{2}{3} k - \frac{2}{3}$

Step 3

Factor $\frac{1}{3}$ out of each term.

$\frac{1}{3} (- 5 k + 9 - 6 k) + \frac{1}{3} (7 + 2 k - 1 \cdot 2)$

Step 4

Factor $\frac{1}{3}$ out of $\frac{1}{3} (- 5 k + 9 - 6 k) + \frac{1}{3} (7 + 2 k - 1 \cdot 2)$ .

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Step 4.1

Reorder the expression.

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Step 4.1.1

Move $9$ .

$\frac{1}{3} (- 5 k - 6 k + 9) + \frac{1}{3} (7 + 2 k - 1 \cdot 2)$

Step 4.1.2

Reorder $7$ and $2 k$ .

$\frac{1}{3} (- 5 k - 6 k + 9) + \frac{1}{3} (2 k + 7 - 1 \cdot 2)$

Step 4.2

Factor $\frac{1}{3}$ out of $\frac{1}{3} (- 5 k - 6 k + 9) + \frac{1}{3} (2 k + 7 - 1 \cdot 2)$ .

$\frac{1}{3} (- 5 k - 6 k + 9 + 2 k + 7 - 1 \cdot 2)$

Step 5

Multiply $- 1$ by $2$ .

$\frac{1}{3} (- 5 k - 6 k + 9 + 2 k + 7 - 2)$

Step 6

Subtract $6 k$ from $- 5 k$ .

$\frac{1}{3} (- 11 k + 9 + 2 k + 7 - 2)$

Step 7

Add $- 11 k$ and $2 k$ .

$\frac{1}{3} (- 9 k + 9 + 7 - 2)$

Step 8

Add $9$ and $7$ .

$\frac{1}{3} (- 9 k + 16 - 2)$

Step 9

Subtract $2$ from $16$ .

$\frac{1}{3} (- 9 k + 14)$

Step 10

Factor.

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Step 10.1

Factor $- 1$ out of $- 9 k + 14$ .

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Step 10.1.1

Factor $- 1$ out of $- 9 k$ .

$\frac{1}{3} \cdot (- (9 k) + 14)$

Step 10.1.2

Rewrite $14$ as $- 1 (- 14)$ .

$\frac{1}{3} \cdot (- (9 k) - 1 (- 14))$

Step 10.1.3

Factor $- 1$ out of $- (9 k) - 1 (- 14)$ .

$\frac{1}{3} \cdot (- (9 k - 14))$

Step 10.2

Remove unnecessary parentheses.

$\frac{1}{3} \cdot - 1 (9 k - 14)$

Step 11

Factor out negative.

$- (\frac{1}{3} (9 k - 14))$

Step 12

Remove unnecessary parentheses.

$- \frac{1}{3} \cdot (9 k - 14)$