Pre-Algebra Examples

$\frac{10}{7} k + \frac{9}{7} - 2 k + \frac{2}{7} + \frac{2}{7} k - 6$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{10}{7} k - 2 k + \frac{2}{7} k - 6 + \frac{9 + 2}{7}$

Step 1.2

Add $9$ and $2$ .

$\frac{10}{7} k - 2 k + \frac{2}{7} k - 6 + \frac{11}{7}$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{10}{7}$ and $k$ .

$\frac{10 k}{7} - 2 k + \frac{2}{7} k - 6 + \frac{11}{7}$

Step 2.2

Combine $\frac{2}{7}$ and $k$ .

$\frac{10 k}{7} - 2 k + \frac{2 k}{7} - 6 + \frac{11}{7}$

Step 3

Simplify terms.

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Step 3.1

Combine the numerators over the common denominator.

$- 2 k - 6 + \frac{10 k + 2 k + 11}{7}$

Step 3.2

Add $10 k$ and $2 k$ .

$- 2 k - 6 + \frac{12 k + 11}{7}$

Step 4

To write $- 2 k$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- 2 k \cdot \frac{7}{7} + \frac{12 k + 11}{7} - 6$

Step 5

Simplify terms.

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Step 5.1

Combine $- 2 k$ and $\frac{7}{7}$ .

$\frac{- 2 k \cdot 7}{7} + \frac{12 k + 11}{7} - 6$

Step 5.2

Combine the numerators over the common denominator.

$\frac{- 2 k \cdot 7 + 12 k + 11}{7} - 6$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $7$ by $- 2$ .

$\frac{- 14 k + 12 k + 11}{7} - 6$

Step 6.2

Add $- 14 k$ and $12 k$ .

$\frac{- 2 k + 11}{7} - 6$

Step 7

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{- 2 k + 11}{7} - 6 \cdot \frac{7}{7}$

Step 8

Simplify terms.

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Step 8.1

Combine $- 6$ and $\frac{7}{7}$ .

$\frac{- 2 k + 11}{7} + \frac{- 6 \cdot 7}{7}$

Step 8.2

Combine the numerators over the common denominator.

$\frac{- 2 k + 11 - 6 \cdot 7}{7}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $- 6$ by $7$ .

$\frac{- 2 k + 11 - 42}{7}$

Step 9.2

Subtract $42$ from $11$ .

$\frac{- 2 k - 31}{7}$

Step 10

Simplify with factoring out.

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Step 10.1

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

$\frac{- (2 k) - 31}{7}$

Step 10.2

Rewrite $- 31$ as $- 1 (31)$ .

$\frac{- (2 k) - 1 (31)}{7}$

Step 10.3

Factor $- 1$ out of $- (2 k) - 1 (31)$ .

$\frac{- (2 k + 31)}{7}$

Step 10.4

Simplify the expression.

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Step 10.4.1

Rewrite $- (2 k + 31)$ as $- 1 (2 k + 31)$ .

$\frac{- 1 (2 k + 31)}{7}$

Step 10.4.2

Move the negative in front of the fraction.

$- \frac{2 k + 31}{7}$