Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Add $6 k$ and $2 k$ .

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

Step 2.3

Factor $8$ out of $8 k + 8$ .

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Step 2.3.1

Factor $8$ out of $8 k$ .

$- 2 k - 5 + \frac{8 (k) + 8}{5}$

Step 2.3.2

Factor $8$ out of $8$ .

$- 2 k - 5 + \frac{8 (k) + 8 (1)}{5}$

Step 2.3.3

Factor $8$ out of $8 (k) + 8 (1)$ .

$- 2 k - 5 + \frac{8 (k + 1)}{5}$

Step 3

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

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

Step 4

Simplify terms.

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Step 4.1

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

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

Step 4.2

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Factor $2$ out of $- 2 k \cdot 5 + 8 (k + 1)$ .

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Step 5.1.1

Factor $2$ out of $- 2 k \cdot 5$ .

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

Step 5.1.2

Factor $2$ out of $8 (k + 1)$ .

$\frac{2 (- k \cdot 5) + 2 (4 (k + 1))}{5} - 5$

Step 5.1.3

Factor $2$ out of $2 (- k \cdot 5) + 2 (4 (k + 1))$ .

$\frac{2 (- k \cdot 5 + 4 (k + 1))}{5} - 5$

Step 5.2

Multiply $5$ by $- 1$ .

$\frac{2 (- 5 k + 4 (k + 1))}{5} - 5$

Step 5.3

Apply the distributive property.

$\frac{2 (- 5 k + 4 k + 4 \cdot 1)}{5} - 5$

Step 5.4

Multiply $4$ by $1$ .

$\frac{2 (- 5 k + 4 k + 4)}{5} - 5$

Step 5.5

Add $- 5 k$ and $4 k$ .

$\frac{2 (- k + 4)}{5} - 5$

Step 6

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

$\frac{2 (- k + 4)}{5} - 5 \cdot \frac{5}{5}$

Step 7

Simplify terms.

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Step 7.1

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

$\frac{2 (- k + 4)}{5} + \frac{- 5 \cdot 5}{5}$

Step 7.2

Combine the numerators over the common denominator.

$\frac{2 (- k + 4) - 5 \cdot 5}{5}$

Step 8

Simplify the numerator.

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Step 8.1

Apply the distributive property.

$\frac{2 (- k) + 2 \cdot 4 - 5 \cdot 5}{5}$

Step 8.2

Multiply $- 1$ by $2$ .

$\frac{- 2 k + 2 \cdot 4 - 5 \cdot 5}{5}$

Step 8.3

Multiply $2$ by $4$ .

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

Step 8.4

Multiply $- 5$ by $5$ .

$\frac{- 2 k + 8 - 25}{5}$

Step 8.5

Subtract $25$ from $8$ .

$\frac{- 2 k - 17}{5}$

Step 9

Simplify with factoring out.

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Step 9.1

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

$\frac{- (2 k) - 17}{5}$

Step 9.2

Rewrite $- 17$ as $- 1 (17)$ .

$\frac{- (2 k) - 1 (17)}{5}$

Step 9.3

Factor $- 1$ out of $- (2 k) - 1 (17)$ .

$\frac{- (2 k + 17)}{5}$

Step 9.4

Simplify the expression.

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Step 9.4.1

Rewrite $- (2 k + 17)$ as $- 1 (2 k + 17)$ .

$\frac{- 1 (2 k + 17)}{5}$

Step 9.4.2

Move the negative in front of the fraction.

$- \frac{2 k + 17}{5}$