Algebra Examples

$(- \frac{1}{8} c + 16) - (\frac{3}{8} + 3 c)$

Step 1

Simplify each term.

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Step 1.1

Combine $c$ and $\frac{1}{8}$ .

$- \frac{c}{8} + 16 - (\frac{3}{8} + 3 c)$

Step 1.2

Apply the distributive property.

$- \frac{c}{8} + 16 - \frac{3}{8} - (3 c)$

Step 1.3

Multiply $3$ by $- 1$ .

$- \frac{c}{8} + 16 - \frac{3}{8} - 3 c$

Step 2

To write $- 3 c$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{c}{8} - 3 c \cdot \frac{8}{8} + 16 - \frac{3}{8}$

Step 3

Combine $- 3 c$ and $\frac{8}{8}$ .

$- \frac{c}{8} + \frac{- 3 c \cdot 8}{8} + 16 - \frac{3}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{- c - 3 c \cdot 8}{8} + 16 - \frac{3}{8}$

Step 5

Combine the numerators over the common denominator.

$16 + \frac{- c - 3 c \cdot 8 - 3}{8}$

Step 6

Multiply $8$ by $- 3$ .

$16 + \frac{- c - 24 c - 3}{8}$

Step 7

Subtract $24 c$ from $- c$ .

$16 + \frac{- 25 c - 3}{8}$

Step 8

To write $16$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$16 \cdot \frac{8}{8} + \frac{- 25 c - 3}{8}$

Step 9

Simplify terms.

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Step 9.1

Combine $16$ and $\frac{8}{8}$ .

$\frac{16 \cdot 8}{8} + \frac{- 25 c - 3}{8}$

Step 9.2

Combine the numerators over the common denominator.

$\frac{16 \cdot 8 - 25 c - 3}{8}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $16$ by $8$ .

$\frac{128 - 25 c - 3}{8}$

Step 10.2

Subtract $3$ from $128$ .

$\frac{- 25 c + 125}{8}$

Step 10.3

Factor $25$ out of $- 25 c + 125$ .

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Step 10.3.1

Factor $25$ out of $- 25 c$ .

$\frac{25 (- c) + 125}{8}$

Step 10.3.2

Factor $25$ out of $125$ .

$\frac{25 (- c) + 25 (5)}{8}$

Step 10.3.3

Factor $25$ out of $25 (- c) + 25 (5)$ .

$\frac{25 (- c + 5)}{8}$

Step 11

Simplify with factoring out.

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Step 11.1

Factor $- 1$ out of $- c$ .

$\frac{25 (- (c) + 5)}{8}$

Step 11.2

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{25 (- (c) - 1 (- 5))}{8}$

Step 11.3

Factor $- 1$ out of $- (c) - 1 (- 5)$ .

$\frac{25 (- (c - 5))}{8}$

Step 11.4

Simplify the expression.

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Step 11.4.1

Rewrite $- (c - 5)$ as $- 1 (c - 5)$ .

$\frac{25 (- 1 (c - 5))}{8}$

Step 11.4.2

Move the negative in front of the fraction.

$- \frac{25 (c - 5)}{8}$