Algebra Examples

$\frac{1}{2} (6 e - 3 f - \frac{3}{4})$

Step 1

To write $6 e$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{2} \cdot (- 3 f + 6 e \cdot \frac{4}{4} - \frac{3}{4})$

Step 2

Combine $6 e$ and $\frac{4}{4}$ .

$\frac{1}{2} \cdot (- 3 f + \frac{6 e \cdot 4}{4} - \frac{3}{4})$

Step 3

Simplify the expression.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot (- 3 f + \frac{6 e \cdot 4 - 3}{4})$

Step 3.2

Multiply $4$ by $6$ .

$\frac{1}{2} \cdot (- 3 f + \frac{24 e - 3}{4})$

Step 4

To write $- 3 f$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{2} \cdot (- 3 f \cdot \frac{4}{4} + \frac{24 e - 3}{4})$

Step 5

Simplify terms.

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Step 5.1

Combine $- 3 f$ and $\frac{4}{4}$ .

$\frac{1}{2} \cdot (\frac{- 3 f \cdot 4}{4} + \frac{24 e - 3}{4})$

Step 5.2

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot \frac{- 3 f \cdot 4 + 24 e - 3}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $3$ out of $- 3 f \cdot 4 + 24 e - 3$ .

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Step 6.1.1

Factor $3$ out of $- 3 f \cdot 4$ .

$\frac{1}{2} \cdot \frac{3 (- f \cdot 4) + 24 e - 3}{4}$

Step 6.1.2

Factor $3$ out of $24 e$ .

$\frac{1}{2} \cdot \frac{3 (- f \cdot 4) + 3 (8 e) - 3}{4}$

Step 6.1.3

Factor $3$ out of $- 3$ .

$\frac{1}{2} \cdot \frac{3 (- f \cdot 4) + 3 (8 e) + 3 (- 1)}{4}$

Step 6.1.4

Factor $3$ out of $3 (- f \cdot 4) + 3 (8 e)$ .

$\frac{1}{2} \cdot \frac{3 (- f \cdot 4 + 8 e) + 3 (- 1)}{4}$

Step 6.1.5

Factor $3$ out of $3 (- f \cdot 4 + 8 e) + 3 (- 1)$ .

$\frac{1}{2} \cdot \frac{3 (- f \cdot 4 + 8 e - 1)}{4}$

Step 6.2

Multiply $4$ by $- 1$ .

$\frac{1}{2} \cdot \frac{3 (- 4 f + 8 e - 1)}{4}$

Step 7

Multiply $\frac{1}{2} \cdot \frac{3 (- 4 f + 8 e - 1)}{4}$ .

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Step 7.1

Multiply $\frac{1}{2}$ by $\frac{3 (- 4 f + 8 e - 1)}{4}$ .

$\frac{3 (- 4 f + 8 e - 1)}{2 \cdot 4}$

Step 7.2

Multiply $2$ by $4$ .

$\frac{3 (- 4 f + 8 e - 1)}{8}$

Step 8

Factor $- 1$ out of $- 4 f$ .

$\frac{3 (- (4 f) + 8 e - 1)}{8}$

Step 9

Factor $- 1$ out of $8 e$ .

$\frac{3 (- (4 f) - (- 8 e) - 1)}{8}$

Step 10

Factor $- 1$ out of $- (4 f) - (- 8 e)$ .

$\frac{3 (- (4 f - 8 e) - 1)}{8}$

Step 11

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

$\frac{3 (- (4 f - 8 e) - 1 (1))}{8}$

Step 12

Factor $- 1$ out of $- (4 f - 8 e) - 1 (1)$ .

$\frac{3 (- (4 f - 8 e + 1))}{8}$

Step 13

Simplify the expression.

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Step 13.1

Rewrite $- (4 f - 8 e + 1)$ as $- 1 (4 f - 8 e + 1)$ .

$\frac{3 (- 1 (4 f - 8 e + 1))}{8}$

Step 13.2

Move the negative in front of the fraction.

$- \frac{3 (4 f - 8 e + 1)}{8}$