Algebra Examples

$\frac{11}{12} - \frac{1}{6} q + \frac{5}{6} q - \frac{1}{3}$

Step 1

Simplify each term.

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Step 1.1

Combine $q$ and $\frac{1}{6}$ .

$\frac{11}{12} - \frac{q}{6} + \frac{5}{6} q - \frac{1}{3}$

Step 1.2

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

$\frac{11}{12} - \frac{q}{6} + \frac{5 q}{6} - \frac{1}{3}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{11}{12} + \frac{- q + 5 q}{6} + \frac{- 1}{3}$

Step 2.2

Add $- q$ and $5 q$ .

$\frac{11}{12} + \frac{4 q}{6} + \frac{- 1}{3}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{4 q}{6}$ by $\frac{2}{2}$ .

$\frac{11}{12} + \frac{4 q}{6} \cdot \frac{2}{2} + \frac{- 1}{3}$

Step 3.2

Multiply $\frac{4 q}{6}$ by $\frac{2}{2}$ .

$\frac{11}{12} + \frac{4 q \cdot 2}{6 \cdot 2} + \frac{- 1}{3}$

Step 3.3

Multiply $\frac{- 1}{3}$ by $\frac{4}{4}$ .

$\frac{11}{12} + \frac{4 q \cdot 2}{6 \cdot 2} + \frac{- 1}{3} \cdot \frac{4}{4}$

Step 3.4

Multiply $\frac{- 1}{3}$ by $\frac{4}{4}$ .

$\frac{11}{12} + \frac{4 q \cdot 2}{6 \cdot 2} + \frac{- 1 \cdot 4}{3 \cdot 4}$

Step 3.5

Reorder the factors of $6 \cdot 2$ .

$\frac{11}{12} + \frac{4 q \cdot 2}{2 \cdot 6} + \frac{- 1 \cdot 4}{3 \cdot 4}$

Step 3.6

Multiply $2$ by $6$ .

$\frac{11}{12} + \frac{4 q \cdot 2}{12} + \frac{- 1 \cdot 4}{3 \cdot 4}$

Step 3.7

Multiply $3$ by $4$ .

$\frac{11}{12} + \frac{4 q \cdot 2}{12} + \frac{- 1 \cdot 4}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{11 + 4 q \cdot 2 - 1 \cdot 4}{12}$

Step 5

Simplify each term.

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Step 5.1

Multiply $2$ by $4$ .

$\frac{11 + 8 q - 1 \cdot 4}{12}$

Step 5.2

Multiply $- 1$ by $4$ .

$\frac{11 + 8 q - 4}{12}$

Step 6

Subtract $4$ from $11$ .

$\frac{8 q + 7}{12}$