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

Simplify each term.

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Step 3.1

Cancel the common factor of $4$ and $6$ .

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Step 3.1.1

Factor $2$ out of $4 q$ .

$\frac{11}{12} + \frac{2 (2 q)}{6} + \frac{- 1}{3}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $2$ out of $6$ .

$\frac{11}{12} + \frac{2 (2 q)}{2 (3)} + \frac{- 1}{3}$

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

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

Step 3.2

Move the negative in front of the fraction.

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

Step 4

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 5

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

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

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

Step 5.2

Multiply $3$ by $4$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Subtract $4$ from $11$ .

$\frac{2 q}{3} + \frac{7}{12}$