Algebra Examples

$\frac{5}{12} a - \frac{1}{4} (\frac{2}{3} a - 8)$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{5}{12}$ and $a$ .

$\frac{5 a}{12} - \frac{1}{4} \cdot (\frac{2}{3} a - 8)$

Step 1.2

Combine $\frac{2}{3}$ and $a$ .

$\frac{5 a}{12} - \frac{1}{4} \cdot (\frac{2 a}{3} - 8)$

Step 1.3

Apply the distributive property.

$\frac{5 a}{12} - \frac{1}{4} \cdot \frac{2 a}{3} - \frac{1}{4} \cdot - 8$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{5 a}{12} + \frac{- 1}{4} \cdot \frac{2 a}{3} - \frac{1}{4} \cdot - 8$

Step 1.4.2

Factor $2$ out of $4$ .

$\frac{5 a}{12} + \frac{- 1}{2 (2)} \cdot \frac{2 a}{3} - \frac{1}{4} \cdot - 8$

Step 1.4.3

Factor $2$ out of $2 a$ .

$\frac{5 a}{12} + \frac{- 1}{2 (2)} \cdot \frac{2 (a)}{3} - \frac{1}{4} \cdot - 8$

Step 1.4.4

Cancel the common factor.

$\frac{5 a}{12} + \frac{- 1}{2 \cdot 2} \cdot \frac{2 a}{3} - \frac{1}{4} \cdot - 8$

Step 1.4.5

Rewrite the expression.

$\frac{5 a}{12} + \frac{- 1}{2} \cdot \frac{a}{3} - \frac{1}{4} \cdot - 8$

Step 1.5

Multiply $\frac{- 1}{2}$ by $\frac{a}{3}$ .

$\frac{5 a}{12} + \frac{- a}{2 \cdot 3} - \frac{1}{4} \cdot - 8$

Step 1.6

Multiply $2$ by $3$ .

$\frac{5 a}{12} + \frac{- a}{6} - \frac{1}{4} \cdot - 8$

Step 1.7

Cancel the common factor of $4$ .

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Step 1.7.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{5 a}{12} + \frac{- a}{6} + \frac{- 1}{4} \cdot - 8$

Step 1.7.2

Factor $4$ out of $- 8$ .

$\frac{5 a}{12} + \frac{- a}{6} + \frac{- 1}{4} \cdot (4 (- 2))$

Step 1.7.3

Cancel the common factor.

$\frac{5 a}{12} + \frac{- a}{6} + \frac{- 1}{4} \cdot (4 \cdot - 2)$

Step 1.7.4

Rewrite the expression.

$\frac{5 a}{12} + \frac{- a}{6} - 1 \cdot - 2$

Step 1.8

Multiply $- 1$ by $- 2$ .

$\frac{5 a}{12} + \frac{- a}{6} + 2$

Step 1.9

Move the negative in front of the fraction.

$\frac{5 a}{12} - \frac{a}{6} + 2$

Step 2

To write $- \frac{a}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 a}{12} - \frac{a}{6} \cdot \frac{2}{2} + 2$

Step 3

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

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Step 3.1

Multiply $\frac{a}{6}$ by $\frac{2}{2}$ .

$\frac{5 a}{12} - \frac{a \cdot 2}{6 \cdot 2} + 2$

Step 3.2

Multiply $6$ by $2$ .

$\frac{5 a}{12} - \frac{a \cdot 2}{12} + 2$

Step 4

Combine the numerators over the common denominator.

$\frac{5 a - a \cdot 2}{12} + 2$

Step 5

Simplify each term.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

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

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Step 5.1.1.1

Factor $a$ out of $5 a$ .

$\frac{a \cdot 5 - a \cdot 2}{12} + 2$

Step 5.1.1.2

Factor $a$ out of $- a \cdot 2$ .

$\frac{a \cdot 5 + a (- 1 \cdot 2)}{12} + 2$

Step 5.1.1.3

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

$\frac{a (5 - 1 \cdot 2)}{12} + 2$

Step 5.1.2

Multiply $- 1$ by $2$ .

$\frac{a (5 - 2)}{12} + 2$

Step 5.1.3

Subtract $2$ from $5$ .

$\frac{a \cdot 3}{12} + 2$

Step 5.2

Cancel the common factor of $3$ and $12$ .

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Step 5.2.1

Factor $3$ out of $a \cdot 3$ .

$\frac{3 \cdot a}{12} + 2$

Step 5.2.2

Cancel the common factors.

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Step 5.2.2.1

Factor $3$ out of $12$ .

$\frac{3 \cdot a}{3 \cdot 4} + 2$

Step 5.2.2.2

Cancel the common factor.

$\frac{3 \cdot a}{3 \cdot 4} + 2$

Step 5.2.2.3

Rewrite the expression.

$\frac{a}{4} + 2$