Pre-Algebra Examples

$\frac{5}{6} - \frac{a}{4} = \frac{1}{3}$

Step 1

Move all terms not containing $a$ to the right side of the equation.

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Step 1.1

Subtract $\frac{5}{6}$ from both sides of the equation.

$- \frac{a}{4} = \frac{1}{3} - \frac{5}{6}$

Step 1.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{a}{4} = \frac{1}{3} \cdot \frac{2}{2} - \frac{5}{6}$

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

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

$- \frac{a}{4} = \frac{2}{3 \cdot 2} - \frac{5}{6}$

Step 1.3.2

Multiply $3$ by $2$ .

$- \frac{a}{4} = \frac{2}{6} - \frac{5}{6}$

Step 1.4

Combine the numerators over the common denominator.

$- \frac{a}{4} = \frac{2 - 5}{6}$

Step 1.5

Subtract $5$ from $2$ .

$- \frac{a}{4} = \frac{- 3}{6}$

Step 1.6

Cancel the common factor of $- 3$ and $6$ .

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Step 1.6.1

Factor $3$ out of $- 3$ .

$- \frac{a}{4} = \frac{3 (- 1)}{6}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $3$ out of $6$ .

$- \frac{a}{4} = \frac{3 \cdot - 1}{3 \cdot 2}$

Step 1.6.2.2

Cancel the common factor.

$- \frac{a}{4} = \frac{3 \cdot - 1}{3 \cdot 2}$

Step 1.6.2.3

Rewrite the expression.

$- \frac{a}{4} = \frac{- 1}{2}$

Step 1.7

Move the negative in front of the fraction.

$- \frac{a}{4} = - \frac{1}{2}$

Step 2

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{a}{4}) = - 4 (- \frac{1}{2})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- 4 (- \frac{a}{4})$ .

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Step 3.1.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1.1

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

$- 4 \frac{- a}{4} = - 4 (- \frac{1}{2})$

Step 3.1.1.1.2

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- a}{4} = - 4 (- \frac{1}{2})$

Step 3.1.1.1.3

Cancel the common factor.

$4 \cdot - 1 \frac{- a}{4} = - 4 (- \frac{1}{2})$

Step 3.1.1.1.4

Rewrite the expression.

$- - a = - 4 (- \frac{1}{2})$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 a = - 4 (- \frac{1}{2})$

Step 3.1.1.2.2

Multiply $a$ by $1$ .

$a = - 4 (- \frac{1}{2})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- 4 (- \frac{1}{2})$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$a = - 4 (\frac{- 1}{2})$

Step 3.2.1.1.2

Factor $2$ out of $- 4$ .

$a = 2 (- 2) \frac{- 1}{2}$

Step 3.2.1.1.3

Cancel the common factor.

$a = 2 \cdot - 2 \frac{- 1}{2}$

Step 3.2.1.1.4

Rewrite the expression.

$a = - 2 \cdot - 1$

Step 3.2.1.2

Multiply $- 2$ by $- 1$ .

$a = 2$