Pre-Algebra Examples

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

Step 1

Combine $\frac{1}{3}$ and $a$ .

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

Step 2

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

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

Step 3

Move all terms containing $a$ to the left side of the equation.

Tap for more steps...

Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

Tap for more steps...

Step 3.3.1

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

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

Step 3.3.2

Multiply $3$ by $2$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Subtract $5 a$ from $a \cdot 2$ .

Tap for more steps...

Step 3.5.1

Reorder $a$ and $2$ .

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

Step 3.5.2

Subtract $5 a$ from $2 \cdot a$ .

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

Step 3.6

Simplify each term.

Tap for more steps...

Step 3.6.1

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

Tap for more steps...

Step 3.6.1.1

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

$\frac{3 (- a)}{6} - \frac{1}{4} = - \frac{3}{2}$

Step 3.6.1.2

Cancel the common factors.

Tap for more steps...

Step 3.6.1.2.1

Factor $3$ out of $6$ .

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

Step 3.6.1.2.2

Cancel the common factor.

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

Step 3.6.1.2.3

Rewrite the expression.

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

Step 3.6.2

Move the negative in front of the fraction.

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

Step 4

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

Tap for more steps...

Step 4.1

Add $\frac{1}{4}$ to both sides of the equation.

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

Step 4.2

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

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

Step 4.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.3.1

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

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

Step 4.3.2

Multiply $2$ by $2$ .

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Simplify the numerator.

Tap for more steps...

Step 4.5.1

Multiply $- 3$ by $2$ .

$- \frac{a}{2} = \frac{- 6 + 1}{4}$

Step 4.5.2

Add $- 6$ and $1$ .

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

Step 4.6

Move the negative in front of the fraction.

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

Step 5

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{a}{2}) = - 2 (- \frac{5}{4})$

Step 6

Simplify both sides of the equation.

Tap for more steps...

Step 6.1

Simplify the left side.

Tap for more steps...

Step 6.1.1

Simplify $- 2 (- \frac{a}{2})$ .

Tap for more steps...

Step 6.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.1.1.1.1

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

$- 2 \frac{- a}{2} = - 2 (- \frac{5}{4})$

Step 6.1.1.1.2

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- a}{2} = - 2 (- \frac{5}{4})$

Step 6.1.1.1.3

Cancel the common factor.

$2 \cdot - 1 \frac{- a}{2} = - 2 (- \frac{5}{4})$

Step 6.1.1.1.4

Rewrite the expression.

$- - a = - 2 (- \frac{5}{4})$

Step 6.1.1.2

Multiply.

Tap for more steps...

Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 a = - 2 (- \frac{5}{4})$

Step 6.1.1.2.2

Multiply $a$ by $1$ .

$a = - 2 (- \frac{5}{4})$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Simplify $- 2 (- \frac{5}{4})$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.2.1.1.1

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$a = - 2 (\frac{- 5}{4})$

Step 6.2.1.1.2

Factor $2$ out of $- 2$ .

$a = 2 (- 1) \frac{- 5}{4}$

Step 6.2.1.1.3

Factor $2$ out of $4$ .

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

Step 6.2.1.1.4

Cancel the common factor.

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

Step 6.2.1.1.5

Rewrite the expression.

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

Step 6.2.1.2

Move the negative in front of the fraction.

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

Step 6.2.1.3

Multiply $- - \frac{5}{2}$ .

Tap for more steps...

Step 6.2.1.3.1

Multiply $- 1$ by $- 1$ .

$a = 1 (\frac{5}{2})$

Step 6.2.1.3.2

Multiply $\frac{5}{2}$ by $1$ .

$a = \frac{5}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$a = \frac{5}{2}$

Decimal Form:

$a = 2.5$

Mixed Number Form:

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