Pre-Algebra Examples

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

Step 1

Multiply both sides of the equation by $\frac{3}{2}$ .

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

Step 2

Simplify both sides of the equation.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $\frac{3}{2} (\frac{2}{3} \cdot (a - 3))$ .

Tap for more steps...

Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

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

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

Step 2.1.1.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.1.1.3.1

Factor $3$ out of $- 3$ .

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

Step 2.1.1.3.2

Cancel the common factor.

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

Step 2.1.1.3.3

Rewrite the expression.

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

Step 2.1.1.4

Multiply $2$ by $- 1$ .

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

Step 2.1.1.5

Apply the distributive property.

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

Step 2.1.1.6

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.1.1.6.1

Cancel the common factor.

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

Step 2.1.1.6.2

Rewrite the expression.

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

Step 2.1.1.7

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.7.1

Factor $2$ out of $2 a$ .

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

Step 2.1.1.7.2

Cancel the common factor.

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

Step 2.1.1.7.3

Rewrite the expression.

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

Step 2.1.1.8

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.8.1

Factor $2$ out of $- 2$ .

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

Step 2.1.1.8.2

Cancel the common factor.

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

Step 2.1.1.8.3

Rewrite the expression.

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

Step 2.1.1.9

Multiply $3$ by $- 1$ .

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

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

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

Step 3

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

Tap for more steps...

Step 3.1

Add $3$ to both sides of the equation.

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Simplify the numerator.

Tap for more steps...

Step 3.5.1

Multiply $3$ by $2$ .

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

Step 3.5.2

Add $1$ and $6$ .

$a = \frac{7}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{7}{2}$

Decimal Form:

$a = 3.5$

Mixed Number Form:

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