Solve for a 2/3a-1/6=1/3

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

Step 1

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

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

Step 2

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

Add $\frac{1}{6}$ to both sides of the equation.

$\frac{2 a}{3} = \frac{1}{3} + \frac{1}{6}$

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

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

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

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

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

Multiply $3$ by $2$ .

$\frac{2 a}{3} = \frac{2}{6} + \frac{1}{6}$

Combine the numerators over the common denominator.

$\frac{2 a}{3} = \frac{2 + 1}{6}$

Add $2$ and $1$ .

$\frac{2 a}{3} = \frac{3}{6}$

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

Factor $3$ out of $3$ .

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

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 a}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $2 a$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

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

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

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

Multiply $2$ by $2$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = 0.75$

Solve for a 2/3a-1/6=1/3

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