Solve for a 5/6=5/6a+1/3

$\frac{5}{6} = \frac{5}{6} a + \frac{1}{3}$

Step 1

Rewrite the equation as $\frac{5}{6} a + \frac{1}{3} = \frac{5}{6}$ .

$\frac{5}{6} a + \frac{1}{3} = \frac{5}{6}$

Step 2

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

$\frac{5 a}{6} + \frac{1}{3} = \frac{5}{6}$

Step 3

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

Subtract $\frac{1}{3}$ from both sides of the equation.

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

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

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

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

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

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

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

Subtract $2$ from $5$ .

$\frac{5 a}{6} = \frac{3}{6}$

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

Factor $3$ out of $3$ .

$\frac{5 a}{6} = \frac{3 (1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 a}{6} = \frac{1}{2}$

Step 4

Multiply both sides of the equation by $\frac{6}{5}$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{5} \cdot \frac{5 a}{6}$ .

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{5} (5 a) = \frac{6}{5} \cdot \frac{1}{2}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 a$ .

$\frac{1}{5} (5 (a)) = \frac{6}{5} \cdot \frac{1}{2}$

Cancel the common factor.

$\frac{1}{5} (5 a) = \frac{6}{5} \cdot \frac{1}{2}$

Rewrite the expression.

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

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$a = \frac{2 (3)}{5} \cdot \frac{1}{2}$

Cancel the common factor.

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

Rewrite the expression.

$a = \frac{3}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = \frac{3}{5}$

Decimal Form:

$a = 0.6$

Solve for a 5/6=5/6a+1/3

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