Algebra Examples

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

Step 1

Rewrite the equation as $a - \frac{2}{3} = - \frac{5}{6}$ .

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

Step 2

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

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Step 2.1

Add $\frac{2}{3}$ to both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Multiply $3$ by $2$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $2$ .

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

Step 2.5.2

Add $- 5$ and $4$ .

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

Step 2.6

Move the negative in front of the fraction.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = - 0.1\overline{6}$