Basic Math Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Add $\frac{1}{3}$ to both sides of the equation.

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

Step 2.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2.3

Combine $- 4$ and $\frac{3}{3}$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 4$ by $3$ .

$\frac{a}{3} = \frac{- 12 + 1}{3}$

Step 2.5.2

Add $- 12$ and $1$ .

$\frac{a}{3} = \frac{- 11}{3}$

Step 2.6

Move the negative in front of the fraction.

$\frac{a}{3} = - \frac{11}{3}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$a = - 11$