Solve for n n-5/11=-1/3

$n - \frac{5}{11} = - \frac{1}{3}$

Step 1

Add $\frac{5}{11}$ to both sides of the equation.

$n = - \frac{1}{3} + \frac{5}{11}$

Step 2

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$n = - \frac{1}{3} \cdot \frac{11}{11} + \frac{5}{11}$

Step 3

To write $\frac{5}{11}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$n = - \frac{1}{3} \cdot \frac{11}{11} + \frac{5}{11} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $33$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{11}{11}$ .

$n = - \frac{11}{3 \cdot 11} + \frac{5}{11} \cdot \frac{3}{3}$

Multiply $3$ by $11$ .

$n = - \frac{11}{33} + \frac{5}{11} \cdot \frac{3}{3}$

Multiply $\frac{5}{11}$ by $\frac{3}{3}$ .

$n = - \frac{11}{33} + \frac{5 \cdot 3}{11 \cdot 3}$

Multiply $11$ by $3$ .

$n = - \frac{11}{33} + \frac{5 \cdot 3}{33}$

Step 5

Combine the numerators over the common denominator.

$n = \frac{- 11 + 5 \cdot 3}{33}$

Step 6

Simplify the numerator.

Multiply $5$ by $3$ .

$n = \frac{- 11 + 15}{33}$

Add $- 11$ and $15$ .

$n = \frac{4}{33}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$n = \frac{4}{33}$

Decimal Form:

$n = 0.\overline{12}$