Basic Math Examples

$\frac{1}{2} + 5 N = \frac{5}{6} - 6 N$

Step 1

Move all terms containing $N$ to the left side of the equation.

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Step 1.1

Add $6 N$ to both sides of the equation.

$\frac{1}{2} + 5 N + 6 N = \frac{5}{6}$

Step 1.2

Add $5 N$ and $6 N$ .

$\frac{1}{2} + 11 N = \frac{5}{6}$

Step 2

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

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Step 2.1

Subtract $\frac{1}{2}$ from both sides of the equation.

$11 N = \frac{5}{6} - \frac{1}{2}$

Step 2.2

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

$11 N = \frac{5}{6} - \frac{1}{2} \cdot \frac{3}{3}$

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

$11 N = \frac{5}{6} - \frac{3}{2 \cdot 3}$

Step 2.3.2

Multiply $2$ by $3$ .

$11 N = \frac{5}{6} - \frac{3}{6}$

Step 2.4

Combine the numerators over the common denominator.

$11 N = \frac{5 - 3}{6}$

Step 2.5

Subtract $3$ from $5$ .

$11 N = \frac{2}{6}$

Step 2.6

Cancel the common factor of $2$ and $6$ .

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Step 2.6.1

Factor $2$ out of $2$ .

$11 N = \frac{2 (1)}{6}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $2$ out of $6$ .

$11 N = \frac{2 \cdot 1}{2 \cdot 3}$

Step 2.6.2.2

Cancel the common factor.

$11 N = \frac{2 \cdot 1}{2 \cdot 3}$

Step 2.6.2.3

Rewrite the expression.

$11 N = \frac{1}{3}$

Step 3

Divide each term in $11 N = \frac{1}{3}$ by $11$ and simplify.

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Step 3.1

Divide each term in $11 N = \frac{1}{3}$ by $11$ .

$\frac{11 N}{11} = \frac{\frac{1}{3}}{11}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $11$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{11 N}{11} = \frac{\frac{1}{3}}{11}$

Step 3.2.1.2

Divide $N$ by $1$ .

$N = \frac{\frac{1}{3}}{11}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$N = \frac{1}{3} \cdot \frac{1}{11}$

Step 3.3.2

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

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Step 3.3.2.1

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

$N = \frac{1}{3 \cdot 11}$

Step 3.3.2.2

Multiply $3$ by $11$ .

$N = \frac{1}{33}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$N = \frac{1}{33}$

Decimal Form:

$N = 0.\overline{03}$