Basic Math Examples

$\frac{n}{2} - 1 = \frac{n}{6} + 1$

Step 1

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

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Step 1.1

Subtract $\frac{n}{6}$ from both sides of the equation.

$\frac{n}{2} - 1 - \frac{n}{6} = 1$

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $3$ .

$\frac{n \cdot 3}{6} - \frac{n}{6} - 1 = 1$

Step 1.4

Combine the numerators over the common denominator.

$\frac{n \cdot 3 - n}{6} - 1 = 1$

Step 1.5

Subtract $n$ from $n \cdot 3$ .

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Step 1.5.1

Reorder $n$ and $3$ .

$\frac{3 \cdot n - n}{6} - 1 = 1$

Step 1.5.2

Subtract $n$ from $3 \cdot n$ .

$\frac{2 \cdot n}{6} - 1 = 1$

Step 1.6

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

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Step 1.6.1

Factor $2$ out of $2 \cdot n$ .

$\frac{2 (n)}{6} - 1 = 1$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $2$ out of $6$ .

$\frac{2 n}{2 \cdot 3} - 1 = 1$

Step 1.6.2.2

Cancel the common factor.

$\frac{2 n}{2 \cdot 3} - 1 = 1$

Step 1.6.2.3

Rewrite the expression.

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

Step 2

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

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Step 2.1

Add $1$ to both sides of the equation.

$\frac{n}{3} = 1 + 1$

Step 2.2

Add $1$ and $1$ .

$\frac{n}{3} = 2$

Step 3

Multiply both sides of the equation by $3$ .

$3 \frac{n}{3} = 3 \cdot 2$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1

Cancel the common factor.

$3 \frac{n}{3} = 3 \cdot 2$

Step 4.1.1.2

Rewrite the expression.

$n = 3 \cdot 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $3$ by $2$ .

$n = 6$