Basic Math Examples

$\frac{1}{2} n + 10 = - \frac{1}{4} n + 54$

Step 1

Combine $\frac{1}{2}$ and $n$ .

$\frac{n}{2} + 10 = - \frac{1}{4} n + 54$

Step 2

Combine $n$ and $\frac{1}{4}$ .

$\frac{n}{2} + 10 = - \frac{n}{4} + 54$

Step 3

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

Tap for more steps...

Step 3.1

Add $\frac{n}{4}$ to both sides of the equation.

$\frac{n}{2} + 10 + \frac{n}{4} = 54$

Step 3.2

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

$\frac{n}{2} \cdot \frac{2}{2} + \frac{n}{4} + 10 = 54$

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.3.1

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

$\frac{n \cdot 2}{2 \cdot 2} + \frac{n}{4} + 10 = 54$

Step 3.3.2

Multiply $2$ by $2$ .

$\frac{n \cdot 2}{4} + \frac{n}{4} + 10 = 54$

Step 3.4

Combine the numerators over the common denominator.

$\frac{n \cdot 2 + n}{4} + 10 = 54$

Step 3.5

Add $n \cdot 2$ and $n$ .

Tap for more steps...

Step 3.5.1

Reorder $n$ and $2$ .

$\frac{2 \cdot n + n}{4} + 10 = 54$

Step 3.5.2

Add $2 \cdot n$ and $n$ .

$\frac{3 \cdot n}{4} + 10 = 54$

$\frac{3 n}{4} + 10 = 54$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $10$ from both sides of the equation.

$\frac{3 n}{4} = 54 - 10$

Step 4.2

Subtract $10$ from $54$ .

$\frac{3 n}{4} = 44$

Step 5

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 n}{4} = \frac{4}{3} \cdot 44$

Step 6

Simplify both sides of the equation.

Tap for more steps...

Step 6.1

Simplify the left side.

Tap for more steps...

Step 6.1.1

Simplify $\frac{4}{3} \cdot \frac{3 n}{4}$ .

Tap for more steps...

Step 6.1.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 6.1.1.1.1

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 n}{4} = \frac{4}{3} \cdot 44$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 n) = \frac{4}{3} \cdot 44$

Step 6.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.1.1.2.1

Factor $3$ out of $3 n$ .

$\frac{1}{3} (3 (n)) = \frac{4}{3} \cdot 44$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 n) = \frac{4}{3} \cdot 44$

Step 6.1.1.2.3

Rewrite the expression.

$n = \frac{4}{3} \cdot 44$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Multiply $\frac{4}{3} \cdot 44$ .

Tap for more steps...

Step 6.2.1.1

Combine $\frac{4}{3}$ and $44$ .

$n = \frac{4 \cdot 44}{3}$

Step 6.2.1.2

Multiply $4$ by $44$ .

$n = \frac{176}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$n = \frac{176}{3}$

Decimal Form:

$n = 58.\overline{6}$

Mixed Number Form:

$n = 58 \frac{2}{3}$