Basic Math Examples

$\frac{5 n}{6} - \frac{1}{4} = \frac{3}{8}$

Step 1

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

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Step 1.1

Add $\frac{1}{4}$ to both sides of the equation.

$\frac{5 n}{6} = \frac{3}{8} + \frac{1}{4}$

Step 1.2

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 n}{6} = \frac{3}{8} + \frac{1}{4} \cdot \frac{2}{2}$

Step 1.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{4}$ by $\frac{2}{2}$ .

$\frac{5 n}{6} = \frac{3}{8} + \frac{2}{4 \cdot 2}$

Step 1.3.2

Multiply $4$ by $2$ .

$\frac{5 n}{6} = \frac{3}{8} + \frac{2}{8}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{5 n}{6} = \frac{3 + 2}{8}$

Step 1.5

Add $3$ and $2$ .

$\frac{5 n}{6} = \frac{5}{8}$

Step 2

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} \cdot \frac{5 n}{6} = \frac{6}{5} \cdot \frac{5}{8}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{6}{5} \cdot \frac{5 n}{6}$ .

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Step 3.1.1.1

Cancel the common factor of $6$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 n}{6} = \frac{6}{5} \cdot \frac{5}{8}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 n) = \frac{6}{5} \cdot \frac{5}{8}$

Step 3.1.1.2

Cancel the common factor of $5$ .

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Step 3.1.1.2.1

Factor $5$ out of $5 n$ .

$\frac{1}{5} (5 (n)) = \frac{6}{5} \cdot \frac{5}{8}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 n) = \frac{6}{5} \cdot \frac{5}{8}$

Step 3.1.1.2.3

Rewrite the expression.

$n = \frac{6}{5} \cdot \frac{5}{8}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{6}{5} \cdot \frac{5}{8}$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Factor $2$ out of $6$ .

$n = \frac{2 (3)}{5} \cdot \frac{5}{8}$

Step 3.2.1.1.2

Factor $2$ out of $8$ .

$n = \frac{2 \cdot 3}{5} \cdot \frac{5}{2 \cdot 4}$

Step 3.2.1.1.3

Cancel the common factor.

$n = \frac{2 \cdot 3}{5} \cdot \frac{5}{2 \cdot 4}$

Step 3.2.1.1.4

Rewrite the expression.

$n = \frac{3}{5} \cdot \frac{5}{4}$

Step 3.2.1.2

Cancel the common factor of $5$ .

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Step 3.2.1.2.1

Cancel the common factor.

$n = \frac{3}{5} \cdot \frac{5}{4}$

Step 3.2.1.2.2

Rewrite the expression.

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

Step 3.2.1.3

Combine $3$ and $\frac{1}{4}$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$n = 0.75$