Basic Math Examples

$\frac{n}{4} - \frac{7 n}{8} = \frac{1}{4}$

Step 1

Simplify $\frac{n}{4} - \frac{7 n}{8}$ .

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Step 1.1

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

$\frac{n}{4} \cdot \frac{2}{2} - \frac{7 n}{8} = \frac{1}{4}$

Step 1.2

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

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Step 1.2.1

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

$\frac{n \cdot 2}{4 \cdot 2} - \frac{7 n}{8} = \frac{1}{4}$

Step 1.2.2

Multiply $4$ by $2$ .

$\frac{n \cdot 2}{8} - \frac{7 n}{8} = \frac{1}{4}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{n \cdot 2 - 7 n}{8} = \frac{1}{4}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Move $2$ to the left of $n$ .

$\frac{2 \cdot n - 7 n}{8} = \frac{1}{4}$

Step 1.4.2

Subtract $7 n$ from $2 n$ .

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

Step 1.5

Move the negative in front of the fraction.

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

Step 2

Multiply both sides of the equation by $- \frac{8}{5}$ .

$- \frac{8}{5} (- \frac{5 n}{8}) = - \frac{8}{5} \cdot \frac{1}{4}$

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 $- \frac{8}{5} (- \frac{5 n}{8})$ .

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Step 3.1.1.1

Cancel the common factor of $8$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{8}{5}$ into the numerator.

$\frac{- 8}{5} (- \frac{5 n}{8}) = - \frac{8}{5} \cdot \frac{1}{4}$

Step 3.1.1.1.2

Move the leading negative in $- \frac{5 n}{8}$ into the numerator.

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

Step 3.1.1.1.3

Factor $8$ out of $- 8$ .

$\frac{8 (- 1)}{5} \cdot \frac{- 5 n}{8} = - \frac{8}{5} \cdot \frac{1}{4}$

Step 3.1.1.1.4

Cancel the common factor.

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

Step 3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 n) = - \frac{8}{5} \cdot \frac{1}{4}$

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 $- 5 n$ .

$\frac{- 1}{5} (5 (- n)) = - \frac{8}{5} \cdot \frac{1}{4}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- n)) = - \frac{8}{5} \cdot \frac{1}{4}$

Step 3.1.1.2.3

Rewrite the expression.

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

Step 3.1.1.3

Multiply.

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Step 3.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.1.3.2

Multiply $n$ by $1$ .

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{8}{5} \cdot \frac{1}{4}$ .

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Step 3.2.1.1

Cancel the common factor of $4$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{8}{5}$ into the numerator.

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

Step 3.2.1.1.2

Factor $4$ out of $- 8$ .

$n = \frac{4 (- 2)}{5} \cdot \frac{1}{4}$

Step 3.2.1.1.3

Cancel the common factor.

$n = \frac{4 \cdot - 2}{5} \cdot \frac{1}{4}$

Step 3.2.1.1.4

Rewrite the expression.

$n = \frac{- 2}{5}$

Step 3.2.1.2

Move the negative in front of the fraction.

$n = - \frac{2}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{2}{5}$

Decimal Form:

$n = - 0.4$