Basic Math Examples

$\frac{- 1}{5} (n - 3) = \frac{1}{5} (n - \frac{3}{4})$

Step 1

Simplify $\frac{- 1}{5} \cdot (n - 3)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{- 1}{5} \cdot (n - 3) = \frac{1}{5} \cdot (n - \frac{3}{4})$

Step 1.2

Move the negative in front of the fraction.

$- \frac{1}{5} \cdot (n - 3) = \frac{1}{5} \cdot (n - \frac{3}{4})$

Step 1.3

Apply the distributive property.

$- \frac{1}{5} n - \frac{1}{5} \cdot - 3 = \frac{1}{5} \cdot (n - \frac{3}{4})$

Step 1.4

Combine $n$ and $\frac{1}{5}$ .

$- \frac{n}{5} - \frac{1}{5} \cdot - 3 = \frac{1}{5} \cdot (n - \frac{3}{4})$

Step 1.5

Multiply $- \frac{1}{5} \cdot - 3$ .

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Step 1.5.1

Multiply $- 3$ by $- 1$ .

$- \frac{n}{5} + 3 (\frac{1}{5}) = \frac{1}{5} \cdot (n - \frac{3}{4})$

Step 1.5.2

Combine $3$ and $\frac{1}{5}$ .

$- \frac{n}{5} + \frac{3}{5} = \frac{1}{5} \cdot (n - \frac{3}{4})$

Step 2

Simplify $\frac{1}{5} \cdot (n - \frac{3}{4})$ .

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Step 2.1

Apply the distributive property.

$- \frac{n}{5} + \frac{3}{5} = \frac{1}{5} n + \frac{1}{5} (- \frac{3}{4})$

Step 2.2

Combine $\frac{1}{5}$ and $n$ .

$- \frac{n}{5} + \frac{3}{5} = \frac{n}{5} + \frac{1}{5} (- \frac{3}{4})$

Step 2.3

Multiply $\frac{1}{5} (- \frac{3}{4})$ .

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Step 2.3.1

Multiply $\frac{1}{5}$ by $\frac{3}{4}$ .

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

Step 2.3.2

Multiply $5$ by $4$ .

$- \frac{n}{5} + \frac{3}{5} = \frac{n}{5} - \frac{3}{20}$

Step 3

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

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Step 3.1

Subtract $\frac{n}{5}$ from both sides of the equation.

$- \frac{n}{5} + \frac{3}{5} - \frac{n}{5} = - \frac{3}{20}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- n + 3 - n}{5} = - \frac{3}{20}$

Step 3.3

Subtract $n$ from $- n$ .

$\frac{- 2 n + 3}{5} = - \frac{3}{20}$

Step 3.4

Factor $- 1$ out of $- 2 n$ .

$\frac{- (2 n) + 3}{5} = - \frac{3}{20}$

Step 3.5

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{- (2 n) - 1 (- 3)}{5} = - \frac{3}{20}$

Step 3.6

Factor $- 1$ out of $- (2 n) - 1 (- 3)$ .

$\frac{- (2 n - 3)}{5} = - \frac{3}{20}$

Step 3.7

Rewrite $- (2 n - 3)$ as $- 1 (2 n - 3)$ .

$\frac{- 1 (2 n - 3)}{5} = - \frac{3}{20}$

Step 3.8

Move the negative in front of the fraction.

$- \frac{2 n - 3}{5} = - \frac{3}{20}$

Step 4

Multiply both sides of the equation by $- 5$ .

$- 5 (- \frac{2 n - 3}{5}) = - 5 (- \frac{3}{20})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- 5 (- \frac{2 n - 3}{5})$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{2 n - 3}{5}$ into the numerator.

$- 5 \frac{- (2 n - 3)}{5} = - 5 (- \frac{3}{20})$

Step 5.1.1.1.2

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{- (2 n - 3)}{5} = - 5 (- \frac{3}{20})$

Step 5.1.1.1.3

Cancel the common factor.

$5 \cdot - 1 \frac{- (2 n - 3)}{5} = - 5 (- \frac{3}{20})$

Step 5.1.1.1.4

Rewrite the expression.

$- - (2 n - 3) = - 5 (- \frac{3}{20})$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (2 n - 3) = - 5 (- \frac{3}{20})$

Step 5.1.1.2.2

Multiply $2 n - 3$ by $1$ .

$2 n - 3 = - 5 (- \frac{3}{20})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- 5 (- \frac{3}{20})$ .

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Step 5.2.1.1

Cancel the common factor of $5$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{3}{20}$ into the numerator.

$2 n - 3 = - 5 (\frac{- 3}{20})$

Step 5.2.1.1.2

Factor $5$ out of $- 5$ .

$2 n - 3 = 5 (- 1) \frac{- 3}{20}$

Step 5.2.1.1.3

Factor $5$ out of $20$ .

$2 n - 3 = 5 \cdot - 1 \frac{- 3}{5 \cdot 4}$

Step 5.2.1.1.4

Cancel the common factor.

$2 n - 3 = 5 \cdot - 1 \frac{- 3}{5 \cdot 4}$

Step 5.2.1.1.5

Rewrite the expression.

$2 n - 3 = - \frac{- 3}{4}$

Step 5.2.1.2

Move the negative in front of the fraction.

$2 n - 3 = - - \frac{3}{4}$

Step 5.2.1.3

Multiply $- - \frac{3}{4}$ .

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Step 5.2.1.3.1

Multiply $- 1$ by $- 1$ .

$2 n - 3 = 1 (\frac{3}{4})$

Step 5.2.1.3.2

Multiply $\frac{3}{4}$ by $1$ .

$2 n - 3 = \frac{3}{4}$

Step 6

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

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Step 6.1

Add $3$ to both sides of the equation.

$2 n = \frac{3}{4} + 3$

Step 6.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 6.3

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

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

Step 6.4

Combine the numerators over the common denominator.

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

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply $3$ by $4$ .

$2 n = \frac{3 + 12}{4}$

Step 6.5.2

Add $3$ and $12$ .

$2 n = \frac{15}{4}$

Step 7

Divide each term in $2 n = \frac{15}{4}$ by $2$ and simplify.

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Step 7.1

Divide each term in $2 n = \frac{15}{4}$ by $2$ .

$\frac{2 n}{2} = \frac{\frac{15}{4}}{2}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $2$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{2 n}{2} = \frac{\frac{15}{4}}{2}$

Step 7.2.1.2

Divide $n$ by $1$ .

$n = \frac{\frac{15}{4}}{2}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Multiply the numerator by the reciprocal of the denominator.

$n = \frac{15}{4} \cdot \frac{1}{2}$

Step 7.3.2

Multiply $\frac{15}{4} \cdot \frac{1}{2}$ .

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Step 7.3.2.1

Multiply $\frac{15}{4}$ by $\frac{1}{2}$ .

$n = \frac{15}{4 \cdot 2}$

Step 7.3.2.2

Multiply $4$ by $2$ .

$n = \frac{15}{8}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$n = \frac{15}{8}$

Decimal Form:

$n = 1.875$

Mixed Number Form:

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