Basic Math Examples

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

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 2.1.1.2

To write $- \frac{n + 1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2.1.1.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.1.3.1

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

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

Step 2.1.1.3.2

Multiply $3$ by $5$ .

$(\frac{5}{15} - \frac{n + 1}{5} \cdot \frac{3}{3}) \cdot 3 = \frac{n}{3} \cdot 3$

Step 2.1.1.3.3

Multiply $\frac{n + 1}{5}$ by $\frac{3}{3}$ .

$(\frac{5}{15} - \frac{(n + 1) \cdot 3}{5 \cdot 3}) \cdot 3 = \frac{n}{3} \cdot 3$

Step 2.1.1.3.4

Multiply $5$ by $3$ .

$(\frac{5}{15} - \frac{(n + 1) \cdot 3}{15}) \cdot 3 = \frac{n}{3} \cdot 3$

Step 2.1.1.4

Combine the numerators over the common denominator.

$\frac{5 - (n + 1) \cdot 3}{15} \cdot 3 = \frac{n}{3} \cdot 3$

Step 2.1.1.5

Simplify the numerator.

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Step 2.1.1.5.1

Apply the distributive property.

$\frac{5 + (- n - 1 \cdot 1) \cdot 3}{15} \cdot 3 = \frac{n}{3} \cdot 3$

Step 2.1.1.5.2

Multiply $- 1$ by $1$ .

$\frac{5 + (- n - 1) \cdot 3}{15} \cdot 3 = \frac{n}{3} \cdot 3$

Step 2.1.1.5.3

Apply the distributive property.

$\frac{5 - n \cdot 3 - 1 \cdot 3}{15} \cdot 3 = \frac{n}{3} \cdot 3$

Step 2.1.1.5.4

Multiply $3$ by $- 1$ .

$\frac{5 - 3 n - 1 \cdot 3}{15} \cdot 3 = \frac{n}{3} \cdot 3$

Step 2.1.1.5.5

Multiply $- 1$ by $3$ .

$\frac{5 - 3 n - 3}{15} \cdot 3 = \frac{n}{3} \cdot 3$

Step 2.1.1.5.6

Subtract $3$ from $5$ .

$\frac{- 3 n + 2}{15} \cdot 3 = \frac{n}{3} \cdot 3$

Step 2.1.1.6

Simplify terms.

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Step 2.1.1.6.1

Cancel the common factor of $3$ .

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Step 2.1.1.6.1.1

Factor $3$ out of $15$ .

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

Step 2.1.1.6.1.2

Cancel the common factor.

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

Step 2.1.1.6.1.3

Rewrite the expression.

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

Step 2.1.1.6.2

Factor $- 1$ out of $- 3 n$ .

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

Step 2.1.1.6.3

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

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

Step 2.1.1.6.4

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

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

Step 2.1.1.6.5

Simplify the expression.

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Step 2.1.1.6.5.1

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

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

Step 2.1.1.6.5.2

Move the negative in front of the fraction.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

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

Step 3

Solve for $n$ .

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Step 3.1

Multiply both sides by $5$ .

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

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

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

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Step 3.2.1.1.1

Cancel the common factor of $5$ .

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Step 3.2.1.1.1.1

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

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

Step 3.2.1.1.1.2

Cancel the common factor.

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

Step 3.2.1.1.1.3

Rewrite the expression.

$- (3 n - 2) = n \cdot 5$

Step 3.2.1.1.2

Apply the distributive property.

$- (3 n) - - 2 = n \cdot 5$

Step 3.2.1.1.3

Multiply.

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Step 3.2.1.1.3.1

Multiply $3$ by $- 1$ .

$- 3 n - - 2 = n \cdot 5$

Step 3.2.1.1.3.2

Multiply $- 1$ by $- 2$ .

$- 3 n + 2 = n \cdot 5$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Move $5$ to the left of $n$ .

$- 3 n + 2 = 5 n$

Step 3.3

Solve for $n$ .

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Step 3.3.1

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

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Step 3.3.1.1

Subtract $5 n$ from both sides of the equation.

$- 3 n + 2 - 5 n = 0$

Step 3.3.1.2

Subtract $5 n$ from $- 3 n$ .

$- 8 n + 2 = 0$

Step 3.3.2

Subtract $2$ from both sides of the equation.

$- 8 n = - 2$

Step 3.3.3

Divide each term in $- 8 n = - 2$ by $- 8$ and simplify.

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Step 3.3.3.1

Divide each term in $- 8 n = - 2$ by $- 8$ .

$\frac{- 8 n}{- 8} = \frac{- 2}{- 8}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $- 8$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{- 8 n}{- 8} = \frac{- 2}{- 8}$

Step 3.3.3.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 2}{- 8}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Cancel the common factor of $- 2$ and $- 8$ .

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Step 3.3.3.3.1.1

Factor $- 2$ out of $- 2$ .

$n = \frac{- 2 (1)}{- 8}$

Step 3.3.3.3.1.2

Cancel the common factors.

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Step 3.3.3.3.1.2.1

Factor $- 2$ out of $- 8$ .

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

Step 3.3.3.3.1.2.2

Cancel the common factor.

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

Step 3.3.3.3.1.2.3

Rewrite the expression.

$n = \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = \frac{1}{4}$

Decimal Form:

$n = 0.25$