Basic Math Examples

$- \frac{8}{3} \cdot (2 n) - \frac{7}{2} - 1 = \frac{32}{3} \cdot (3 n)$

Step 1

Simplify $- \frac{8}{3} \cdot (2 n) - \frac{7}{2} - 1$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Multiply $- \frac{8}{3} (2 n)$ .

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Step 1.1.1.1

Multiply $2$ by $- 1$ .

$- 2 (\frac{8}{3}) n - \frac{7}{2} - 1 = \frac{32}{3} \cdot (3 n)$

Step 1.1.1.2

Combine $- 2$ and $\frac{8}{3}$ .

$\frac{- 2 \cdot 8}{3} n - \frac{7}{2} - 1 = \frac{32}{3} \cdot (3 n)$

Step 1.1.1.3

Multiply $- 2$ by $8$ .

$\frac{- 16}{3} n - \frac{7}{2} - 1 = \frac{32}{3} \cdot (3 n)$

Step 1.1.1.4

Combine $\frac{- 16}{3}$ and $n$ .

$\frac{- 16 n}{3} - \frac{7}{2} - 1 = \frac{32}{3} \cdot (3 n)$

Step 1.1.2

Move the negative in front of the fraction.

$- \frac{16 n}{3} - \frac{7}{2} - 1 = \frac{32}{3} \cdot (3 n)$

Step 1.2

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

$- \frac{16 n}{3} - \frac{7}{2} - 1 \cdot \frac{2}{2} = \frac{32}{3} \cdot (3 n)$

Step 1.3

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

$- \frac{16 n}{3} - \frac{7}{2} + \frac{- 1 \cdot 2}{2} = \frac{32}{3} \cdot (3 n)$

Step 1.4

Combine the numerators over the common denominator.

$- \frac{16 n}{3} + \frac{- 7 - 1 \cdot 2}{2} = \frac{32}{3} \cdot (3 n)$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 1$ by $2$ .

$- \frac{16 n}{3} + \frac{- 7 - 2}{2} = \frac{32}{3} \cdot (3 n)$

Step 1.5.2

Subtract $2$ from $- 7$ .

$- \frac{16 n}{3} + \frac{- 9}{2} = \frac{32}{3} \cdot (3 n)$

Step 1.6

Move the negative in front of the fraction.

$- \frac{16 n}{3} - \frac{9}{2} = \frac{32}{3} \cdot (3 n)$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Factor $3$ out of $3 n$ .

$- \frac{16 n}{3} - \frac{9}{2} = \frac{32}{3} \cdot (3 (n))$

Step 2.2

Cancel the common factor.

$- \frac{16 n}{3} - \frac{9}{2} = \frac{32}{3} \cdot (3 n)$

Step 2.3

Rewrite the expression.

$- \frac{16 n}{3} - \frac{9}{2} = 32 \cdot n$

$- \frac{16 n}{3} - \frac{9}{2} = 32 n$

Step 3

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

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Step 3.1

Subtract $32 n$ from both sides of the equation.

$- \frac{16 n}{3} - \frac{9}{2} - 32 n = 0$

Step 3.2

To write $- 32 n$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{16 n}{3} - 32 n \cdot \frac{3}{3} - \frac{9}{2} = 0$

Step 3.3

Combine $- 32 n$ and $\frac{3}{3}$ .

$- \frac{16 n}{3} + \frac{- 32 n \cdot 3}{3} - \frac{9}{2} = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{- 16 n - 32 n \cdot 3}{3} - \frac{9}{2} = 0$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $16 n$ out of $- 16 n - 32 n \cdot 3$ .

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Step 3.5.1.1.1

Factor $16 n$ out of $- 16 n$ .

$\frac{16 n (- 1) - 32 n \cdot 3}{3} - \frac{9}{2} = 0$

Step 3.5.1.1.2

Factor $16 n$ out of $- 32 n \cdot 3$ .

$\frac{16 n (- 1) + 16 n (- 2 \cdot 3)}{3} - \frac{9}{2} = 0$

Step 3.5.1.1.3

Factor $16 n$ out of $16 n (- 1) + 16 n (- 2 \cdot 3)$ .

$\frac{16 n (- 1 - 2 \cdot 3)}{3} - \frac{9}{2} = 0$

Step 3.5.1.2

Multiply $- 2$ by $3$ .

$\frac{16 n (- 1 - 6)}{3} - \frac{9}{2} = 0$

Step 3.5.1.3

Subtract $6$ from $- 1$ .

$\frac{16 n \cdot - 7}{3} - \frac{9}{2} = 0$

Step 3.5.1.4

Multiply $- 7$ by $16$ .

$\frac{- 112 n}{3} - \frac{9}{2} = 0$

Step 3.5.2

Move the negative in front of the fraction.

$- \frac{112 n}{3} - \frac{9}{2} = 0$

Step 4

Add $\frac{9}{2}$ to both sides of the equation.

$- \frac{112 n}{3} = \frac{9}{2}$

Step 5

Multiply both sides of the equation by $- \frac{3}{112}$ .

$- \frac{3}{112} (- \frac{112 n}{3}) = - \frac{3}{112} \cdot \frac{9}{2}$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $- \frac{3}{112} (- \frac{112 n}{3})$ .

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Step 6.1.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{3}{112}$ into the numerator.

$\frac{- 3}{112} (- \frac{112 n}{3}) = - \frac{3}{112} \cdot \frac{9}{2}$

Step 6.1.1.1.2

Move the leading negative in $- \frac{112 n}{3}$ into the numerator.

$\frac{- 3}{112} \cdot \frac{- 112 n}{3} = - \frac{3}{112} \cdot \frac{9}{2}$

Step 6.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{112} \cdot \frac{- 112 n}{3} = - \frac{3}{112} \cdot \frac{9}{2}$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{112} \cdot \frac{- 112 n}{3} = - \frac{3}{112} \cdot \frac{9}{2}$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{112} (- 112 n) = - \frac{3}{112} \cdot \frac{9}{2}$

Step 6.1.1.2

Cancel the common factor of $112$ .

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Step 6.1.1.2.1

Factor $112$ out of $- 112 n$ .

$\frac{- 1}{112} (112 (- n)) = - \frac{3}{112} \cdot \frac{9}{2}$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{112} (112 (- n)) = - \frac{3}{112} \cdot \frac{9}{2}$

Step 6.1.1.2.3

Rewrite the expression.

$- - n = - \frac{3}{112} \cdot \frac{9}{2}$

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 n = - \frac{3}{112} \cdot \frac{9}{2}$

Step 6.1.1.3.2

Multiply $n$ by $1$ .

$n = - \frac{3}{112} \cdot \frac{9}{2}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- \frac{3}{112} \cdot \frac{9}{2}$ .

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Step 6.2.1.1

Multiply $\frac{9}{2}$ by $\frac{3}{112}$ .

$n = - \frac{9 \cdot 3}{2 \cdot 112}$

Step 6.2.1.2

Multiply $9$ by $3$ .

$n = - \frac{27}{2 \cdot 112}$

Step 6.2.1.3

Multiply $2$ by $112$ .

$n = - \frac{27}{224}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{27}{224}$

Decimal Form:

$n = - 0.12053571 \dots$