Basic Math Examples

$\frac{v - 8}{20} + 0.4 + \frac{v}{10} + \frac{v + 4}{10} = 0$

Step 1

Simplify $\frac{v - 8}{20} + 0.4 + \frac{v}{10} + \frac{v + 4}{10}$ .

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Step 1.1

Combine the numerators over the common denominator.

$0.4 + \frac{v - 8}{20} + \frac{v + v + 4}{10} = 0$

Step 1.2

Add $v$ and $v$ .

$0.4 + \frac{v - 8}{20} + \frac{2 v + 4}{10} = 0$

Step 1.3

Find the common denominator.

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Step 1.3.1

Write $0.4$ as a fraction with denominator $1$ .

$\frac{0.4}{1} + \frac{v - 8}{20} + \frac{2 v + 4}{10} = 0$

Step 1.3.2

Multiply $\frac{0.4}{1}$ by $\frac{20}{20}$ .

$\frac{0.4}{1} \cdot \frac{20}{20} + \frac{v - 8}{20} + \frac{2 v + 4}{10} = 0$

Step 1.3.3

Multiply $\frac{0.4}{1}$ by $\frac{20}{20}$ .

$\frac{0.4 \cdot 20}{20} + \frac{v - 8}{20} + \frac{2 v + 4}{10} = 0$

Step 1.3.4

Multiply $\frac{2 v + 4}{10}$ by $\frac{2}{2}$ .

$\frac{0.4 \cdot 20}{20} + \frac{v - 8}{20} + \frac{2 v + 4}{10} \cdot \frac{2}{2} = 0$

Step 1.3.5

Multiply $\frac{2 v + 4}{10}$ by $\frac{2}{2}$ .

$\frac{0.4 \cdot 20}{20} + \frac{v - 8}{20} + \frac{(2 v + 4) \cdot 2}{10 \cdot 2} = 0$

Step 1.3.6

Reorder the factors of $10 \cdot 2$ .

$\frac{0.4 \cdot 20}{20} + \frac{v - 8}{20} + \frac{(2 v + 4) \cdot 2}{2 \cdot 10} = 0$

Step 1.3.7

Multiply $2$ by $10$ .

$\frac{0.4 \cdot 20}{20} + \frac{v - 8}{20} + \frac{(2 v + 4) \cdot 2}{20} = 0$

Step 1.4

Combine the numerators over the common denominator.

$\frac{0.4 \cdot 20 + v - 8 + (2 v + 4) \cdot 2}{20} = 0$

Step 1.5

Simplify each term.

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Step 1.5.1

Multiply $0.4$ by $20$ .

$\frac{8 + v - 8 + (2 v + 4) \cdot 2}{20} = 0$

Step 1.5.2

Apply the distributive property.

$\frac{8 + v - 8 + 2 v \cdot 2 + 4 \cdot 2}{20} = 0$

Step 1.5.3

Multiply $2$ by $2$ .

$\frac{8 + v - 8 + 4 v + 4 \cdot 2}{20} = 0$

Step 1.5.4

Multiply $4$ by $2$ .

$\frac{8 + v - 8 + 4 v + 8}{20} = 0$

Step 1.6

Simplify terms.

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Step 1.6.1

Combine the opposite terms in $8 + v - 8 + 4 v + 8$ .

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Step 1.6.1.1

Add $- 8$ and $8$ .

$\frac{8 + v + 4 v + 0}{20} = 0$

Step 1.6.1.2

Add $8 + v + 4 v$ and $0$ .

$\frac{8 + v + 4 v}{20} = 0$

Step 1.6.2

Add $v$ and $4 v$ .

$\frac{8 + 5 v}{20} = 0$

Step 1.6.3

Cancel the common factor of $8 + 5 v$ and $20$ .

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Step 1.6.3.1

Rewrite $8$ as $1 (8)$ .

$\frac{1 (8) + 5 v}{20} = 0$

Step 1.6.3.2

Factor $1$ out of $5 v$ .

$\frac{1 (8) + 1 (5 v)}{20} = 0$

Step 1.6.3.3

Factor $1$ out of $1 (8) + 1 (5 v)$ .

$\frac{1 (8 + 5 v)}{20} = 0$

Step 1.6.3.4

Cancel the common factors.

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Step 1.6.3.4.1

Rewrite $20$ as $1 (20)$ .

$\frac{1 (8 + 5 v)}{1 \cdot 20} = 0$

Step 1.6.3.4.2

Cancel the common factor.

$\frac{1 (8 + 5 v)}{1 \cdot 20} = 0$

Step 1.6.3.4.3

Rewrite the expression.

$\frac{8 + 5 v}{20} = 0$

Step 2

Set the numerator equal to zero.

$8 + 5 v = 0$

Step 3

Solve the equation for $v$ .

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Step 3.1

Subtract $8$ from both sides of the equation.

$5 v = - 8$

Step 3.2

Divide each term in $5 v = - 8$ by $5$ and simplify.

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Step 3.2.1

Divide each term in $5 v = - 8$ by $5$ .

$\frac{5 v}{5} = \frac{- 8}{5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 v}{5} = \frac{- 8}{5}$

Step 3.2.2.1.2

Divide $v$ by $1$ .

$v = \frac{- 8}{5}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$v = - \frac{8}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$v = - \frac{8}{5}$

Decimal Form:

$v = - 1.6$

Mixed Number Form:

$v = - 1 \frac{3}{5}$