Basic Math Examples

$- \frac{3}{4} v = \frac{2}{4} v + \frac{5}{6}$

Step 1

Simplify $- \frac{3}{4} v$ .

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Step 1.1

Rewrite.

$0 + 0 - \frac{3}{4} v = \frac{2}{4} v + \frac{5}{6}$

Step 1.2

Simplify by adding zeros.

$- \frac{3}{4} v = \frac{2}{4} v + \frac{5}{6}$

Step 1.3

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

$- \frac{v \cdot 3}{4} = \frac{2}{4} v + \frac{5}{6}$

Step 1.4

Move $3$ to the left of $v$ .

$- \frac{3 v}{4} = \frac{2}{4} v + \frac{5}{6}$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $2$ and $4$ .

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Step 2.1.1

Factor $2$ out of $2$ .

$- \frac{3 v}{4} = \frac{2 (1)}{4} v + \frac{5}{6}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $4$ .

$- \frac{3 v}{4} = \frac{2 \cdot 1}{2 \cdot 2} v + \frac{5}{6}$

Step 2.1.2.2

Cancel the common factor.

$- \frac{3 v}{4} = \frac{2 \cdot 1}{2 \cdot 2} v + \frac{5}{6}$

Step 2.1.2.3

Rewrite the expression.

$- \frac{3 v}{4} = \frac{1}{2} v + \frac{5}{6}$

Step 2.2

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

$- \frac{3 v}{4} = \frac{v}{2} + \frac{5}{6}$

Step 3

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

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Step 3.1

Subtract $\frac{v}{2}$ from both sides of the equation.

$- \frac{3 v}{4} - \frac{v}{2} = \frac{5}{6}$

Step 3.2

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

$- \frac{3 v}{4} - \frac{v}{2} \cdot \frac{2}{2} = \frac{5}{6}$

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{v}{2}$ by $\frac{2}{2}$ .

$- \frac{3 v}{4} - \frac{v \cdot 2}{2 \cdot 2} = \frac{5}{6}$

Step 3.3.2

Multiply $2$ by $2$ .

$- \frac{3 v}{4} - \frac{v \cdot 2}{4} = \frac{5}{6}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{- 3 v - v \cdot 2}{4} = \frac{5}{6}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Factor $v$ out of $- 3 v - v \cdot 2$ .

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Step 3.5.1.1

Factor $v$ out of $- 3 v$ .

$\frac{v \cdot - 3 - v \cdot 2}{4} = \frac{5}{6}$

Step 3.5.1.2

Factor $v$ out of $- v \cdot 2$ .

$\frac{v \cdot - 3 + v (- 1 \cdot 2)}{4} = \frac{5}{6}$

Step 3.5.1.3

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

$\frac{v (- 3 - 1 \cdot 2)}{4} = \frac{5}{6}$

Step 3.5.2

Multiply $- 1$ by $2$ .

$\frac{v (- 3 - 2)}{4} = \frac{5}{6}$

Step 3.5.3

Subtract $2$ from $- 3$ .

$\frac{v \cdot - 5}{4} = \frac{5}{6}$

Step 3.6

Move $- 5$ to the left of $v$ .

$\frac{- 5 \cdot v}{4} = \frac{5}{6}$

Step 3.7

Move the negative in front of the fraction.

$- \frac{5 v}{4} = \frac{5}{6}$

Step 4

Multiply both sides of the equation by $- \frac{4}{5}$ .

$- \frac{4}{5} (- \frac{5 v}{4}) = - \frac{4}{5} \cdot \frac{5}{6}$

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 $- \frac{4}{5} (- \frac{5 v}{4})$ .

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Step 5.1.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$\frac{- 4}{5} (- \frac{5 v}{4}) = - \frac{4}{5} \cdot \frac{5}{6}$

Step 5.1.1.1.2

Move the leading negative in $- \frac{5 v}{4}$ into the numerator.

$\frac{- 4}{5} \cdot \frac{- 5 v}{4} = - \frac{4}{5} \cdot \frac{5}{6}$

Step 5.1.1.1.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{5} \cdot \frac{- 5 v}{4} = - \frac{4}{5} \cdot \frac{5}{6}$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{4 \cdot - 1}{5} \cdot \frac{- 5 v}{4} = - \frac{4}{5} \cdot \frac{5}{6}$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 v) = - \frac{4}{5} \cdot \frac{5}{6}$

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $- 5 v$ .

$\frac{- 1}{5} (5 (- v)) = - \frac{4}{5} \cdot \frac{5}{6}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- v)) = - \frac{4}{5} \cdot \frac{5}{6}$

Step 5.1.1.2.3

Rewrite the expression.

$- - v = - \frac{4}{5} \cdot \frac{5}{6}$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 v = - \frac{4}{5} \cdot \frac{5}{6}$

Step 5.1.1.3.2

Multiply $v$ by $1$ .

$v = - \frac{4}{5} \cdot \frac{5}{6}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{4}{5} \cdot \frac{5}{6}$ .

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$v = \frac{- 4}{5} \cdot \frac{5}{6}$

Step 5.2.1.1.2

Factor $2$ out of $- 4$ .

$v = \frac{2 (- 2)}{5} \cdot \frac{5}{6}$

Step 5.2.1.1.3

Factor $2$ out of $6$ .

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

Step 5.2.1.1.4

Cancel the common factor.

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

Step 5.2.1.1.5

Rewrite the expression.

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

Step 5.2.1.2

Cancel the common factor of $5$ .

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Step 5.2.1.2.1

Cancel the common factor.

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

Step 5.2.1.2.2

Rewrite the expression.

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

Step 5.2.1.3

Combine $- 2$ and $\frac{1}{3}$ .

$v = \frac{- 2}{3}$

Step 5.2.1.4

Move the negative in front of the fraction.

$v = - \frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$v = - \frac{2}{3}$

Decimal Form:

$v = - 0.\overline{6}$