Basic Math Examples

$- \frac{5}{3} v + \frac{4}{3} v = \frac{- 2}{7} - \frac{2}{7}$

Step 1

Simplify $- \frac{5}{3} v + \frac{4}{3} v$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$- \frac{v \cdot 5}{3} + \frac{4}{3} v = \frac{- 2}{7} - \frac{2}{7}$

Step 1.1.2

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

$- \frac{5 \cdot v}{3} + \frac{4}{3} v = \frac{- 2}{7} - \frac{2}{7}$

Step 1.1.3

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

$- \frac{5 v}{3} + \frac{4 v}{3} = \frac{- 2}{7} - \frac{2}{7}$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$\frac{- 5 v + 4 v}{3} = \frac{- 2}{7} - \frac{2}{7}$

Step 1.2.2

Add $- 5 v$ and $4 v$ .

$\frac{- v}{3} = \frac{- 2}{7} - \frac{2}{7}$

Step 1.2.3

Move the negative in front of the fraction.

$- \frac{v}{3} = \frac{- 2}{7} - \frac{2}{7}$

Step 2

Simplify $\frac{- 2}{7} - \frac{2}{7}$ .

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Step 2.1

Combine the numerators over the common denominator.

$- \frac{v}{3} = \frac{- 2 - 2}{7}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $2$ from $- 2$ .

$- \frac{v}{3} = \frac{- 4}{7}$

Step 2.2.2

Move the negative in front of the fraction.

$- \frac{v}{3} = - \frac{4}{7}$

Step 3

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{v}{3}) = - 3 (- \frac{4}{7})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- 3 (- \frac{v}{3})$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

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

$- 3 \frac{- v}{3} = - 3 (- \frac{4}{7})$

Step 4.1.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- v}{3} = - 3 (- \frac{4}{7})$

Step 4.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- v}{3} = - 3 (- \frac{4}{7})$

Step 4.1.1.1.4

Rewrite the expression.

$- - v = - 3 (- \frac{4}{7})$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 v = - 3 (- \frac{4}{7})$

Step 4.1.1.2.2

Multiply $v$ by $1$ .

$v = - 3 (- \frac{4}{7})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 3 (- \frac{4}{7})$ .

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Step 4.2.1.1

Multiply $- 1$ by $- 3$ .

$v = 3 (\frac{4}{7})$

Step 4.2.1.2

Combine $3$ and $\frac{4}{7}$ .

$v = \frac{3 \cdot 4}{7}$

Step 4.2.1.3

Multiply $3$ by $4$ .

$v = \frac{12}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$v = \frac{12}{7}$

Decimal Form:

$v = 1.\overline{714285}$

Mixed Number Form:

$v = 1 \frac{5}{7}$