Basic Math Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Subtract $\frac{5 v}{3}$ from both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Combine the numerators over the common denominator.

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

Step 2.6

Multiply $3$ by $- 5$ .

$\frac{- 15 v - 5 v - 4}{3} = - \frac{1}{5}$

Step 2.7

Subtract $5 v$ from $- 15 v$ .

$\frac{- 20 v - 4}{3} = - \frac{1}{5}$

Step 2.8

Factor $4$ out of $- 20 v - 4$ .

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Step 2.8.1

Factor $4$ out of $- 20 v$ .

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

Step 2.8.2

Factor $4$ out of $- 4$ .

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

Step 2.8.3

Factor $4$ out of $4 (- 5 v) + 4 (- 1)$ .

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

Step 2.9

Factor $- 1$ out of $- 5 v$ .

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

Step 2.10

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

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

Step 2.11

Factor $- 1$ out of $- (5 v) - 1 (1)$ .

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

Step 2.12

Rewrite $- (5 v + 1)$ as $- 1 (5 v + 1)$ .

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

Step 2.13

Move the negative in front of the fraction.

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

Step 3

Multiply both sides of the equation by $- \frac{3}{4}$ .

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

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 $- \frac{3}{4} (- \frac{4 (5 v + 1)}{3})$ .

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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 $- \frac{3}{4}$ into the numerator.

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

Step 4.1.1.1.2

Move the leading negative in $- \frac{4 (5 v + 1)}{3}$ into the numerator.

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

Step 4.1.1.1.3

Factor $3$ out of $- 3$ .

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

Step 4.1.1.1.4

Cancel the common factor.

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

Step 4.1.1.1.5

Rewrite the expression.

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

Step 4.1.1.2

Cancel the common factor of $4$ .

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Step 4.1.1.2.1

Factor $4$ out of $- 4 (5 v + 1)$ .

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

Step 4.1.1.2.2

Cancel the common factor.

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

Step 4.1.1.2.3

Rewrite the expression.

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

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 4.1.1.3.2

Multiply $5 v + 1$ by $1$ .

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- \frac{3}{4} (- \frac{1}{5})$ .

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Step 4.2.1.1

Multiply $- 1$ by $- 1$ .

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

Step 4.2.1.2

Multiply $\frac{3}{4}$ by $1$ .

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

Step 4.2.1.3

Multiply $\frac{3}{4}$ by $\frac{1}{5}$ .

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

Step 4.2.1.4

Multiply $4$ by $5$ .

$5 v + 1 = \frac{3}{20}$

Step 5

Move all terms not containing $v$ to the right side of the equation.

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Step 5.1

Subtract $1$ from both sides of the equation.

$5 v = \frac{3}{20} - 1$

Step 5.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$5 v = \frac{3}{20} - 1 \cdot \frac{20}{20}$

Step 5.3

Combine $- 1$ and $\frac{20}{20}$ .

$5 v = \frac{3}{20} + \frac{- 1 \cdot 20}{20}$

Step 5.4

Combine the numerators over the common denominator.

$5 v = \frac{3 - 1 \cdot 20}{20}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $- 1$ by $20$ .

$5 v = \frac{3 - 20}{20}$

Step 5.5.2

Subtract $20$ from $3$ .

$5 v = \frac{- 17}{20}$

Step 5.6

Move the negative in front of the fraction.

$5 v = - \frac{17}{20}$

Step 6

Divide each term in $5 v = - \frac{17}{20}$ by $5$ and simplify.

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Step 6.1

Divide each term in $5 v = - \frac{17}{20}$ by $5$ .

$\frac{5 v}{5} = \frac{- \frac{17}{20}}{5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{5 v}{5} = \frac{- \frac{17}{20}}{5}$

Step 6.2.1.2

Divide $v$ by $1$ .

$v = \frac{- \frac{17}{20}}{5}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Multiply the numerator by the reciprocal of the denominator.

$v = - \frac{17}{20} \cdot \frac{1}{5}$

Step 6.3.2

Multiply $- \frac{17}{20} \cdot \frac{1}{5}$ .

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Step 6.3.2.1

Multiply $\frac{1}{5}$ by $\frac{17}{20}$ .

$v = - \frac{17}{5 \cdot 20}$

Step 6.3.2.2

Multiply $5$ by $20$ .

$v = - \frac{17}{100}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$v = - \frac{17}{100}$

Decimal Form:

$v = - 0.17$