Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Combine $v$ and $\frac{3}{2}$ .

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

Step 1.2

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

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

Step 2

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

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Step 2.1

Subtract $\frac{4}{7}$ from both sides of the equation.

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

Step 2.2

To write $- \frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

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

Step 2.3

To write $- \frac{4}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 2.4

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{4}{5}$ by $\frac{7}{7}$ .

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

Step 2.4.2

Multiply $5$ by $7$ .

$- \frac{3 v}{2} = - \frac{4 \cdot 7}{35} - \frac{4}{7} \cdot \frac{5}{5}$

Step 2.4.3

Multiply $\frac{4}{7}$ by $\frac{5}{5}$ .

$- \frac{3 v}{2} = - \frac{4 \cdot 7}{35} - \frac{4 \cdot 5}{7 \cdot 5}$

Step 2.4.4

Multiply $7$ by $5$ .

$- \frac{3 v}{2} = - \frac{4 \cdot 7}{35} - \frac{4 \cdot 5}{35}$

Step 2.5

Combine the numerators over the common denominator.

$- \frac{3 v}{2} = \frac{- 4 \cdot 7 - 4 \cdot 5}{35}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $- 4$ by $7$ .

$- \frac{3 v}{2} = \frac{- 28 - 4 \cdot 5}{35}$

Step 2.6.2

Multiply $- 4$ by $5$ .

$- \frac{3 v}{2} = \frac{- 28 - 20}{35}$

Step 2.6.3

Subtract $20$ from $- 28$ .

$- \frac{3 v}{2} = \frac{- 48}{35}$

Step 2.7

Move the negative in front of the fraction.

$- \frac{3 v}{2} = - \frac{48}{35}$

Step 3

Multiply both sides of the equation by $- \frac{2}{3}$ .

$- \frac{2}{3} (- \frac{3 v}{2}) = - \frac{2}{3} (- \frac{48}{35})$

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 $- \frac{2}{3} (- \frac{3 v}{2})$ .

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- \frac{3 v}{2}) = - \frac{2}{3} (- \frac{48}{35})$

Step 4.1.1.1.2

Move the leading negative in $- \frac{3 v}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 v}{2} = - \frac{2}{3} (- \frac{48}{35})$

Step 4.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 v}{2} = - \frac{2}{3} (- \frac{48}{35})$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 v}{2} = - \frac{2}{3} (- \frac{48}{35})$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 v) = - \frac{2}{3} (- \frac{48}{35})$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

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

$\frac{- 1}{3} (3 (- v)) = - \frac{2}{3} (- \frac{48}{35})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- v)) = - \frac{2}{3} (- \frac{48}{35})$

Step 4.1.1.2.3

Rewrite the expression.

$- - v = - \frac{2}{3} (- \frac{48}{35})$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 v = - \frac{2}{3} (- \frac{48}{35})$

Step 4.1.1.3.2

Multiply $v$ by $1$ .

$v = - \frac{2}{3} (- \frac{48}{35})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{2}{3} (- \frac{48}{35})$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$v = \frac{- 2}{3} (- \frac{48}{35})$

Step 4.2.1.1.2

Move the leading negative in $- \frac{48}{35}$ into the numerator.

$v = \frac{- 2}{3} \cdot \frac{- 48}{35}$

Step 4.2.1.1.3

Factor $3$ out of $- 48$ .

$v = \frac{- 2}{3} \cdot \frac{3 (- 16)}{35}$

Step 4.2.1.1.4

Cancel the common factor.

$v = \frac{- 2}{3} \cdot \frac{3 \cdot - 16}{35}$

Step 4.2.1.1.5

Rewrite the expression.

$v = - 2 (\frac{- 16}{35})$

Step 4.2.1.2

Combine $- 2$ and $\frac{- 16}{35}$ .

$v = \frac{- 2 \cdot - 16}{35}$

Step 4.2.1.3

Multiply $- 2$ by $- 16$ .

$v = \frac{32}{35}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$v = \frac{32}{35}$

Decimal Form:

$v = 0.9\overline{142857}$