Algebra Examples

$\frac{3}{v} = \frac{8}{13}$

Step 1

Subtract $\frac{8}{13}$ from both sides of the equation.

$\frac{3}{v} - \frac{8}{13} = 0$

Step 2

To write $\frac{3}{v}$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$\frac{3}{v} \cdot \frac{13}{13} - \frac{8}{13} = 0$

Step 3

To write $- \frac{8}{13}$ as a fraction with a common denominator, multiply by $\frac{v}{v}$ .

$\frac{3}{v} \cdot \frac{13}{13} - \frac{8}{13} \cdot \frac{v}{v} = 0$

Step 4

Write each expression with a common denominator of $v \cdot 13$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{v}$ by $\frac{13}{13}$ .

$\frac{3 \cdot 13}{v \cdot 13} - \frac{8}{13} \cdot \frac{v}{v} = 0$

Step 4.2

Multiply $\frac{8}{13}$ by $\frac{v}{v}$ .

$\frac{3 \cdot 13}{v \cdot 13} - \frac{8 v}{13 v} = 0$

Step 4.3

Reorder the factors of $v \cdot 13$ .

$\frac{3 \cdot 13}{13 v} - \frac{8 v}{13 v} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{3 \cdot 13 - 8 v}{13 v} = 0$

Step 6

Multiply $3$ by $13$ .

$\frac{39 - 8 v}{13 v} = 0$

Step 7

Set the numerator equal to zero.

$39 - 8 v = 0$

Step 8

Solve the equation for $v$ .

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Step 8.1

Subtract $39$ from both sides of the equation.

$- 8 v = - 39$

Step 8.2

Divide each term in $- 8 v = - 39$ by $- 8$ and simplify.

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Step 8.2.1

Divide each term in $- 8 v = - 39$ by $- 8$ .

$\frac{- 8 v}{- 8} = \frac{- 39}{- 8}$

Step 8.2.2

Simplify the left side.

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Step 8.2.2.1

Cancel the common factor of $- 8$ .

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Step 8.2.2.1.1

Cancel the common factor.

$\frac{- 8 v}{- 8} = \frac{- 39}{- 8}$

Step 8.2.2.1.2

Divide $v$ by $1$ .

$v = \frac{- 39}{- 8}$

Step 8.2.3

Simplify the right side.

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Step 8.2.3.1

Dividing two negative values results in a positive value.

$v = \frac{39}{8}$