Basic Math Examples

$\frac{v - 8}{9} = \frac{6}{4}$

Step 1

Multiply both sides of the equation by $9$ .

$9 \frac{v - 8}{9} = 9 (\frac{6}{4})$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $9$ .

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Step 2.1.1.1

Cancel the common factor.

$9 \frac{v - 8}{9} = 9 (\frac{6}{4})$

Step 2.1.1.2

Rewrite the expression.

$v - 8 = 9 (\frac{6}{4})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $9 (\frac{6}{4})$ .

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Step 2.2.1.1

Cancel the common factor of $6$ and $4$ .

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Step 2.2.1.1.1

Factor $2$ out of $6$ .

$v - 8 = 9 \frac{2 (3)}{4}$

Step 2.2.1.1.2

Cancel the common factors.

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Step 2.2.1.1.2.1

Factor $2$ out of $4$ .

$v - 8 = 9 \frac{2 \cdot 3}{2 \cdot 2}$

Step 2.2.1.1.2.2

Cancel the common factor.

$v - 8 = 9 \frac{2 \cdot 3}{2 \cdot 2}$

Step 2.2.1.1.2.3

Rewrite the expression.

$v - 8 = 9 (\frac{3}{2})$

Step 2.2.1.2

Multiply $9 (\frac{3}{2})$ .

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Step 2.2.1.2.1

Combine $9$ and $\frac{3}{2}$ .

$v - 8 = \frac{9 \cdot 3}{2}$

Step 2.2.1.2.2

Multiply $9$ by $3$ .

$v - 8 = \frac{27}{2}$

Step 3

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

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Step 3.1

Add $8$ to both sides of the equation.

$v = \frac{27}{2} + 8$

Step 3.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$v = \frac{27}{2} + 8 \cdot \frac{2}{2}$

Step 3.3

Combine $8$ and $\frac{2}{2}$ .

$v = \frac{27}{2} + \frac{8 \cdot 2}{2}$

Step 3.4

Combine the numerators over the common denominator.

$v = \frac{27 + 8 \cdot 2}{2}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $8$ by $2$ .

$v = \frac{27 + 16}{2}$

Step 3.5.2

Add $27$ and $16$ .

$v = \frac{43}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$v = \frac{43}{2}$

Decimal Form:

$v = 21.5$

Mixed Number Form:

$v = 21 \frac{1}{2}$