Basic Math Examples

$9 v - \frac{1}{4} + 5 v + \frac{6}{3} = 37$

Step 1

Simplify $9 v - \frac{1}{4} + 5 v + \frac{6}{3}$ .

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Step 1.1

Divide $6$ by $3$ .

$9 v - \frac{1}{4} + 5 v + 2 = 37$

Step 1.2

Add $9 v$ and $5 v$ .

$14 v - \frac{1}{4} + 2 = 37$

Step 1.3

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$14 v - \frac{1}{4} + 2 \cdot \frac{4}{4} = 37$

Step 1.4

Combine $2$ and $\frac{4}{4}$ .

$14 v - \frac{1}{4} + \frac{2 \cdot 4}{4} = 37$

Step 1.5

Combine the numerators over the common denominator.

$14 v + \frac{- 1 + 2 \cdot 4}{4} = 37$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $2$ by $4$ .

$14 v + \frac{- 1 + 8}{4} = 37$

Step 1.6.2

Add $- 1$ and $8$ .

$14 v + \frac{7}{4} = 37$

Step 2

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

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Step 2.1

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

$14 v = 37 - \frac{7}{4}$

Step 2.2

To write $37$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$14 v = 37 \cdot \frac{4}{4} - \frac{7}{4}$

Step 2.3

Combine $37$ and $\frac{4}{4}$ .

$14 v = \frac{37 \cdot 4}{4} - \frac{7}{4}$

Step 2.4

Combine the numerators over the common denominator.

$14 v = \frac{37 \cdot 4 - 7}{4}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $37$ by $4$ .

$14 v = \frac{148 - 7}{4}$

Step 2.5.2

Subtract $7$ from $148$ .

$14 v = \frac{141}{4}$

Step 3

Divide each term in $14 v = \frac{141}{4}$ by $14$ and simplify.

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Step 3.1

Divide each term in $14 v = \frac{141}{4}$ by $14$ .

$\frac{14 v}{14} = \frac{\frac{141}{4}}{14}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $14$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{14 v}{14} = \frac{\frac{141}{4}}{14}$

Step 3.2.1.2

Divide $v$ by $1$ .

$v = \frac{\frac{141}{4}}{14}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$v = \frac{141}{4} \cdot \frac{1}{14}$

Step 3.3.2

Multiply $\frac{141}{4} \cdot \frac{1}{14}$ .

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Step 3.3.2.1

Multiply $\frac{141}{4}$ by $\frac{1}{14}$ .

$v = \frac{141}{4 \cdot 14}$

Step 3.3.2.2

Multiply $4$ by $14$ .

$v = \frac{141}{56}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$v = \frac{141}{56}$

Decimal Form:

$v = 2.51785714 \dots$

Mixed Number Form:

$v = 2 \frac{29}{56}$