Algebra Examples

$(3 v + 2) - (\frac{2}{3} v - \frac{1}{4})$

Step 1

Simplify each term.

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Step 1.1

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

$3 v + 2 - (\frac{2 v}{3} - \frac{1}{4})$

Step 1.2

Apply the distributive property.

$3 v + 2 - \frac{2 v}{3} - - \frac{1}{4}$

Step 1.3

Multiply $- - \frac{1}{4}$ .

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Step 1.3.1

Multiply $- 1$ by $- 1$ .

$3 v + 2 - \frac{2 v}{3} + 1 (\frac{1}{4})$

Step 1.3.2

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

$3 v + 2 - \frac{2 v}{3} + \frac{1}{4}$

Step 2

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

$3 v \cdot \frac{3}{3} - \frac{2 v}{3} + 2 + \frac{1}{4}$

Step 3

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

$\frac{3 v \cdot 3}{3} - \frac{2 v}{3} + 2 + \frac{1}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 v \cdot 3 - 2 v}{3} + 2 + \frac{1}{4}$

Step 5

Find the common denominator.

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Step 5.1

Multiply $\frac{3 v \cdot 3 - 2 v}{3}$ by $\frac{4}{4}$ .

$\frac{3 v \cdot 3 - 2 v}{3} \cdot \frac{4}{4} + 2 + \frac{1}{4}$

Step 5.2

Multiply $\frac{3 v \cdot 3 - 2 v}{3}$ by $\frac{4}{4}$ .

$\frac{(3 v \cdot 3 - 2 v) \cdot 4}{3 \cdot 4} + 2 + \frac{1}{4}$

Step 5.3

Write $2$ as a fraction with denominator $1$ .

$\frac{(3 v \cdot 3 - 2 v) \cdot 4}{3 \cdot 4} + \frac{2}{1} + \frac{1}{4}$

Step 5.4

Multiply $\frac{2}{1}$ by $\frac{12}{12}$ .

$\frac{(3 v \cdot 3 - 2 v) \cdot 4}{3 \cdot 4} + \frac{2}{1} \cdot \frac{12}{12} + \frac{1}{4}$

Step 5.5

Multiply $\frac{2}{1}$ by $\frac{12}{12}$ .

$\frac{(3 v \cdot 3 - 2 v) \cdot 4}{3 \cdot 4} + \frac{2 \cdot 12}{12} + \frac{1}{4}$

Step 5.6

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

$\frac{(3 v \cdot 3 - 2 v) \cdot 4}{3 \cdot 4} + \frac{2 \cdot 12}{12} + \frac{1}{4} \cdot \frac{3}{3}$

Step 5.7

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

$\frac{(3 v \cdot 3 - 2 v) \cdot 4}{3 \cdot 4} + \frac{2 \cdot 12}{12} + \frac{3}{4 \cdot 3}$

Step 5.8

Multiply $3$ by $4$ .

$\frac{(3 v \cdot 3 - 2 v) \cdot 4}{12} + \frac{2 \cdot 12}{12} + \frac{3}{4 \cdot 3}$

Step 5.9

Reorder the factors of $4 \cdot 3$ .

$\frac{(3 v \cdot 3 - 2 v) \cdot 4}{12} + \frac{2 \cdot 12}{12} + \frac{3}{3 \cdot 4}$

Step 5.10

Multiply $3$ by $4$ .

$\frac{(3 v \cdot 3 - 2 v) \cdot 4}{12} + \frac{2 \cdot 12}{12} + \frac{3}{12}$

Step 6

Combine the numerators over the common denominator.

$\frac{(3 v \cdot 3 - 2 v) \cdot 4 + 2 \cdot 12 + 3}{12}$

Step 7

Simplify each term.

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Step 7.1

Multiply $3$ by $3$ .

$\frac{(9 v - 2 v) \cdot 4 + 2 \cdot 12 + 3}{12}$

Step 7.2

Subtract $2 v$ from $9 v$ .

$\frac{7 v \cdot 4 + 2 \cdot 12 + 3}{12}$

Step 7.3

Multiply $4$ by $7$ .

$\frac{28 v + 2 \cdot 12 + 3}{12}$

Step 7.4

Multiply $2$ by $12$ .

$\frac{28 v + 24 + 3}{12}$

Step 8

Add $24$ and $3$ .

$\frac{28 v + 27}{12}$