Pre-Algebra Examples

$- 7 v + \frac{5}{3} + \frac{3}{5} v - \frac{2}{3}$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$- 7 v + \frac{3}{5} v + \frac{5 - 2}{3}$

Step 1.2

Subtract $2$ from $5$ .

$- 7 v + \frac{3}{5} v + \frac{3}{3}$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{3}{5}$ and $v$ .

$- 7 v + \frac{3 v}{5} + \frac{3}{3}$

Step 2.2

Divide $3$ by $3$ .

$- 7 v + \frac{3 v}{5} + 1$

Step 3

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

$- 7 v \cdot \frac{5}{5} + \frac{3 v}{5} + 1$

Step 4

Simplify terms.

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Step 4.1

Combine $- 7 v$ and $\frac{5}{5}$ .

$\frac{- 7 v \cdot 5}{5} + \frac{3 v}{5} + 1$

Step 4.2

Combine the numerators over the common denominator.

$\frac{- 7 v \cdot 5 + 3 v}{5} + 1$

Step 5

Simplify each term.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Factor $v$ out of $- 7 v \cdot 5 + 3 v$ .

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Step 5.1.1.1

Factor $v$ out of $- 7 v \cdot 5$ .

$\frac{v (- 7 \cdot 5) + 3 v}{5} + 1$

Step 5.1.1.2

Factor $v$ out of $3 v$ .

$\frac{v (- 7 \cdot 5) + v \cdot 3}{5} + 1$

Step 5.1.1.3

Factor $v$ out of $v (- 7 \cdot 5) + v \cdot 3$ .

$\frac{v (- 7 \cdot 5 + 3)}{5} + 1$

Step 5.1.2

Multiply $- 7$ by $5$ .

$\frac{v (- 35 + 3)}{5} + 1$

Step 5.1.3

Add $- 35$ and $3$ .

$\frac{v \cdot - 32}{5} + 1$

Step 5.2

Move $- 32$ to the left of $v$ .

$\frac{- 32 \cdot v}{5} + 1$

Step 5.3

Move the negative in front of the fraction.

$- \frac{32 v}{5} + 1$