Pre-Algebra Examples

$- \frac{3 x}{6} + \frac{2 x}{5}$

Step 1

Cancel the common factor of $3$ and $6$ .

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Step 1.1

Factor $3$ out of $3 x$ .

$- \frac{3 (x)}{6} + \frac{2 x}{5}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $6$ .

$- \frac{3 x}{3 \cdot 2} + \frac{2 x}{5}$

Step 1.2.2

Cancel the common factor.

$- \frac{3 x}{3 \cdot 2} + \frac{2 x}{5}$

Step 1.2.3

Rewrite the expression.

$- \frac{x}{2} + \frac{2 x}{5}$

Step 2

To write $- \frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{x}{2} \cdot \frac{5}{5} + \frac{2 x}{5}$

Step 3

To write $\frac{2 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x}{2} \cdot \frac{5}{5} + \frac{2 x}{5} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{x}{2}$ by $\frac{5}{5}$ .

$- \frac{x \cdot 5}{2 \cdot 5} + \frac{2 x}{5} \cdot \frac{2}{2}$

Step 4.2

Multiply $2$ by $5$ .

$- \frac{x \cdot 5}{10} + \frac{2 x}{5} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{2 x}{5}$ by $\frac{2}{2}$ .

$- \frac{x \cdot 5}{10} + \frac{2 x \cdot 2}{5 \cdot 2}$

Step 4.4

Multiply $5$ by $2$ .

$- \frac{x \cdot 5}{10} + \frac{2 x \cdot 2}{10}$

Step 5

Combine the numerators over the common denominator.

$\frac{- x \cdot 5 + 2 x \cdot 2}{10}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $x$ out of $- x \cdot 5 + 2 x \cdot 2$ .

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Step 6.1.1

Factor $x$ out of $- x \cdot 5$ .

$\frac{x (- 1 \cdot 5) + 2 x \cdot 2}{10}$

Step 6.1.2

Factor $x$ out of $2 x \cdot 2$ .

$\frac{x (- 1 \cdot 5) + x (2 \cdot 2)}{10}$

Step 6.1.3

Factor $x$ out of $x (- 1 \cdot 5) + x (2 \cdot 2)$ .

$\frac{x (- 1 \cdot 5 + 2 \cdot 2)}{10}$

Step 6.2

Multiply $- 1$ by $5$ .

$\frac{x (- 5 + 2 \cdot 2)}{10}$

Step 6.3

Multiply $2$ by $2$ .

$\frac{x (- 5 + 4)}{10}$

Step 6.4

Add $- 5$ and $4$ .

$\frac{x \cdot - 1}{10}$

Step 7

Simplify the expression.

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Step 7.1

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{10}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{x}{10}$

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