Algebra Examples

$(\frac{1}{4} x - \frac{2}{5}) + (\frac{1}{10} x - \frac{3}{5})$

Step 1

Combine fractions.

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Step 1.1

Remove parentheses.

$\frac{1}{4} x - \frac{2}{5} + \frac{1}{10} x - \frac{3}{5}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{1}{4} x + \frac{1}{10} x + \frac{- 2 - 3}{5}$

Step 1.3

Subtract $3$ from $- 2$ .

$\frac{1}{4} x + \frac{1}{10} x + \frac{- 5}{5}$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} + \frac{1}{10} x + \frac{- 5}{5}$

Step 2.2

Combine $\frac{1}{10}$ and $x$ .

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

Step 2.3

Divide $- 5$ by $5$ .

$\frac{x}{4} + \frac{x}{10} - 1$

Step 3

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{4} \cdot \frac{5}{5} + \frac{x}{10} - 1$

Step 4

To write $\frac{x}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{4} \cdot \frac{5}{5} + \frac{x}{10} \cdot \frac{2}{2} - 1$

Step 5

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{x}{4}$ by $\frac{5}{5}$ .

$\frac{x \cdot 5}{4 \cdot 5} + \frac{x}{10} \cdot \frac{2}{2} - 1$

Step 5.2

Multiply $4$ by $5$ .

$\frac{x \cdot 5}{20} + \frac{x}{10} \cdot \frac{2}{2} - 1$

Step 5.3

Multiply $\frac{x}{10}$ by $\frac{2}{2}$ .

$\frac{x \cdot 5}{20} + \frac{x \cdot 2}{10 \cdot 2} - 1$

Step 5.4

Multiply $10$ by $2$ .

$\frac{x \cdot 5}{20} + \frac{x \cdot 2}{20} - 1$

Step 6

Combine the numerators over the common denominator.

$\frac{x \cdot 5 + x \cdot 2}{20} - 1$

Step 7

Reorder $x$ and $2$ .

$\frac{5 \cdot x + 2 \cdot x}{20} - 1$

Step 8

Add $5 \cdot x$ and $2 \cdot x$ .

$\frac{7 x}{20} - 1$