Pre-Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{1}{3}$ and $x$ .

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

Step 2.2

Combine $\frac{1}{2}$ and $x$ .

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

Step 3

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4

To write $\frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{x}{3}$ by $\frac{2}{2}$ .

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

Step 5.2

Multiply $3$ by $2$ .

$\frac{x \cdot 2}{6} + \frac{x}{2} \cdot \frac{3}{3} + \frac{1}{4} - \frac{2}{3}$

Step 5.3

Multiply $\frac{x}{2}$ by $\frac{3}{3}$ .

$\frac{x \cdot 2}{6} + \frac{x \cdot 3}{2 \cdot 3} + \frac{1}{4} - \frac{2}{3}$

Step 5.4

Multiply $2$ by $3$ .

$\frac{x \cdot 2}{6} + \frac{x \cdot 3}{6} + \frac{1}{4} - \frac{2}{3}$

Step 6

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + x \cdot 3}{6} + \frac{1}{4} - \frac{2}{3}$

Step 7

Reorder $x$ and $3$ .

$\frac{2 \cdot x + 3 \cdot x}{6} + \frac{1}{4} - \frac{2}{3}$

Step 8

Add $2 \cdot x$ and $3 \cdot x$ .

$\frac{5 \cdot x}{6} + \frac{1}{4} - \frac{2}{3}$

Step 9

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 x}{6} + \frac{1}{4} \cdot \frac{3}{3} - \frac{2}{3}$

Step 10

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 x}{6} + \frac{1}{4} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{4}{4}$

Step 11

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 11.1

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

$\frac{5 x}{6} + \frac{3}{4 \cdot 3} - \frac{2}{3} \cdot \frac{4}{4}$

Step 11.2

Multiply $4$ by $3$ .

$\frac{5 x}{6} + \frac{3}{12} - \frac{2}{3} \cdot \frac{4}{4}$

Step 11.3

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$\frac{5 x}{6} + \frac{3}{12} - \frac{2 \cdot 4}{3 \cdot 4}$

Step 11.4

Multiply $3$ by $4$ .

$\frac{5 x}{6} + \frac{3}{12} - \frac{2 \cdot 4}{12}$

Step 12

Combine the numerators over the common denominator.

$\frac{5 x}{6} + \frac{3 - 2 \cdot 4}{12}$

Step 13

Simplify the numerator.

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Step 13.1

Multiply $- 2$ by $4$ .

$\frac{5 x}{6} + \frac{3 - 8}{12}$

Step 13.2

Subtract $8$ from $3$ .

$\frac{5 x}{6} + \frac{- 5}{12}$

Step 14

Move the negative in front of the fraction.

$\frac{5 x}{6} - \frac{5}{12}$