Simplify x/2+y/3-z/4

$\frac{x}{2} + \frac{y}{3} - \frac{z}{4}$

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

Multiply $2$ by $3$ .

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

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

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

Multiply $3$ by $2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Move $3$ to the left of $x$ .

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

Move $2$ to the left of $y$ .

$\frac{3 x + 2 y}{6} - \frac{z}{4}$

Step 6

To write $\frac{3 x + 2 y}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 7

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

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

Step 8

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

Multiply $\frac{3 x + 2 y}{6}$ by $\frac{2}{2}$ .

$\frac{(3 x + 2 y) \cdot 2}{6 \cdot 2} - \frac{z}{4} \cdot \frac{3}{3}$

Multiply $6$ by $2$ .

$\frac{(3 x + 2 y) \cdot 2}{12} - \frac{z}{4} \cdot \frac{3}{3}$

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

$\frac{(3 x + 2 y) \cdot 2}{12} - \frac{z \cdot 3}{4 \cdot 3}$

Multiply $4$ by $3$ .

$\frac{(3 x + 2 y) \cdot 2}{12} - \frac{z \cdot 3}{12}$

Step 9

Combine the numerators over the common denominator.

$\frac{(3 x + 2 y) \cdot 2 - z \cdot 3}{12}$

Step 10

Simplify the numerator.

Apply the distributive property.

$\frac{3 x \cdot 2 + 2 y \cdot 2 - z \cdot 3}{12}$

Multiply $2$ by $3$ .

$\frac{6 x + 2 y \cdot 2 - z \cdot 3}{12}$

Multiply $2$ by $2$ .

$\frac{6 x + 4 y - z \cdot 3}{12}$

Multiply $3$ by $- 1$ .

$\frac{6 x + 4 y - 3 z}{12}$

Simplify x/2+y/3-z/4

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