Algebra Examples

$\frac{4}{5} x + \frac{2}{3} x$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{4}{5}$ and $x$ .

$\frac{4 x}{5} + \frac{2}{3} x$

Step 1.2

Combine $\frac{2}{3}$ and $x$ .

$\frac{4 x}{5} + \frac{2 x}{3}$

Step 2

To write $\frac{4 x}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

To write $\frac{2 x}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{4 x}{5}$ by $\frac{3}{3}$ .

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

Step 4.2

Multiply $5$ by $3$ .

$\frac{4 x \cdot 3}{15} + \frac{2 x}{3} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{2 x}{3}$ by $\frac{5}{5}$ .

$\frac{4 x \cdot 3}{15} + \frac{2 x \cdot 5}{3 \cdot 5}$

Step 4.4

Multiply $3$ by $5$ .

$\frac{4 x \cdot 3}{15} + \frac{2 x \cdot 5}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 x \cdot 3 + 2 x \cdot 5}{15}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $2 x$ out of $4 x \cdot 3 + 2 x \cdot 5$ .

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Step 6.1.1

Factor $2 x$ out of $4 x \cdot 3$ .

$\frac{2 x (2 \cdot 3) + 2 x \cdot 5}{15}$

Step 6.1.2

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

$\frac{2 x (2 \cdot 3) + 2 x (5)}{15}$

Step 6.1.3

Factor $2 x$ out of $2 x (2 \cdot 3) + 2 x (5)$ .

$\frac{2 x (2 \cdot 3 + 5)}{15}$

Step 6.2

Multiply $2$ by $3$ .

$\frac{2 x (6 + 5)}{15}$

Step 6.3

Add $6$ and $5$ .

$\frac{2 x \cdot 11}{15}$

Step 6.4

Multiply $11$ by $2$ .

$\frac{22 x}{15}$