Algebra Examples

$\frac{3}{4} (z + \frac{2}{5}) + 2 z$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Combine $\frac{3}{4}$ and $z$ .

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

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $4$ .

$\frac{3 z}{4} + \frac{3}{2 (2)} \cdot \frac{2}{5} + 2 z$

Step 1.3.2

Cancel the common factor.

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

Step 1.3.3

Rewrite the expression.

$\frac{3 z}{4} + \frac{3}{2} \cdot \frac{1}{5} + 2 z$

Step 1.4

Multiply $\frac{3}{2}$ by $\frac{1}{5}$ .

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

Step 1.5

Multiply $2$ by $5$ .

$\frac{3 z}{4} + \frac{3}{10} + 2 z$

Step 2

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

$\frac{3 z}{4} + 2 z \cdot \frac{4}{4} + \frac{3}{10}$

Step 3

Simplify terms.

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Step 3.1

Combine $2 z$ and $\frac{4}{4}$ .

$\frac{3 z}{4} + \frac{2 z \cdot 4}{4} + \frac{3}{10}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3 z + 2 z \cdot 4}{4} + \frac{3}{10}$

Step 4

Simplify each term.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Factor $z$ out of $3 z + 2 z \cdot 4$ .

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Step 4.1.1.1

Factor $z$ out of $3 z$ .

$\frac{z \cdot 3 + 2 z \cdot 4}{4} + \frac{3}{10}$

Step 4.1.1.2

Factor $z$ out of $2 z \cdot 4$ .

$\frac{z \cdot 3 + z (2 \cdot 4)}{4} + \frac{3}{10}$

Step 4.1.1.3

Factor $z$ out of $z \cdot 3 + z (2 \cdot 4)$ .

$\frac{z (3 + 2 \cdot 4)}{4} + \frac{3}{10}$

Step 4.1.2

Multiply $2$ by $4$ .

$\frac{z (3 + 8)}{4} + \frac{3}{10}$

Step 4.1.3

Add $3$ and $8$ .

$\frac{z \cdot 11}{4} + \frac{3}{10}$

Step 4.2

Move $11$ to the left of $z$ .

$\frac{11 z}{4} + \frac{3}{10}$