Basic Math Examples

$\frac{5}{7} \cdot (z + y) - \frac{1}{7} \cdot (z - 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{5}{7} z + \frac{5}{7} y - \frac{1}{7} \cdot (z - 1)$

Step 1.2

Combine $\frac{5}{7}$ and $z$ .

$\frac{5 z}{7} + \frac{5}{7} y - \frac{1}{7} \cdot (z - 1)$

Step 1.3

Combine $\frac{5}{7}$ and $y$ .

$\frac{5 z}{7} + \frac{5 y}{7} - \frac{1}{7} \cdot (z - 1)$

Step 1.4

Apply the distributive property.

$\frac{5 z}{7} + \frac{5 y}{7} - \frac{1}{7} z - \frac{1}{7} \cdot - 1$

Step 1.5

Combine $z$ and $\frac{1}{7}$ .

$\frac{5 z}{7} + \frac{5 y}{7} - \frac{z}{7} - \frac{1}{7} \cdot - 1$

Step 1.6

Multiply $- \frac{1}{7} \cdot - 1$ .

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Step 1.6.1

Multiply $- 1$ by $- 1$ .

$\frac{5 z}{7} + \frac{5 y}{7} - \frac{z}{7} + 1 (\frac{1}{7})$

Step 1.6.2

Multiply $\frac{1}{7}$ by $1$ .

$\frac{5 z}{7} + \frac{5 y}{7} - \frac{z}{7} + \frac{1}{7}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{5 z + 5 y - z + 1}{7}$

Step 2.2

Subtract $z$ from $5 z$ .

$\frac{5 y + 4 z + 1}{7}$