Basic Math Examples

$\frac{2 z + 5}{4} - \frac{z - 1}{2}$

Step 1

To write $- \frac{z - 1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{z - 1}{2}$ by $\frac{2}{2}$ .

$\frac{2 z + 5}{4} - \frac{(z - 1) \cdot 2}{2 \cdot 2}$

Step 2.2

Multiply $2$ by $2$ .

$\frac{2 z + 5}{4} - \frac{(z - 1) \cdot 2}{4}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 z + 5 - (z - 1) \cdot 2}{4}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{2 z + 5 + (- z - - 1) \cdot 2}{4}$

Step 4.2

Multiply $- 1$ by $- 1$ .

$\frac{2 z + 5 + (- z + 1) \cdot 2}{4}$

Step 4.3

Apply the distributive property.

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

Step 4.4

Multiply $2$ by $- 1$ .

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

Step 4.5

Multiply $2$ by $1$ .

$\frac{2 z + 5 - 2 z + 2}{4}$

Step 4.6

Subtract $2 z$ from $2 z$ .

$\frac{0 + 5 + 2}{4}$

Step 4.7

Add $0$ and $5$ .

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

Step 4.8

Add $5$ and $2$ .

$\frac{7}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{4}$

Decimal Form:

$1.75$

Mixed Number Form:

$1 \frac{3}{4}$