Basic Math Examples

$(18 a b - 12) - (\frac{9 a b}{2} - 3)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$18 a b - 12 - \frac{9 a b}{2} - - 3$

Step 1.2

Multiply $- 1$ by $- 3$ .

$18 a b - 12 - \frac{9 a b}{2} + 3$

Step 2

To write $18 a b$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$18 a b \cdot \frac{2}{2} - \frac{9 a b}{2} - 12 + 3$

Step 3

Simplify terms.

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Step 3.1

Combine $18 a b$ and $\frac{2}{2}$ .

$\frac{18 a b \cdot 2}{2} - \frac{9 a b}{2} - 12 + 3$

Step 3.2

Combine the numerators over the common denominator.

$\frac{18 a b \cdot 2 - 9 a b}{2} - 12 + 3$

Step 4

Simplify the numerator.

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Step 4.1

Factor $9 a b$ out of $18 a b \cdot 2 - 9 a b$ .

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Step 4.1.1

Factor $9 a b$ out of $18 a b \cdot 2$ .

$\frac{9 a b (2 \cdot 2) - 9 a b}{2} - 12 + 3$

Step 4.1.2

Factor $9 a b$ out of $- 9 a b$ .

$\frac{9 a b (2 \cdot 2) + 9 a b (- 1)}{2} - 12 + 3$

Step 4.1.3

Factor $9 a b$ out of $9 a b (2 \cdot 2) + 9 a b (- 1)$ .

$\frac{9 a b (2 \cdot 2 - 1)}{2} - 12 + 3$

Step 4.2

Multiply $2$ by $2$ .

$\frac{9 a b (4 - 1)}{2} - 12 + 3$

Step 4.3

Subtract $1$ from $4$ .

$\frac{9 a b \cdot 3}{2} - 12 + 3$

Step 4.4

Multiply $3$ by $9$ .

$\frac{27 a b}{2} - 12 + 3$

Step 5

Add $- 12$ and $3$ .

$\frac{27 a b}{2} - 9$