Basic Math Examples

$18 {mm}^{2} = \frac{1}{2} \cdot (4 mm (a + 1 mm))$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (4 mm (a + 1 mm)) = 18 {mm}^{2}$ .

$\frac{1}{2} \cdot (4 mm (a + 1 mm)) = 18 {mm}^{2}$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (4 mm (a + 1 mm))) = 2 (18 {mm}^{2})$

Step 3

Simplify the left side.

Tap for more steps...

Step 3.1

Simplify $2 (\frac{1}{2} \cdot (4 mm (a + 1 mm)))$ .

Tap for more steps...

Step 3.1.1

Apply the distributive property.

$2 (\frac{1}{2} \cdot (4 mm a + 4 mm (1 mm))) = 2 (18 {mm}^{2})$

Step 3.1.2

Apply the distributive property.

$2 (\frac{1}{2} (4 mm a) + \frac{1}{2} (4 mm (1 mm))) = 2 (18 {mm}^{2})$

Step 3.1.3

Multiply $\frac{1}{2} (4 mm a)$ .

Tap for more steps...

Step 3.1.3.1

Combine $4 mm$ and $\frac{1}{2}$ .

$2 (\frac{4 mm}{2} a + \frac{1}{2} (4 mm (1 mm))) = 2 (18 {mm}^{2})$

Step 3.1.3.2

Combine $\frac{4 mm}{2}$ and $a$ .

$2 (\frac{4 mm a}{2} + \frac{1}{2} (4 mm (1 mm))) = 2 (18 {mm}^{2})$

Step 3.1.4

Multiply $\frac{1}{2} (4 mm (1 mm))$ .

Tap for more steps...

Step 3.1.4.1

Combine $4 mm$ and $\frac{1}{2}$ .

$2 (\frac{4 mm a}{2} + \frac{4 mm}{2} (1 mm)) = 2 (18 {mm}^{2})$

Step 3.1.4.2

Combine $\frac{4 mm}{2}$ and $1 mm$ .

$2 (\frac{4 mm a}{2} + \frac{4 mm (1 mm)}{2}) = 2 (18 {mm}^{2})$

Step 3.1.5

Apply the distributive property.

$2 \frac{4 mm a}{2} + 2 \frac{4 mm (1 mm)}{2} = 2 (18 {mm}^{2})$

Step 3.1.6

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.6.1

Cancel the common factor.

$2 \frac{4 mm a}{2} + 2 \frac{4 mm (1 mm)}{2} = 2 (18 {mm}^{2})$

Step 3.1.6.2

Rewrite the expression.

$4 mm a + 2 \frac{4 mm (1 mm)}{2} = 2 (18 {mm}^{2})$

Step 3.1.7

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.7.1

Cancel the common factor.

$4 mm a + 2 \frac{4 mm (1 mm)}{2} = 2 (18 {mm}^{2})$

Step 3.1.7.2

Rewrite the expression.

$4 mm a + 4 mm (1 mm) = 2 (18 {mm}^{2})$

Step 4

Subtract $4 mm (1 mm)$ from both sides of the equation.

$4 mm a = 2 (18 {mm}^{2}) - (4 mm) (1 mm)$

Step 5

Divide each term in $4 mm a = 2 (18 {mm}^{2}) - (4 mm) (1 mm)$ by $4 mm$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $4 mm a = 2 (18 {mm}^{2}) - (4 mm) (1 mm)$ by $4 mm$ .

$\frac{4 mm a}{4 mm} = \frac{2 (18 {mm}^{2})}{4 mm} + \frac{- (4 mm) (1 mm)}{4 mm}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $4 mm$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{4 mm a}{4 mm} = \frac{2 (18 {mm}^{2})}{4 mm} + \frac{- (4 mm) (1 mm)}{4 mm}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{2 (18 {mm}^{2})}{4 mm} + \frac{- (4 mm) (1 mm)}{4 mm}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Simplify each term.

Tap for more steps...

Step 5.3.1.1

Cancel the common factor of $4 mm$ .

Tap for more steps...

Step 5.3.1.1.1

Cancel the common factor.

$a = \frac{2 (18 {mm}^{2})}{4 mm} + \frac{- (4 mm) (1 mm)}{4 mm}$

Step 5.3.1.1.2

Divide $- 1 (1 mm)$ by $1$ .

$a = \frac{2 (18 {mm}^{2})}{4 mm} - 1 (1 mm)$

Step 5.3.1.2

Rewrite $- 1 (1 mm)$ as $- (1 mm)$ .

$a = \frac{2 (18 {mm}^{2})}{4 mm} - (1 mm)$

Step 6

Simplify $a = \frac{2 (18 {mm}^{2})}{4 mm} - (1 mm)$ .

Tap for more steps...

Step 6.1

Simplify each term.

Tap for more steps...

Step 6.1.1

Cancel the common factors.

Tap for more steps...

Step 6.1.1.1

Factor $2$ out of $4 mm$ .

$a = \frac{2 (18 {mm}^{2})}{2 (2 mm)} - (1 mm)$

Step 6.1.1.2

Cancel the common factor.

$a = \frac{2 (18 {mm}^{2})}{2 (2 mm)} - (1 mm)$

Step 6.1.1.3

Rewrite the expression.

$a = \frac{18 {mm}^{2}}{2 mm} - (1 mm)$

Step 6.1.2

Cancel the common factor of $18$ and $2$ .

Tap for more steps...

Step 6.1.2.1

Factor $2$ out of $18 {mm}^{2}$ .

$a = \frac{2 (9 {mm}^{2})}{2 mm} - (1 mm)$

Step 6.1.2.2

Cancel the common factors.

Tap for more steps...

Step 6.1.2.2.1

Factor $2$ out of $2 mm$ .

$a = \frac{2 (9 {mm}^{2})}{2 (1 mm)} - (1 mm)$

Step 6.1.2.2.2

Cancel the common factor.

$a = \frac{2 (9 {mm}^{2})}{2 (1 mm)} - (1 mm)$

Step 6.1.2.2.3

Rewrite the expression.

$a = \frac{9 {mm}^{2}}{1 mm} - (1 mm)$

Step 6.1.3

Cancel $mm$ .

$a = \frac{9 {mm}^{2}}{1 mm} - (1 mm)$

Step 6.1.4

Rewrite the expression.

$a = 9 mm - (1 mm)$

Step 6.1.5

Multiply $- 1$ by $1$ .

$a = 9 mm - mm$

Step 6.2

Subtract $mm$ from $9 mm$ .

$a = 8 mm$