Basic Math Examples

$\frac{1}{2} \cdot (6 (5 + b)) = 60 {cm}^{2}$

Step 1

Multiply both sides of the equation by $\frac{1}{\frac{1}{2} \cdot 6}$ .

$\frac{1}{\frac{1}{2} \cdot 6} (\frac{1}{2} \cdot (6 (5 + b))) = \frac{1}{\frac{1}{2} \cdot 6} (60 {cm}^{2})$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{1}{\frac{1}{2} \cdot 6} (\frac{1}{2} \cdot (6 (5 + b)))$ .

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Step 2.1.1.1

Combine $\frac{1}{2}$ and $6$ .

$\frac{1}{\frac{6}{2}} (\frac{1}{2} \cdot (6 (5 + b))) = \frac{1}{\frac{1}{2} \cdot 6} (60 {cm}^{2})$

Step 2.1.1.2

Divide $6$ by $2$ .

$\frac{1}{3} (\frac{1}{2} \cdot (6 (5 + b))) = \frac{1}{\frac{1}{2} \cdot 6} (60 {cm}^{2})$

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Factor $3$ out of $\frac{1}{2} \cdot (6 (5 + b))$ .

$\frac{1}{3} (3 (\frac{1}{2} \cdot (2 (5 + b)))) = \frac{1}{\frac{1}{2} \cdot 6} (60 {cm}^{2})$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{1}{3} (3 (\frac{1}{2} \cdot (2 (5 + b)))) = \frac{1}{\frac{1}{2} \cdot 6} (60 {cm}^{2})$

Step 2.1.1.3.3

Rewrite the expression.

$\frac{1}{2} \cdot (2 (5 + b)) = \frac{1}{\frac{1}{2} \cdot 6} (60 {cm}^{2})$

Step 2.1.1.4

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

$\frac{2}{2} \cdot (5 + b) = \frac{1}{\frac{1}{2} \cdot 6} (60 {cm}^{2})$

Step 2.1.1.5

Simplify the expression.

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Step 2.1.1.5.1

Divide $2$ by $2$ .

$1 \cdot (5 + b) = \frac{1}{\frac{1}{2} \cdot 6} (60 {cm}^{2})$

Step 2.1.1.5.2

Multiply $5 + b$ by $1$ .

$5 + b = \frac{1}{\frac{1}{2} \cdot 6} (60 {cm}^{2})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{1}{\frac{1}{2} \cdot 6} (60 {cm}^{2})$ .

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Step 2.2.1.1

Combine $\frac{1}{2}$ and $6$ .

$5 + b = \frac{1}{\frac{6}{2}} (60 {cm}^{2})$

Step 2.2.1.2

Divide $6$ by $2$ .

$5 + b = \frac{1}{3} (60 {cm}^{2})$

Step 2.2.1.3

Combine $\frac{1}{3}$ and $60 {cm}^{2}$ .

$5 + b = \frac{60 {cm}^{2}}{3}$

Step 3

Subtract $5$ from both sides of the equation.

$b = \frac{60 {cm}^{2}}{3} - 5$

Step 4

Cancel the common factor of $60$ and $3$ .

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Step 4.1

Factor $3$ out of $60 {cm}^{2}$ .

$b = \frac{3 (20 {cm}^{2})}{3} - 5$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $3$ .

$b = \frac{3 (20 {cm}^{2})}{3 (1)} - 5$

Step 4.2.2

Cancel the common factor.

$b = \frac{3 (20 {cm}^{2})}{3 \cdot 1} - 5$

Step 4.2.3

Rewrite the expression.

$b = \frac{20 {cm}^{2}}{1} - 5$

Step 4.2.4

Divide $20 {cm}^{2}$ by $1$ .

$b = 20 {cm}^{2} - 5$