Finite Math Examples

$200 = \frac{1}{2} \cdot (h (10 + 15))$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (h (10 + 15)) = 200$ .

$\frac{1}{2} \cdot (h (10 + 15)) = 200$

Step 2

Multiply both sides of the equation by $\frac{1}{\frac{1}{2} (10 + 15)}$ .

$\frac{1}{\frac{1}{2} (10 + 15)} (\frac{1}{2} \cdot (h (10 + 15))) = \frac{1}{\frac{1}{2} (10 + 15)} \cdot 200$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $\frac{1}{2} \cdot (10 + 15)$ .

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Step 3.1.1.1

Factor $\frac{1}{2} \cdot (10 + 15)$ out of $\frac{1}{2} \cdot (h (10 + 15))$ .

$\frac{1}{\frac{1}{2} (10 + 15)} (\frac{1}{2} (10 + 15) (h)) = \frac{1}{\frac{1}{2} (10 + 15)} \cdot 200$

Step 3.1.1.2

Cancel the common factor.

$\frac{1}{\frac{1}{2} (10 + 15)} (\frac{1}{2} (10 + 15) h) = \frac{1}{\frac{1}{2} (10 + 15)} \cdot 200$

Step 3.1.1.3

Rewrite the expression.

$h = \frac{1}{\frac{1}{2} (10 + 15)} \cdot 200$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{1}{\frac{1}{2} (10 + 15)} \cdot 200$ .

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Step 3.2.1.1

Add $10$ and $15$ .

$h = \frac{1}{\frac{1}{2} \cdot 25} \cdot 200$

Step 3.2.1.2

Combine $\frac{1}{2}$ and $25$ .

$h = \frac{1}{\frac{25}{2}} \cdot 200$

Step 3.2.1.3

Multiply the numerator by the reciprocal of the denominator.

$h = 1 (\frac{2}{25}) \cdot 200$

Step 3.2.1.4

Multiply $\frac{2}{25}$ by $1$ .

$h = \frac{2}{25} \cdot 200$

Step 3.2.1.5

Cancel the common factor of $25$ .

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Step 3.2.1.5.1

Factor $25$ out of $200$ .

$h = \frac{2}{25} \cdot (25 (8))$

Step 3.2.1.5.2

Cancel the common factor.

$h = \frac{2}{25} \cdot (25 \cdot 8)$

Step 3.2.1.5.3

Rewrite the expression.

$h = 2 \cdot 8$

Step 3.2.1.6

Multiply $2$ by $8$ .

$h = 16$