To solve the given equation [tex]\(a \cdot b = c \cdot d \cdot e\)[/tex] for [tex]\(e\)[/tex], follow these steps:
### Step 1: Identify the target variable
We need to isolate [tex]\(e\)[/tex] on one side of the equation.
### Step 2: Think about the balancing operation
To isolate [tex]\(e\)[/tex], we need to eliminate the [tex]\(c \cdot d\)[/tex] that is multiplying [tex]\(e\)[/tex]. We can do this by dividing both sides of the equation by [tex]\(c \cdot d\)[/tex].
### Step 3: Apply the balancing operation to both sides
Multiply both sides by [tex]\(\frac{1}{c \cdot d}\)[/tex]:
[tex]\[
a \cdot b \times \frac{1}{c \cdot d} = c \cdot d \cdot e \times \frac{1}{c \cdot d}
\][/tex]
### Step 4: Simplify the equation
On the right side, [tex]\(c \cdot d\)[/tex] cancels out:
[tex]\[
e = \frac{a \cdot b}{c \cdot d}
\][/tex]
### Final Result
The value of [tex]\(e\)[/tex] is:
[tex]\[
e = \frac{a \cdot b}{c \cdot d}
\][/tex]
