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How do you write an algebraic expression that models the word phrase ‘product of $e$ and 4, divided by 12’?

Last updated date: 20th Jun 2024
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Hint: We first try to make the given written statement in its mathematical form. We assume the variable $m$ to as the required number. Then we form the relationship. We apply the binary operation of multiplication. Then we need to multiply the exponential value with 4. We then solve the given linear equation where we are finding the quotient of the multiplied number and 12. We get the value of the variable $m$ as the solution.

Complete step-by-step solution:
The given statement about the required number $m$ is that it is equal to the product of $e$ and 4, divided by 12.
Let’s assume the solution as $m$.
Now we multiply $e$ with 4 which gives $4\times \left( e \right)$. This is equal to $4e$
Now, we find the division where we need the quotient of the multiplied number and 12 which means here $4e$ is the dividend or the numerator for its fraction form and 12 is the divisor or the denominator for its fraction form.
We form the mathematical statement as fraction form.
In a fraction $\dfrac{a}{b}$, the terms $a$ and $b$ are the numerator and denominator for the fraction.
Forming according to this we get the mathematical form as $\dfrac{4e}{12}$.
Therefore, the final algebraic expression of the product of $e$ and 4, divided by 12 is $\dfrac{4e}{12}$.

Note: We can also solve the system according to the value of $m$. As the required number is equal to $\dfrac{4e}{12}$, we can say that $\dfrac{4e}{12}=m$. Now in that case we are taking the extra variable which is unnecessary. But we can mention the variable to make it a single equation form.