Question

How do you write the phrase “The quotient of 37 and the product of a number and 25” as a variable expression?

Answer 1

Hint: This question is from the topic of algebra. In this question, we will first understand about the term quotient. After that, we will understand about the term product. After that, we will use the terms quotient and product and then find the best suitable mathematical term of the phrase given in the question.

Complete step-by-step answer:
Let us solve this question.
In this question, we have asked to find the mathematical form of the phrase “The quotient of 37 and the product of a number and 25.”
So, let us first understand about the term quotient.
The term quotient is used where there is a division. Whenever, we divide a number by a different number, then after division we get quotient and remainder. The quotient is the answer to a division problem. Let us understand this from the following examples:
\[\dfrac{35}{7}=5\] or we can write this as \[7\overset{5}{\overline{\left){\begin{align}
  & 35 \\
 & \underline{35} \\
 & 00 \\
\end{align}}\right.}}\]
If we divide 35 by 7, then we will get 5 as quotient and 0 as remainder.
Similarly, we can see below for another example.
\[9\overset{5}{\overline{\left){\begin{align}
  & 48 \\
 & \underline{45} \\
 & \times 3 \\
\end{align}}\right.}}\]
Here, we can see that if we divide 48 by 9, then we will get 5 as quotient and 3 as remainder.
If it is saying quotient, then it is saying for division.
Now, let us understand the term product.
The term product is used for multiplication.
For example, if we say product of 9 and 10, then it will be written as \[9\times 10=90\].
So, we can say that the product of a number and 25 will be \[x\times 25=25x\] (let the number be x).
Now, we can say that “The quotient of 37 and the product of a number and 25” as a variable expression will be \[\dfrac{37}{25x}\].

Note: We should have a better knowledge in the topic of algebra to solve this type of question easily. We should know about the terms quotient. We should know about the term product. Always remember that, \[\text{Dividend}=\text{Divisor}\times \text{Quotient}+\text{Remainder}\]. We can understand this from the following example:
\[9\overset{5}{\overline{\left){\begin{align}
  & 48 \\
 & \underline{45} \\
 & \times 3 \\
\end{align}}\right.}}\]
Where, 48 is dividend, 9 is divisor, 5 is quotient, and 3 is remainder.