Question

How do you write an algebraic expression for the phrase: the quotient of twenty and a number?

Answer 1

Hint: For writing the expression for the phrase given in the question, we need to find the mathematical equivalent of each of the terms present in the phrase. In the phrase given, we are told about the quotient of twenty and a number. The quotient, as we know, is the result of the division of two numbers. So the algebraic expression for the given phrase will be expressed as a fraction of twenty and a number. Since the number is unknown to us, we have to assume it by a particular variable, say $n$.

Complete step by step answer:
The phrase written in the above is given as: the quotient of twenty and a number.
Since we are not told anything about the number, we assume the number by the variable $n$. Now, we know that the term quotient is related to the division of two numbers. In fact, the quotient is equal to the result when one number is divided by the other number. Mathematically, the division of two numbers is expressed as the fraction composed of the two numbers. So the quotient of twenty and the number $n$ is expressed as $\dfrac{20}{n}$.

Hence, the algebraic expression corresponding to the phrase: “the quotient of twenty and a number” is equivalent to $\dfrac{20}{n}$.

Note: Do not be confused regarding the numerator and the denominator while writing the algebraic expression of the given phrase. Since the number twenty is mentioned first in the given phrase, so it is written in the numerator. And the unknown number is mentioned later, so it is written in the denominator.