Question

What is “two more than the quotient of six and a number $n$” written as an algebraic expression?

Answer 1

Hint: When we convert a word phrase into the corresponding algebraic expression, we need to know each and every mathematical counterpart of the given words. And we know that an expression that includes a variable is known as an algebraic expression.

Complete step by step answer:
Let us consider the given word phrase, “two more than the quotient of six and a number $n$”
We are asked to convert the given word phrase into an algebraic expression.
We know that an algebraic expression is an expression that includes an unknown variable.
Now, we need to analyze each word in the given word phrase in order to find their mathematical counterpart and then to convert the word phrase into an algebraic expression.
Let us consider the word phrase in the reverse order. That is, we will analyze each word of the word phrase from right to left.
So, we can see that the last terms are “a number $n$”
So, in the given word phrase, $n$ is the unknown variable.
As we know, we can replace six by $6$
Then, we can see the part “quotient of”
We know that the word quotient implies the output of the operation division.
So, we can say that the quotient of six and the unknown number implies that six is the dividend and the unknown variable is the divisor.
So, we will get this part as $\dfrac{6}{n}.$
We know that “more than” implies addition.
So, we need to add $2$ to the above obtained number.
Then, we will get $\dfrac{6}{n}+2.$

Hence the algebraic expression is $\dfrac{6}{n}+2.$

Note: We can always convert a word phrase into an algebraic expression and an algebraic expression into a word phrase by knowing the mathematical counterparts of each word. We need to find out the unknown number first and then the operations and the remaining numbers will be joined to the unknown variable.