Question

How do you write an expression for the verbal phrase, “The quotient of fifteen and the product of two times x”?

Answer 1

Hint: To expression a verbal phrase as an algebraic expression, we need to break the phrase into different parts. Write the mathematical expression for each part, and finally combine the expressions for all the parts, we get the algebraic expression for the given phrase. Also, for this question we should know, a quotient is the solution to a division problem, for example \[\dfrac{a}{b}=c\], here c is the quotient of division of \[a\And b\].

Complete step-by-step answer:
The given phrase is the quotient of fifteen and the product of two times x. We will break this phrase into two parts.
The first part is ‘the quotient of’. We know that the quotient of the solution of a division problem. This means that we have to take division of the quantities.
The second part of the phrase is ‘fifteen and the product of two times x’. We already know that we need to take the quotient the given quantities are 15 and two twice x which is algebraically expressed as \[2x\].
Now that we have converted both parts into mathematical expressions, we need to combine them to form the expression for the given phrase. By doing this we get
\[\Rightarrow \dfrac{15}{2x}\]
Hence, the expression for the given phrase is \[\dfrac{15}{2x}\].

Note: We can do a similar thing to convert an algebraic expression to a verbal phrase. We need to break the equation into different parts and write verbal meaning for each part. After this after combining the verbal meaning of each phrase, we get the verbal expression.