Question

How do you define a variable and write an algebraic expression for the phrase: 10 plus quotient of a number and 15?

Answer 1

Hint: To express 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 10 plus quotient of a number and 15. We will break this phrase into two parts.
The first part is ‘10 plus’ is pretty simple to translate into symbols; it just becomes \[10+....\].
The second part of the phrase is ‘quotient of a number and 15’. We know that the quotient of the solution of a division problem. Let the number in this part of the phrase is \[x\], as we have to take the quotient of the number and 15. The quotient is \[\dfrac{x}{15}\].
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
\[\Rightarrow \dfrac{x}{15}+10\]

Hence, the expression for the given phrase is \[\dfrac{x}{15}+10\].

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.