Question

How do you convert the following phrases into math expressions: the quotient of 14 and the difference between a number and -7?

Answer 1

Hint: First understand the definition of an algebraic expression using examples. Now, assume the unknown number as ‘x’. Take the difference of this variable x and -7. Divide the given numerical value 14 with the obtained relation in x to get the required expression and answer. Take the exponent of x equal to 1.

Complete step by step answer:
Here, we have been provided with the sentence ‘the quotient of 14 and the difference between a number and -7’. We have been asked to convert it into the mathematical expression. But first we need to understand the term ‘algebraic expression’.
In mathematics, an algebraic expression is an expression that contains constants, variables and algebraic operations like: - addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number. For example: - \[5{{x}^{3}}-3{{x}^{2}}y+xy+10\] is an algebraic expression.
Let us come to the question. We have to write the algebraic expression for the sentence: - the quotient of 14 and the difference between a number and -7. Let us assume the unknown number as x and its exponent as 1. Let us assume the required expression as E.
Now, considering the difference of x and -7, we get,
$\Rightarrow x-\left( -7 \right)=x+7$
Now, the term ‘quotient’ is used when we divide any number by another number, here we have to take the quotient of 14 and x + 7, so dividing 14 by x + 7, we get,
\[\Rightarrow E=\dfrac{14}{x+7}\]
Hence, the above expression is our required mathematical expression.

Note:
One may note that we must not substitute the obtained algebraic expression equal to 0. This is because if we do so then the algebraic expression will become an algebraic equation. Note that for the obtained expression to be defined the denominator must not be 0, so x must not be equal to -7.