Question

How do you write an expression to represent: nine minus the quotient of two and a number x?

Answer 1

Hint: We first try to make the given written statement in its mathematical form. We assume the variable $m$ to as the required number. Then we form the relationship. We then solve the given linear equation where we are finding the quotient of two and a number x. We apply the binary operation of division. Then we need to subtract the quotient value from nine. We get the value of the variable $m$ as the solution.

Complete step-by-step solution:
The given statement about the required number $m$ is that it is equal to nine minus the quotient of two and a number x.
Let’s assume the solution as $m$.
First, we find the division where we need the quotient of two and a number x which means here 2 is the dividend or the numerator for its fraction form and $x$ is the divisor or the denominator for its fraction form.
We form the mathematical statement as fraction form.
In a fraction $\dfrac{a}{b}$, the terms $a$ and $b$ are the numerator and denominator for the fraction.
Forming according to this we get the mathematical form as $\dfrac{2}{x}$.
Therefore, the algebraic expression is $\dfrac{2}{x}$.
Now we subtract $\dfrac{2}{x}$ from 9 which gives $\left( 9-\dfrac{2}{x} \right)$.
Therefore, the final algebraic expression of nine minus the quotient of two and a number x is $\left( 9-\dfrac{2}{x} \right)$.

Note: We can also solve the system according to the value of $m$. As the required number is equal to $\left( 9-\dfrac{2}{x} \right)$, we can say that $\left( 9-\dfrac{2}{x} \right)=m$. Now in that case we are taking the extra variable which is unnecessary. But we can mention the variable to make it a single equation form.