Question

How do you translate the word phrase into a variable expression: seven less than the quotient of $x$ and 9?

Answer 1

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 $x$ and 9. We apply the binary operation of division. Then we need to subtract 7 from the quotient value.

Complete step by step solution:
The given statement about the required number $m$ is that it is equal to seven less than the quotient of $x$ and 9.
Let’s assume the solution as $m$.
First, we find the division where we need the quotient of $x$ and 9 which means here $x$ is the dividend or the numerator for its fraction form and 9 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 $\dfrac{x}{9}$.
Therefore, the algebraic expression is $\dfrac{x}{9}$.
Now we subtract 7 from $\dfrac{x}{9}$ which gives $\left( \dfrac{x}{9}-7 \right)$.
Therefore, the final algebraic expression of seven less than the quotient of $x$ and 9 is $\left(\dfrac{x}{9}-7 \right)$.

Note: we can also solve the system according to the value of $m$. As the required number is equal to $\dfrac{x}{9}$, we can say that $\dfrac{x}{9}=m$. 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.