Question

How do you write the given phrase as a variable expression “quotient of a number and 3 is decreased by 1”?

Answer 1

Hint: We start solving the problem by assuming the variable for the given number. We then make use of the fact that the algebraic expression of phrase “quotient of a and b” is defined as $\dfrac{a}{b}$ to find the algebraic expression for the phrase “quotient of a number and 3”. We then subtract 1 from the obtained expression to get the variable expression for “quotient of a number and 3 is decreased by 1”.

Complete step-by-step answer:
According to the problem, we are asked to write the given phrase “quotient of a number and 3 is decreased by 1” as a variable expression.
Let us assume the number be x.
We know that the algebraic expression of the phrase “quotient of a and b” is defined as $\dfrac{a}{b}$. Let us use this for the given phrase.
So, we get the algebraic expression “quotient of a number and 3” is $\dfrac{x}{3}$. Now, this is to be decreased by 1 to get the algebraic expression of the phrase “quotient of a number and 3 is decreased by 1” which is $\dfrac{x}{3}-1$.
So, we have found the variable expression for the given phrase “quotient of a number and 3 is decreased by 1” as $\dfrac{x}{3}-1$.
$\therefore $ The variable expression for the given phrase “quotient of a number and 3 is decreased by 1” is $\dfrac{x}{3}-1$.

Note: Whenever we get this type of problems, we first assume variables for the unknowns present in the problem to avoid confusion. We should know that “quotient of a number and 3” can also be given as “3 is divided into x”. We should not add 1 in the last step which is the common mistake done by students. Similarly, we can expect problems to find the algebraic expression for “10 is divided into y and is decreased by x”.