Question

How do you write the expression for: eight plus the quotient of a number and 3 is -2?

Answer 1

Hint: To find the expression for a given statement, we have to crack the given statement. The toughest part of solving the question is at the part ‘the quotient of a number and 3’. Here we have to consider the unknown value as x and we have to remember that quotient means the answer to a division.

Complete step by step answer:
From the question, the given statement is “eight plus the quotient of a number and 3 is -2.”
Now we have to write the expression for the given statement.
To write the expression let the statement be taken as equation (1).
So, eight plus the quotient of a number and 3 is -2 \[..........\left( 1 \right)\].
Let’s break down the statement to find out the expression.
Let’s break it out into \[3\] parts.
Now, look at the first part “eight plus” which is taken as equation (2).
i.e. \[8+...........\left( 2 \right)\].
Now look at the \[{{2}^{nd}}\]part “quotient of the number is\[3\]”.
Now, \[{{2}^{nd}}\]part converts to \[\dfrac{x}{3}\] because "quotient" means the answer to a division; and since we don't know what the number is, we input 'x'.
Therefore, \[\dfrac{x}{3}..........\left( 3 \right)\].
Now, look at the remaining part “-2” and it can be written as “=-2”.
Therefore, \[-2=..................(4)\].
To make an expression from the given statement (which we took as equation (1)), we have to combine the three equations (2, 3, 4).
i.e. \[8+\dfrac{x}{3}=-2\].
Therefore, the required expression is\[8+\dfrac{x}{3}=-2\].

Note:
Students should be well aware of this concept. Questionnaires may ask this type of question in many forms. The statement “the quotient of a number” should be understand carefully. If we consider it as $\dfrac{3}{x}$ instead of $\dfrac{x}{3}$ then the result will change.