Question

How do you write “ the quotient of a number and 8” as an algebraic expression?

Answer 1

As we know that in mathematics, an algebraic expression is an expression built up from integer constants, variables and the algebraic operations. If a whole number $N$ is the result of a division between two numbers $a$ and $b$, then $N$ is called the quotient of $a$and $b$.
Also we know that Dividend$\div$Divisor $=$Quotient. As for example $12 \div 3 = 4,$ $4$is the quotient here. $4$is a whole number here as quotient is always a whole number.

Complete step by step solution:
Here we will assume the number be $x$.
Keep in mind that when we write a statement in algebraic form we write the expression which evaluates to the same result for every variable substitution as the substitution of a variable in that expression.
We know that quotients are the result of division between two numbers, so quotients of $8$ and $x$ are given by $x \div 8$ or $\dfrac{x}{8}$.
Hence the answer in algebraic expression is $\dfrac{x}{8}$ .

Note: If we are not sure whether we simplified an expression correctly or not, we should always check our work by evaluating the original expression and the simplified expression for some values and check for the statements too. Here the original expression is Dividend $\div$ Divisor $=$ Quotient. For example $2$ is the quotient of $10$ and $5$ because of $10 \div 5 = 2$ . Note that a quotient is always a whole number. If the result of division is not a whole number, then the quotient is the whole number part only.