Question

How do you phrase as an algebraic expression: the quotient of 6 and the product of 8 and m?

Answer 1

Hint: We will first find the product of the numbers 8 and m as required in the solution, then we will just have to find the quotient, so we will divide 6 by the product calculated.

Complete step-by-step solution:
We are given that we are required to phrase as an algebraic expression the statement given by: the quotient of 6 and the product of 8 and m.
Since, we are given that we need to find the product of 8 and m.
So, we will first do that.
Product of 8 and m = $8 \times m$.
Simplifying it, we will then obtain:- Product of 8 and m = 8m
Now, we need to find the quotient of 6 and the product of 8 and m.

Therefore, the required answer is $\dfrac{6}{{8m}}$.

Note: The students must note that they may also further simplify the expression by writing the expression as $\dfrac{{2 \times 3}}{{2 \times 4m}}$.
Now, we can cross off the 2, then we will obtain: $\dfrac{3}{{4m}}$.
(The students must note that we could cross off the 2 from both the numerator and the denominator, because we are damn sure that 2 is never equal to 0. We can never cancel out any such variable which has even the slightest possibility of being 0 at any point)
But, now if you try to convert this expression in a phrase, you will always tend to say that: “the quotient of 3 and the product of 4 and m” which is different from the given phrase.
Therefore, in the final answer, we did not convert it into lowest terms and left it there only.
The students must also know that whenever we write division of any two numbers normally, it means that we are seeking its quotient instead of anything else.