4 less than the quotient of a number x and 5
The Correct Answer and Explanation is:
Correct algebraic expression:
x5−4\frac{x}{5} – 45x−4
Explanation (about 300 words):
The phrase “4 less than the quotient of a number x and 5” can be translated into an algebraic expression by breaking it down step by step.
First, let’s look at “the quotient of a number x and 5.” The word “quotient” refers to the result of a division problem. So, “the quotient of x and 5” means we divide x by 5. This is written as:
x5\frac{x}{5}5x
Next, we have “4 less than” this quotient. The phrase “less than” in mathematics often signals subtraction, but it also tells us to reverse the order of the terms. That means we are subtracting 4 from the expression x5\frac{x}{5}5x, not the other way around.
So, “4 less than the quotient of a number x and 5” becomes:
x5−4\frac{x}{5} – 45x−4
This expression means: take the number x, divide it by 5, then subtract 4 from the result.
A common mistake is to reverse the subtraction incorrectly and write it as:
4−x54 – \frac{x}{5}4−5x
However, that would mean “the quotient of a number x and 5 less than 4,” which is not the same thing.
Here’s a quick example to illustrate:
If x=10x = 10x=10, then
x5=105=2\frac{x}{5} = \frac{10}{5} = 25x=510=2
Now subtract 4:
2−4=−22 – 4 = -22−4=−2
This matches the expression x5−4\frac{x}{5} – 45x−4, and not 4−x54 – \frac{x}{5}4−5x, which would be 4−2=24 – 2 = 24−2=2.
Understanding how phrases like “less than,” “more than,” or “the difference between” affect the order of operations is key when translating words into algebra.
