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Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.

The product of 9 and the difference of a number and 2.

User Wesley Galindo
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1 Answer

10 votes
10 votes

Answer:

9 · (x - 2)

Explanation:

Since the problem tells us to let "a number" be the letter x, let's rewrite the sentence to include x instead of the term "a number". Doing so gives us the sentence "The product of 9 and the difference of x and 2."

Step 1: Multiplication

Now, let's work from left to right. The first word we see is "product", which refers to the operation of multiplication, as this term is used to describe the resultant quantity from multiplying 2 numbers. From the sentence, we see that the two terms we are multiplying are "9" and "the difference of x and 2". Note that we include the difference in one of our terms because of the structure of the sentence - we usually describe a product as being a product of [one term] and [another term] as it is here.

To denote multiplication, we can use the symbol "×", but to avoid confusion between this symbol and the letter x, let's use the symbol "·". Now, we have the expression 9 · (the difference of x and 2).

Step 2: Subtraction

We still aren't done, however, because we still have some words left to "translate" into algebra. The use of the word "difference" tells us that the operation to be used is subtraction, as this term is used to describe the resultant quantity from subtracting 2 numbers. Again, the sentence tells us that the terms we are subtracting are x and 2, but which order do they go in? (This is important to consider because unlike multiplication, subtraction is not a commutative property - in other words, a - b does not necessarily equal b - a, but a · b always equals b · a.)

To answer this question, we refer again to the sentence. When dealing with a non-commutative operation, we write out the terms in the order they appear in. Therefore, "the difference of x and 2" can be represented as x - 2 (note that we use the "-" symbol as we are subtracting quantities).

Step 3: Combine the 2 Operations

Putting all of this information together, we get the algebraic expression of 9 · (x - 2). Remember to put x - 2 in parentheses, otherwise it looks like we are multiplying 9 and x and then subtracting 2 from that quantity, which is not what our original sentence was.

User Bernhard Josephus
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