Question

Translate the English phrase into an algebraic expression:
(a) Four times the sum of p and q.
(b) The sum of four times p and q.

Short answer

$$\begin{gathered} a)4(p+q\left) \\ b\right)4p+q \end{gathered}$$

Step-by-step solution

Using Concept  

• The "$a+b$" expression is being used to conduct an addition operation, with the term bbeing greater than a being used as a phrase for this operation.
• The "$ab$" expression is being used to conduct a multiplication operation, while the expression ab is used to perform this operation.

Part (a) step 1. Write Algebraic expression of four times the sum of p and q.

There are two operation words in the question: "times" for multiplication and "sum" for addition.
As already said, the crucial word is the sum, hence the two phrases will be combined together. "More than" is a phrase that implies "added to."
We need parenthesis around "the sum of p and q, $(p+q)$" since we are multiplying the amount four times.
As a result, the sum is calculated first. It's now essential to mention the terms "of" and "and" in the statement.
Therefore, the "four times the sum of p and q" is "$4(p+q)$".

Part (b) step 2. Write Algebraic expression of the sum of four times p and q.

There are two control words for multiplying and addition: "times" for multiplying and "sum" for addition.
Since previously said, one important word is the sum, hence the two terms will be added. "More than" refers to something that has been added to something else.
Even if we're multiplying 4 times p, we'll add to q. As a result, multiplication comes first.
Now it's critical to emphasize the terms "of" and "and" in the statement.
Therefore, "The sum of four times p and q" is "$4p+q$".