Question

What is the algebraic expression for “4 times the sum of p and q” ?

Answer 1

Hint: The given expression is in the written (statement) form. We will break the statement to our understanding and then convert it into an algebraic expression. We will make use of the fact that, wordings like “times” means ‘to calculate the product’ and “sum” means to ‘to add the given quantities’ .

Complete step-by-step answer:
The statement given to us in the problem is: “4 times the sum of p and q”.
Here, we can clearly see that our statement consists of two operators. These operators are “times” for multiplication and “sum” for addition. We will now break the statement in a step by step manner. This will be done by converting the part of the statement which is easy to understand first and then the second part.
This can be done as follows:
$=$ 4 times “the sum of p and q”

Mathematically, the term inside the apostrophe could be written as:
$=$ 4 times $\left( p+q \right)$

We will now further break our above statement as follows:
$\begin{align}
  & =4\times \left( p+q \right) \\
 & =4\left( p+q \right) \\
\end{align}$

Thus, our statement has been completely converted into an algebraic expression.
This algebraic expression is equal to $4\left( p+q \right)$ .
Hence, the algebraic expression for “4 times the sum of p and q” is equal to $4\left( p+q \right)$.

Note: Whenever an equation is given in the written form or in the form of a mathematical statement, we should be very careful while writing its algebraic expression. Also, these expressions are generally written in English, so we should have a good vocabulary grasp as written equations are very common in the chapter of permutations and combinations in Mathematics.