Question

How do you translate "16 less than twice a number" into a mathematical expression?

Answer 1

Hint: We will look at the given statement and isolate certain words from it. We will see the meaning of these words in a mathematical context. We will associate a mathematical operation or label to these words. Then we will make a mathematical expression that will represent the given statement. We will do this using the association of the words and the mathematical operations.

Complete step-by-step solution:
The given statement is "16 less than twice a number". We will look at the following words and their meanings: less; twice; a number. The word 'less' in this statement is giving us the relation between two numbers, saying that a number and the other number have a difference of 16. The word 'less' or 'difference' is therefore associated with the subtraction operation. Next is the word 'twice', which means 'two times'. Looking at the word 'times', we know that this word is associated with the multiplication operation. Then, we have 'a number'. This literally means that we need a number that will fit into the mathematical expression to be obtained. So, we assign a variable or a label for this number, say $x$.
Now, we have "twice a number", which is two times the variable and hence we get $2x$. Therefore, "16 less than twice a number" is $2x-16$. Thus, we have obtained the required mathematical expression.

Note: It is important to understand the meaning of phrases in the mathematical context before converting them into mathematical expressions. Every arithmetic operation has indicating words or phrases. For example, the words 'add' or 'sum' point towards the addition operation. The words 'distribute' or 'divide' indicate that the division operation has to take place.