Pay attention to the word phrase and the operations that are described. Is there anything that tells you which operation to perform first?
See solution.
Practice makes perfect
Let's start with analyzing the given word phrase.
$2$ less than $5$ divided by a number $n$
The phrase 5 divided by a number n corresponds to the following algebraic expression.
5 divided by a numbern
5 ÷ nWhat is more, 2 less indicates that to get the final algebraic expression, we need to subtract 2 from 5÷ n.
2 less than 5 divided by a numbern
5 ÷ n - 2
By the order of operations, the division is calculated before the subtraction. Therefore, we can put the first operation into the parentheses.
(5 ÷ n) - 2
This is the exact same expression that our friend wrote. Therefore, they were correct. Is it the only possible representation? Notice that the given phrase gives no information about what operation should be done first, so the subtraction can be calculated first.
2 less than 5
5 - 2
Now, we can perform the division by a number n.
2 less than 5 divided by a numbern
( 5 - 2) ÷ n
Therefore, our expression can also represent the given phrase. We conclude that both are reasonable interpretations. As we can see, verbal descriptions can indeed lack precision, because using the given phrase we cannot identify one corresponding expression.
