3

At our school we have a "summer packet" we have to complete. In this packet was the following problem:

enter image description here

At first the "sum" part puzzled me. I had no idea why they would quiz us on basic arithmetic in 6th grade. But then I realized, the exercise is not about just adding area and perimeter, it is (probably) about adding the units. Area+Perimeter is $inches+inches^2$ which I have no idea how to do. Wolfram alpha said they were incompatible units. We all know from area that $inches\times inches = inches^2$ but my question is, what unit is $inches+inches^2$?

TIWARI
  • 757
  • This is closer to a physics question. Either way, mathematically you can go nuts and just add them. Physically, they lose all meaning. If you're familiar with vectors, it's analogous to why we don't just add the components together rather than keep them in component form. – Zach466920 Jun 23 '15 at 15:02
  • 3
    You are right, the units are incomparable. This means that if the area is $100 in^{2}$ and the perimeter is $10 in$ then the sum is just $100 in^{2}+10in$--although, you could senselessly add the numbers and say 110... but the units on that number are meaningless. – TravisJ Jun 23 '15 at 15:02
  • 1
    Just to add another comment to what's already been said, and what I think you probably already understand: asking for the sum of the area and the perimeter is like asking for the sum of the current temperature outside (here it is $73^{\circ}$ F) and the average speed limit of US highways (which I think might be $70$ mph). We can add them and get $73 + 70 = 143$, but what is the significance of this number? The two numbers we added each had significance, but the meaning is lost when we add them. The sum simply doesn't have meaning -- unless you decide to attribute your own meaning to it. – layman Jun 23 '15 at 15:18
  • 1
    Also, if you know any algebra, you probably learned that if we want to add $7x + 5x + 3y$, we can only add "like terms". So this would equal $12x + 3y$, and we can't really combine the $12x$ and $3y$ because they aren't "like terms". Still, we are adding them, but we are expressing the sum as $12x + 3y$ because there is no other way to combine them. – layman Jun 23 '15 at 15:21

1 Answers1

2

Good for you, you found a mistake (or a trick on your teacher's part) in your summer homework. There are two ways to acknowledge the mistake and still answer.

You could write that there is no answer because you can't add different units.
Alternatively you could write the sum of the numbers and indicate that there are no units because you can't add inches and inches squared.

Amy B
  • 440