Question

Annabelle and Navene are multiplying (4275)(4372).



Annabelle's Work Navene's Work
(4275)(4372) = 42 + 375 + 2 = 4577 (4275)(4372) = 42⋅375⋅2 = 46710

Is either of them correct? Explain your reasoning.

Answer 1

Well, let's start with Annabelle, do you think she is correct?

Answer 2

gut feeling, yes

Answer 3

OK, let's check that gut feeling now. So, multiplication is repeated addition, right?
That's why 3*70 is 70 + 70 + 70.

So, do you think it makes sense that 4275*4372 = 4577 if you think about it this way?

Answer 4

Basically, you are adding 4372 a bunch of times
4372 + 4372 + 4372 + 4372 + 4372 + 4372 + 4372 + 4372 + 4372 + 4372 + ...
Seems like chances are slim that this will add up to only 4577... :)

Answer 5

Does that make sense? Do you still think Annabelle is correct?

Answer 6

no

Answer 7

Maybe I should have spread out my questions. :)
No, it doesn't make sense.
Or no Annabelle is wrong?

Answer 8

no annabelle is wrong

Answer 9

OK, great. I agree with that. :)

Answer 10

Now Navene is doing something a little different... but let's see what we think...

Answer 11

Before I go on, do you know the trick that if you multiply something by 10 you just add a 0 to the end? So, like 10*543 = 5430.

Answer 12

yes

Answer 13

OK, cool. To bust Navene's answer, I'm going to use a similar idea. I'll multiply by 100, which just adds two 0s instead of one.

Look and see that
(100)(4372) = 437200
this is already WAY bigger than Navene's answer of 46710.
So (4275)(4372) has to be even bigger than (100)(4372). No way Navene, that's not right.

Does that make sense to you?

Answer 14

so there both wrong , can you do me a favor and sum that up into a paragraph

Answer 15

If there is something lime (a)(b) then it means a x b i.e, it means multiplication.
So if we compare we can see that navene has expanded the problem properly but he has done some calxulation mistake due to which he gets the wrong answer

Answer 16

Yes, they are both wrong. I'll let someone else take a shot at writing it up, but I think you can do it. Here are the main points:
1) Annabelle is wrong since multiplication is just repeated addition.
2) Navene is wrong since we know that multiplying by 100 adds two 0s.

You can probably cut and paste from my previous explanations to make your own paragraph that makes sense to you. Show some calculations like I did to prove your point. Good luck!