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Math people, why am I wrong? AoPS


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There is a question I don’t understand why my way of solving it is wrong. I can see that it is, and I even used a calculator to check it was and it wasn’t just an arithmetic mistake.

I also understand what they did and why it works, but I don’t understand why my solution doesn’t also work.

The question. The number 222,222 is equal to the product 37,037*6. What is the product of 37,037 and 27?

AoPS solution is as follows: Because 6 times 37,037 is 222,222, we know that 3 times 37,037 is 111,111. So we have 

27*37,037=9*3*37,037=9*111,111=999,999

I understand this and can see why it is correct BUT I don’t know why my different solution didn’t work.

My solution. The difference between 6 and 27 is 21 so the product will be 21 times bigger than 222,222.

so. 222,222*20 plus another 37,037 making 27 times 37,037. But I was really really wrong! Why? 
 

Thank you. 😀

Edited by Kit
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Ohhhhh oho oh oh oh oh oh.....I think I have it!

 

I was just reading through the post to check for silly spelling mistakes etc and I think I saw the answer.

I multiplied the product of 6*37,037 by 21 not the 37,037 itself! Is that right? Is that what I did wrong?

so I should have multiplied 37,037 by 21 and then added the 222,222? 
 

obviously their way is simpler.  🤣☺️

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Just now, square_25 said:

Right! But what’s an easy way to figure out 21*37037? 😉

An easy way to do 21* 37,037?

well 10*37,037 would be easy...370,370. So double it and add another 37,037?

Lets see if it works

370370+370370= 740740   And 740740+37037=777,777  😥 wrong......back to the drawing board. I’ll be back in a moment ........

 

 

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1 minute ago, Kit said:

An easy way to do 21* 37,037?

well 10*37,037 would be easy...370,370. So double it and add another 37,037?

Lets see if it works

370370+370370= 740740   And 740740+37037=777,777  😥 wrong......back to the drawing board. I’ll be back in a moment ........

 

 

Oppps....plus the 222,222! 
Now it’s 999,999!

I get the rotten egg award for that one 🤣🤣🤣🤣🤣

 

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Just now, square_25 said:

Wait, wait, i think you're right!! You just need add on the missing bit. 

Yes...got it whilst you were typing! Thank you so much for your help square. I’m feeling so much better now. We got it worked out!

 

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Square 25, The next chapter is exponents. All I know about them is squares and that is the number doubled...time 2.....and that is it. Do you think I should bash on with AoPS or do them first with Khan academy, and then try the chapter? I like AoPS and I’m enjoying the challenge and the little grey cells working, but am I setting myself up for disaster here?

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Just now, square_25 said:

No problem at all! Happy to help :-). Feel free to tag me when you post these, if you like -- my oldest is only 7, so I'm not always on this board (although I am sometimes, since I've taught older kids before and like answering questions about it occasionally :-).) 

How do I tag you?

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Just now, square_25 said:

They ought to define them, I think! They aren't so bad. As a definition, 

x^n = x * x * .... * x, n times. 

(I'm using the short hand x^n to mean "x to the power of n," which mostly would be written with the n on top as a superscript. But I can't type that into here :-).)  

So, for example, 

4^2 = 4*4 = 16. 

And what are 3^2, 2^3, and 2^4? 😄

3^2 is 3*3. (I just deleted my first reply i did 3*2 =6 🤭) so 3^2=9

2^3= 2*2*2? So 8?

and if the above is correct then 2^4 would = 2*2*2*2=16

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3 minutes ago, square_25 said:

The other thing you could do is to keep posting on the same thread... then everyone who's following the thread would get notifications. (Plus, we'd have a fun AoPS Prealgebra thread people could look through if they wanted!) 

That’s a great idea if you think people would be interested.

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1 minute ago, square_25 said:

Yep, exactly :-). See, they are really not that bad. Multiplication is repeated addition of the same number, and exponentiation is repeated multiplication of the same number :-). 

Exponentiation! What a brilliant word. I will be learning exponentiation next !!!

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OP, one thing that I sometimes do when I get mucked up the way you described is to substitute smaller/easier numbers.  So in the case of your problem, if you substitute 10 for 37037, you get 6 x 10 = 60 and 27 x 10 = 270, and it becomes easier to see what you did wrong with the 21 (because 21 x 10 = 210 and 60 + 210 = 270).

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(Threads like these make me so happy. I was convinced at a very early age that I was "just bad at math", which is why it seemed hard to me. As an adult, in an effort to truly help my own children, I have given "Dreadful Math" another chance, and . . . oh, I'm just so thankful! It's BEAUTIFUL and MYSTERIOUS and TANTALIZING, not dreadful at all! (And it has even informed my faith, too!) And there are ever so many ways to keep puzzling through and people to ask when I am stuck. I can actually say with enthusiasm that I now LOVE math, even though I am still self-educating through high school stuff. 😉 I share this just as an encouragement - so much joy in this journey. I am currently in pre-calculus and QUITE EXCELLENT at algebra. A statement that - if you knew my childhood - is truly astonishing. Here's to all the students and all the teachers out there, no matter how old or clever you are.)

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31 minutes ago, Lucy the Valiant said:

(Threads like these make me so happy. I was convinced at a very early age that I was "just bad at math", which is why it seemed hard to me. As an adult, in an effort to truly help my own children, I have given "Dreadful Math" another chance, and . . . oh, I'm just so thankful! It's BEAUTIFUL and MYSTERIOUS and TANTALIZING, not dreadful at all! (And it has even informed my faith, too!) And there are ever so many ways to keep puzzling through and people to ask when I am stuck. I can actually say with enthusiasm that I now LOVE math, even though I am still self-educating through high school stuff. 😉 I share this just as an encouragement - so much joy in this journey. I am currently in pre-calculus and QUITE EXCELLENT at algebra. A statement that - if you knew my childhood - is truly astonishing. Here's to all the students and all the teachers out there, no matter how old or clever you are.)

Thank you for posting Lucy. It makes me very happy, and it’s very inspiring to hear another math ‘duffer’ has found her way through and to Pre Calculus no less! How exciting is that! Maybe one day I will be writing a post like this to encourage others on this mathy journey.

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1 hour ago, EKS said:

OP, one thing that I sometimes do when I get mucked up the way you described is to substitute smaller/easier numbers.  So in the case of your problem, if you substitute 10 for 37037, you get 6 x 10 = 60 and 27 x 10 = 270, and it becomes easier to see what you did wrong with the 21 (because 21 x 10 = 210 and 60 + 210 = 270).

Yes, this is a really good idea, and I need to remember to do this. 😀

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