Doodlebug Posted March 13, 2014 Share Posted March 13, 2014 While skip counting 9s, my son asked me why the numbers invert themselves after 45. 54 (45), 63 (36), 72 (27), etc... All I could manage was a WHOAH, THATS COOL! I've googled with no results. Help! Stella Quote Link to comment Share on other sites More sharing options...
dauphin Posted March 13, 2014 Share Posted March 13, 2014 I don't know about explaining it but I'd point out that there's a pattern of up-one (tens) down-one (units). You're starting low/high, so eventually you meet in the middle/cross over (numbers are high/low). Also the up-one (tens) down-one (units) is happening because 9 is the same as ten minus one. So you're adding (+10-1) each time. Don't know if that helps but I love math patterns! Quote Link to comment Share on other sites More sharing options...
kiana Posted March 13, 2014 Share Posted March 13, 2014 It is because we are in base ten. So every time we add 9, we are adding (10-1), so we add one to the tens place and subtract one from the ones place. The same thing will happen when you skip count by 7s in base 8. Sorry, it won't let me line up the numbers for a nice chart, but I've listed the same numbers in each row. Base 10: 7 14 21 28 35 42 49 56 63 70 77 84 91 98 Base 8: 7 16 25 34 43 52 61 70 77 106 115 124 133 142 Quote Link to comment Share on other sites More sharing options...
Doodlebug Posted March 13, 2014 Author Share Posted March 13, 2014 I love those patterns, too!!! I tend to notice repetitions. And I think somehow the patterns Im familiar with are related to DS's find today. I have never noticed a pattern with inverses carrying all the way back, in order, to the original number, though! I just called my DH and told him, 1) write out your 9s horizontally, in a straight line. 2) put a vertical line between 45 and 54. 3) why are the numbers on either side of the line mirror images? His response : (silence) Well look at that! Lol! We 're all going to start analyzing number patterns now! Stella Quote Link to comment Share on other sites More sharing options...
Doodlebug Posted March 13, 2014 Author Share Posted March 13, 2014 Kiana, Thank you!!! I am off to google bases... It's a vague memory I hope to revive! Stella Quote Link to comment Share on other sites More sharing options...
Doodlebug Posted March 13, 2014 Author Share Posted March 13, 2014 Kiana, You've totally opened a new world to us! Thank you, again! http://www.felderbooks.com/papers/bases.html Stella Quote Link to comment Share on other sites More sharing options...
TianXiaXueXiao Posted March 13, 2014 Share Posted March 13, 2014 The other neat pattern is that all digits that are multiples of 9 also add up to 9 until you get to 9*10 and then they add up to 18 until you get to 9*20 and then add up to 27 until you get to 9*30 and so on. 9*2=18, 1+8=9,...9*10=90, 9+0=9 9*11=99, 9+9=18,...9*20=180, 1+8+0=18 9*21=189, 18+9=27, ...9*30=270, 27+0=27 Quote Link to comment Share on other sites More sharing options...
kiana Posted March 13, 2014 Share Posted March 13, 2014 The other neat pattern is that all digits that are multiples of 9 also add up to 9 until you get to 9*10 and then they add up to 18 until you get to 9*20 and then add up to 27 until you get to 9*30 and so on. 9*2=18, 1+8=9,...9*10=90, 9+0=9 9*11=99, 9+9=18,...9*20=180, 1+8+0=18 9*21=189, 18+9=27, ...9*30=270, 27+0=27 Furthermore, if you keep adding the digits, you will keep getting 9. Allow me to illustrate. Let's take 99,999,999,999, which is obviously divisible by 9. Now, when I add up the digits of this, I get 11*9 = 99. So I add up the digits of 99 and get 18. So then I add up the digits of 18 and get 9! Quote Link to comment Share on other sites More sharing options...
Lissande Posted March 13, 2014 Share Posted March 13, 2014 TWells already implied this above, but to spell it out - the numbers invert themselves because multiples of 9 add up to 9 (or add up to a multiple of 9 for higher numbers, as mentioned). So it has to be ...36, 45, 54, 63... because they have to add up to 9. :) Quote Link to comment Share on other sites More sharing options...
dauphin Posted March 13, 2014 Share Posted March 13, 2014 Ooh, shiny! Math pattern talk! :lurk5: :party: Quote Link to comment Share on other sites More sharing options...
Doodlebug Posted March 13, 2014 Author Share Posted March 13, 2014 TWells -- I was familiar with the multiples of nine/digits add to 9 thing... But I just NO WAY-ed out loud with the digits adding up to multiples of nine after 910, 920, etc. Off to read the casting out nines thread. The number nine--this should be a curriculum! Stella Quote Link to comment Share on other sites More sharing options...
TianXiaXueXiao Posted March 13, 2014 Share Posted March 13, 2014 Here is a fun series on the magic of 9 http://www.quickanddirtytips.com/education/math/the-magic-of-number-9-part-1 Quote Link to comment Share on other sites More sharing options...
chelsmm Posted March 15, 2014 Share Posted March 15, 2014 This thread just made my night. :) Last week while on vacation, I showed my kids the thing about the multiples of nine and how they add up to nine and how the tens place goes up one while the ones place goes down. They are first and second grade, so place value gets talked about a lot. They were so excited. I can't wait to tell them the rest. Quote Link to comment Share on other sites More sharing options...
duckens Posted March 15, 2014 Share Posted March 15, 2014 Stellaluny, it gets better! Try this for multiplying 9s: Lay your 10 fingers out before you, palms down.We are going to multiply 3 x 9. Start counting fingers from your left. Put down your 3rd finger (because we are multiplying 9 by 3). This should be the middle finger on your left hand.How many fingers are to the left of the one put down? (2) How many fingers are to the right of the one put down? (7)What is 3 x 9? 27 Now let's do7 x 9.Counting fingers from the left, put down your 7th finger (because we are multiplying 9 by 7). This should be the pointer finger on your right hand. How many fingers are to the left of the one put down? (6)How many fingers are to the right of the one put down? (3) What is 7 x 9? 63 Try some other 9ers! Quote Link to comment Share on other sites More sharing options...
SorrelZG Posted March 15, 2014 Share Posted March 15, 2014 Base 10: 7 14 21 28 35 42 49 56 63 70 77 84 91 98 I notice that while under base 8, adding the digits of each multiple until a single digit is reached will always result in 7, under base 10, starting from 7 and going as far as you have listed here, they end up like this: 7, 5, 3, 1, 8, 6, 4, 2, 9, 7, 5, 3, 1, 8 That's kind of cool too. :) Quote Link to comment Share on other sites More sharing options...
Doodlebug Posted March 15, 2014 Author Share Posted March 15, 2014 Stellaluny, it gets better! Try this for multiplying 9s: Lay your 10 fingers out before you, palms down. We are going to multiply 3 x 9. Start counting fingers from your left. Put down your 3rd finger (because we are multiplying 9 by 3). This should be the middle finger on your left hand. How many fingers are to the left of the one put down? (2) How many fingers are to the right of the one put down? (7) What is 3 x 9? 27 Now let's do7 x 9. Counting fingers from the left, put down your 7th finger (because we are multiplying 9 by 7). This should be the pointer finger on your right hand. How many fingers are to the left of the one put down? (6) How many fingers are to the right of the one put down? (3) What is 7 x 9? 63 Try some other 9ers! That is NUTS! Off to share this COOL trick with the hubs and boy. Stella Quote Link to comment Share on other sites More sharing options...
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