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Factoring Tricks August 29, 2009

Posted by Ms. Miller in Algebra I, Geometry.
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It’s important, if you are trying to find the LCM of some numbers (such as trying to find a common denominator), that you be able to tell immediately what factors go into a number. My 6th grade teacher, Mrs. Dana, taught me the following tricks, which I want to share with you:

“Casting Out Nines”
This is the name of a process of adding up the digits of a number; it will come in handy as we try to find factors. When we talk about “adding up the digits of a number”, what you should do is:

  • Cross out any 9s that are in the number.
  • If there are any pairs of digits that add up to 9, cross them out as well.
  • Add up the remaining digits. If the sum is greater than 9, continue to add the digits together until you have a one-digit answer. This is the number we are interested in.

Example: What is the sum of the digits of the number 96,216?
We cross off the 9, and then add 6+2+1+6=15. We then find the sum of 15, which is 1+5=6. So the sum of the digits is 6.

(This method also has uses in checking arithmetic, but we’re not concerned about that right now. If you’re interested in reading further about it, check out Wikipedia’s entry on the subject.)

Now, let’s look at how we know whether certain numbers are factors:

Factor Divisible By If …
1 Goes into everything
2 Number ends in 0, 2, 4, 6, or 8
3 The sum of the digits is 3, 6, or 9
4 The last two digits are divisible by 4. Ex. 87,665,9\underline{24}
5 Number ends in 0 or 5
6 Number is divisible by 2 and 3 (Even number whose digits sum to 3, 6, or 9)
7 No rule exists.
8 The last three digits are divisible by 8. Ex. 2783738273\underline{064}
9 The sum of the digits is 9.
10 Number ends in 0
12 Number is divisible by 3 and by 4.
25 Last two digits are divisible by 25 (00, 25, 50, 75).

Working with Integers August 28, 2009

Posted by Ms. Miller in Algebra I.
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When you add or subtract integers (positive and negative numbers), keep the following in mind:

If the signs are the SAME Add the numbers and keep the sign. Ex. 7+2=9 and -3-7=-10
If the signs are DIFFERENT Subtract the smaller number from the larger. The answer takes the sign of the larger number. Ex. (-8)+5=-3 and 9+(-2)=7

Here’s a story that may help you remember what to do when multiplying or dividing positive and negative numbers:

In an Old West town, there are good guys (positive) and bad guys (negative) who are entering (positive) or leaving (negative) the town:

If the good guys (+) enter (+) the town, that is good (+) for the town. (+)(+)=+
If the good guys (+) leave (-) the town, that is bad (-) for the town. (+)(-)= -
If the bad guys (-) enter (+) the town, that is bad (-) for the town. (-)(+)= -
If the bad guys (-) leave (-) the town, that is good (+) for the town. (-)(-)=-

New Calendars! August 27, 2009

Posted by Ms. Miller in Algebra I, Geometry.
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The 1st Six Weeks calendars have been posted for both Algebra I and Geometry. I have just listed the A days on Geometry, but 5th Period will follow the same schedule.

Welcome! August 27, 2009

Posted by Ms. Miller in General.
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Welcome to a new school year! I hope to keep this site updated with information for each of my classes. Since not everything I will write will apply to everyone, be sure to keep an eye on the post categories:

  • Geometry
  • Algebra I
  • MathScience Calculator — for our UIL Calculator team
  • UTA — for those students attending the SCIE 4101 course I am team-teaching