This blog is to help you with Math. It's not to confuse you more. I want to give you clear, no nonsense directions on how and why you're doing something. An explanation that everyone can understand.
What do they mean?
They mean that you will be multiplying the same thing (the base) by itself as many times as that exponent says. Examples:
Also, you might have noticed that anything raised to the zero power is equal to 1, not zero, as most people would guess. I will show you why in this video.
There is also the problem of having negative exponents. That can be switched to positive and most textbooks will want you to answer with only positive exponents. Check out the example below to see how you would switch you answer, and the video will explain it.
Don't forget to to watch the previous video once again to understand short cuts to exponents.
Exponents, the little number above and to the right of the regular number or variable, or both. It really means how many of that number you will multiply. Why, you ask, would you ever need this? Well, you'll use it for many many things, so understanding the basics is necessary. You'll need this when dealing with science, really big or really small things. You'll also need to understand exponents when dealing with different interest rates, which is something most of us will deal with at some point.
The video shows you what the rules are listed below, and there's a guest star in it today!
Click here to see the Introduction to Exponents Rules Click
Exponents: 1. With adding and subtracting- You don't do anything to exponents when the operation is addition or subtraction. You can only add or subtract the coefficient's if they have the same base to the same exponent - see video
2. With Multiplying (must have the same base)- you will add the exponents and KEEP that base. If there are coefficients, numbers in front of a variable, then you multiply those like normal.
3. With Dividing (must have the same base) - you will subtract exponents, top subtract bottom and KEEP that base. If there are coefficients, numbers in front of a variable, then you divide those like normal.
More exponent rules to come later. Lindsey and I just wanted to give you the introduction.
It's all about that base. Lindsey will tell you! Please watch the video if you haven't already. This one has a guest who is a good singer. ;)
Why learn order of operations?
So you don't have to be that person that gets the Facebook feed problem wrong, but posts the answer as if they are correct. Please! Just kidding, clearly, that is only one reason, as there are many other reasons! Reasons: to be well rounded, to know what you're doing in your math class, to know what your children or grandchildren are doing in their classes, etc....
Side note: If you're needing real help with Math (or any subject) please check out this site: WyzAnt Tutoring and get a free $20 off your first tutoring session! This site connects you with real people in your area, with different backgrounds and prices. Don't wait any longer!
The order of operations is needed to do any type of math class. If you forgot it, well, it's here. If you think it's too hard, then please don't ever drive a car, build anything, or cook around fire, because usually those take steps. Oh, so you're saying you can follow steps? Then you can follow the order of operations. Done and done.
You know the drill. Please Excuse My Dear Aunt Sally. Aka, PEMDAS. Aka: Parentheses (grouping symbols from the inside out) Exponents Multiply and Divide - from left to right Add and Subtract - from left to right
Now, notice how I put the multiplication and division on the same line, and the addition and subtraction on the same line? That is because it's exactly how it says it is right there. You do not do multiplication first, even though it seems that way.
Same with addition and subtraction. I wish there was a better way to remember this, maybe: PE (MD)(AS), but that doesn't look right, so maybe: Please Excuse MarylanD's AppleS. Somehow you must remember that the MD and the AS happen from left to right not in the order you see the letters. I tried to make the letters in the same words with that second idea. What did you think? No go? I hope that video made it all clear. Be sure to watch it!
One other thing. Parentheses stand for all grouping symbols from the inside out. Therefore if you had brackets with parentheses within, you would do the parentheses within. Also, a fraction bar with numbers on the top or bottom, act as a grouping symbol (as seen in the video). Other that that, there's not really anything else to think about, expect the order. Check out the video with examples. I DARE you to even work some out before me. GO, if you haven't already! Go again, if you didn't work them out before me, and try them on your own. :)
Here's the video link again, in case you missed it. :) Video.
It's Pi Day!!!!!! 3.14 Get it? March 14th. 3/14. :)
The best part is pi is really equal to 3.14159......and even more if we had time...BUT the year after it this year (the 15) goes right with the number of pi, so that's exciting! Well...
Anyway, today's date is 3/14/15. Yes this is special to a math teacher and/or math nerd. If you had me as a teacher, you know it all too well, but you probably loved it, because we ate pie to celebrate. After measuring some stuff of course, I wasn't that nice! Even my family knows how nerdy I am, and I got a Pi-Pie Pan for Christmas one year. (Thank you, Tommy!)
Christmas 2009
But, what is pi? Where does this number come from?
It has no pattern to the decimals and it never ends! This makes it an irrational number. That means if you know the numbers it's because you have memorized them. Good job! I haven't done that.
I'll tell you what Pi is, but only if you remember it for the rest of your LIVES!! Just kidding, but not really. The video is about 2 minutes. Watch it for Pi Day!
This is for every single circle in the world! That's the outside divided by line through the middle of the inside. Also known as the circumference divided by the diameter, or the ratio of the circumference to the diameter.
Examples include: bottom of pencil holders, bottoms of cups, pizza, circular cookies, and of course pie! ANYTHING THAT IS A CIRCLE! I have told people this before, students, my sister, etc., and some did not believe me. I hope you believed it!
We are going to continue on with more algebra, so for those of you who are still thinking you can't do it, please stop the doubt! Remember it's all about how you look at it. I realize you may not have practiced it and you won't until you need to. That's fine. But please know that these explanations are here, and there are many other videos and other help out there. Please stop making excuses if you want to improve on something in your life, but your math skills are holding you back. You can look at these blogs/videos now, and just know that they are do-able, and do-able for you!
Now we will take this a step further. Remember, it's another step. Do NOT try running before walking. Yes, it's a baby reference, and it's over-used, and I said it.
Here is what you will learn to solve; 2x - 1 + 3x = 19 and stuff like 7x + 4 = 2x - 6 + x .
2. Get all your numbers to one side of the equal sign and variables to the other side of the equal sign (Moving around an equal sign is when you do the opposite, same as Solving for a Variable - step 2)
Shopping is fun. Real shopping. Not grocery shopping, since that's clearly survival. I'm talking clothes, or fun household stuff or outdoor stuff or toy shopping, etc.. I totally intend to do these 'shoppings' when this teaching degree is paid for. ;)
I would like to share with you the easiest way to make sure your items are discounted properly. If you have discounts for groceries, you can use this too, but I just wanted to think about fun stuff! Now I have a real problem with people standing there in the aisles of stores thinking so hard. I know right!~? Me have a problem with people over-analyzing math!? HA! Kind of like this post about finding the tip, right? Here's that video.
Now, let's get serious, because shopping, is serious.
If you see a sign that says an item is discounted by 20%, and has a sales tax of 6%, most people will do the following steps to find the complete total:
(I'm hoping this will become your old way.) 1. Take total and find 20% (multiply it by .20) 2. Subtract that 20% from the total- for the NEW Total 3. Take NEW Total and multiply it by .06 to get the Sales Tax 4. Take and add NEW Total and the Sales Tax to find the Complete Total This always will work, so if you love it, then you can always use it. That being said, I don't know why you would do that again after I show you this. I'm going to do the same problem, quicker. You know you have your cell phone when you're shopping. It has a calculator, so do these steps instead.
First if it's a 20% discount then you're paying 80% of the total.. .right?
If it's a 30% discount then you're paying 70% of the total... see what we're doing here?
If it's a 25% discount then you're paying 75% of the total. You got it now right!?
Now, let's get serious, because shopping, is serious.
(I'm hoping this becomes your new way.) If you see a sign that says an item is discounted by 20%, and has a sales tax of 6%, THIS IS WHAT YOU SHOULD DO: 1. Take the total and find 80% of it (multiply by .80) for the NEW Total 2. The the NEW Total and multiply it by 1.06 - for the 6% sales tax to find the Complete Total
That 1.06 means you take 1 (100%) and the extra .06 (6%) of the NEW Total.
If you have 7% sales tax you would do 1.07, 9% would be 1.09 and so on.
I do realize that their are signs in most places telling you the amount the discount is now, but sometimes those don't have that one thing you want on there. You also should always check, as sometimes things are wrong. You CAN be smarter than a sign. You got this! :)
You might be doing some Math for the first time in forever, (Yes, I have watched Frozen, a lot, and if you have too, then you know what I'm talking about.) and negative numbers might be unclear to you and annoying. You must understand how they work in order to get other problems correct. It might seem too easy for you, but trust me, it's these little mistakes that stop people from doing math, and it SHOULDN'T!
These problem areas can be worked on for maybe 30 minutes, or maybe 10 minutes, 3 times a week for 3 weeks and completely fixed. Yes, I totally made up those times, because I do not know you and your situation. You can be the judge of that. Here's what I'm going to show you today.
1. How to add and subtract with negative numbers
2. How to multiply and divide with negative numbers
Let's get right to it.
How to Add and Subtract with Negative Numbers
1. Change all subtractions to adding the opposite
2. If they are the same sign, add and use that sign
3. If they are different signs, (act like they're positive) subtract smallest from largest, and use the sign of the larger one
Please note, for these steps to work you must do the first one correctly. Please watch this video to ensure you understand.
Next: How to Multiply and Divide with Negative Numbers
1. Ignore the signs and multiply and/or divide from left to right
2. It the problem started with an even amount of negative values then the product is positive
3. If the problem started with an odd amount of negative values, then the product is negative
You can also do this step by step, but the odd and even number seems to be the easiest, especially if you don't use it for a while. Please watch the video to ensure you understand.
I hope this has helped you! Remember this will all build up to allow you to do more and more math. Share with your friends who claim they can't learn it, and let me know your feedback! Thanks!
