Algebra - Variables, Expressions, Equations, and Solving Equations - 1512

Solving equations - not my idea of a fun afternoon, that's for sure. But, solving equations isn't a miserable as I remember it being in high school. Now that I have gone back over equations again, I feel a bit more confident in my abilities to write them and solve them. YouTube, once again, has been a great resource for me this summer in my math adventures and here are a couple of videos that provides plenty of information you might possibly want to know regarding equations.

 

I know that I'm a total visual learner, but I also know that many people would much prefer to read their information. Therefore, I'm also going to include a link here to a site that provides much of the same information. Here, there is information about the language of algebra, the basics of algebra, equations and inequalities, and graphing equations and inequalities so you will surely be able to find information about writing and solving equations here. I have used this site for many other math related topics and it's really awesome!
Algebra Information

Operations with Decimals - 1510

Fractions and decimals always throw me for a loop - like I've mentioned before, I'm not very good at math, nor have I been using it much since I'm out of grade school. At least, I haven't been using it much without using my calculator or simply Googling the answer. When I recently was asked to multiply and divide decimals, I had kind of forgotten that I even use those operations, but I sure do! The grocery store or other retail shops are the most common places I use them.

Adding, subtracting, multiplying and dividing are all operations that can be done with decimal numbers. I am a HUGE fan of videos to help me understand things, and I also really enjoy finding tips or tricks that help me remember how or when to do something. This is especially true for math. Here is a video that covers the different operations with decimals and also offers neat tricks, like "drop like a rock", which you will see:

Measurement Formulas - 1512

Wow! There are a ton of formulas when it comes to measurement. There are so many that when I was covering this topic, I couldn't keep them straight! I thought it would be rather handy to have them all in one page, so that's what I'm doing today. This post includes links with lists of all the formulas you'll need for elementary measurement from perimeters ans surface areas, to volumes of different objects. I hope it proves helpful to have them all in one area!

Perimeter of Objects

Area Formulas

Surface Area of Objects

Volume Formulas

Circles

Polygon Info and Formulas

The website that these links all go to is a great site to go to if you need to know anything about math! One important thing that I found helpful when working with these formulas is to make sure that you double check your work. It's so easy to plug a wrong number in somewhere or to forget a part of the formula, or even to mix one formula up with another, because a few of them are similar to others.

Also, when it comes to anything related to circles or spheres, you run into the symbol, or pi. This is a big long number, and can be annoying to try to type into a calculator or write out on paper. Many people and math books suggest the quick and easy, shortened version of this symbol, which is 3.14. Ah, much better! :) And much more manageable!

Absolute Value: What it is and how to work with it - 1510

I have not been in grade school for many years, and in my college career I have not used a great deal of math. In this time, I seemed to have forgotten about the idea of absolute value! This was never a tricky idea to me back when I was using it, but after not having used it for so long, it became a little slow-going when trying to work with it again. I have found that in order to deal with absolute value, I have to take my time and check my work! Those two things have really helped me when dealing with this topic.

So, what is absolute value anyway?Absolute value can be defined as the number of units an integer is from 0 on a number line. For all numbers not = 0, the absolute value is positive.
The following link talks about absolute value in very easy to understand terms, and includes a number line, practice problems and examples that you can check out!

Math is Fun - Absolute Value

This seems really simple, doesn't it! It's not confusing, at all. The confusing part comes when you try to add, subtract, multiply and divide with numbers calling for an absolute value. This video here shows how to do those operations when also dealing with absolute value. I found it very helpful, simply to watch another person doing it! I hope it helps you, too.

Problems with Probability - 1512

Today, I want to talk about probability, particularly odds in favor and against an event. I got really confused when it came time to calculate odds in favor and against in my summer math class, recently. Reading about this topic just didn't make it sink in so I have watched several videos and I think I have the hang of it, now.  If you're struggling with this concept, this might help you!

So, to start, you certainly have to understand what is meant when one says odds. Like many people, I have always thought of the odds of winning the lottery or the odds when you talk about horse-racing. If you consider the odds of winning something, those odds come from the ratio of the probability that you would win to the probability that you would not.

This is how to calculate odds in favor:

Odds in favor of A = P(A)/1-P(A)

The odds against:


Odds against A = 1-P(A)/P(A)

There are just the opposite calculations! It's really not as confusing as it seemed, now that I look at it written on my own blog :) One thing to remember is that you have to have the probability to calculate the odds, and sometimes that means you have to actually calculate the probability, as well.

If you're like me, it's the variable in the expressions and knowing where to plug numbers in that gets me all confused when it comes to solving these kinds of problems. Once again, here is a great series of videos that helps these formulas come to life and make sense out of a bunch of "foreign" language:

                 
                              

Divisibility - 1510

Have you ever wondered just how to know when a number can be divided by another? Especially when it's a number that doesn't end in 2, 5 or 0??? Well, there are these great techniques for determining divisibility of a number and I'm going to talk divisibility here, and include some links and videos that can be referenced for further understanding.

First, what is divisibility? Here is the "formal" definition:
For whole numbers a & b, with a not = 0, a divides b if and only if there is a whole number x, so that ax=b. Also, a is a divisor of b or b is divisible by a.

OK, so what does this really mean? In easier terms, think of 20 apples and 10 people - can the apples be divided evenly amongst the people without any being leftover? If so, then 20 is divisible by 10. In this case, if you gave each person one apple, that would use up 10, and there would still be 10. Every person could have another apple, meaning each person gets 2.

20/2=10

Therefore, 20 IS divisible by 10.

That's pretty easy, and if you know your division that one you can do in your head easily. But what about bigger numbers and divisors like 7, 9 or 11? Then things start to get a little more difficult. That's why there are these handy divisibility tests. Here is a link to a list of them:

 Math is Fun - List of Divisibility Tests and Examples

Here is a video, too, that shows the divisibility tests in action, if you would rather watch a video or if you're more of a visual learner (like me!): 

Compound Interest is NOT my Interest - 1512

I hate to seem like I whining about math, because I'm really not, but I just find so many ideas and concepts that I don't get, I don't like or I don't remember (or that I don't find useful!). Recently, I have been asked to calculate compound interest. Before that, it was simple interest, and it stays true to it's name - it's pretty simple.

Compound interest, on the other hand, takes me a long time to work out. I never seem to get the right answer the first time. It's because there are so many different variables to work with and things to plug in. It makes my mind go crazy! But...if I take it slow and double check my work, I can usually get it to come out right, now that I've gone over the things I will share with you below.

So, here's the formula for compound interest:

  A= P (1 + r/n) ^nt

where
    P = future value
    A= amount of initial deposit
    r = interest rate (expressed as a fraction: eg. 0.06)
    n = # of times per year interest is compounded
    t = number of years invested

Here is the formula explained and an example of how to work a problem using that formula: