I get emails occasionally asking me about what the easiest ways are to learn specific topics in algebra. I often get asked about how to do percentages, and even though it’s not technically algebra, I’m going to cover percentages here in a way that should make it clear to anyone who starts off by understanding how to do multiplication. I hope that people enjoy this instructional about percentages and feel free to email me with any questions or comments at [email protected]
A percentage is a way to compare portions by looking at how many parts out of 100 are used. For example, a quarter is 25 percent of a dollar, and it’s easy to remember because the word “cent” is used in percent. If you have a pizza that is cut up into four pieces, then one piece will be 25 percent of the pizza. These are two simple examples that can introduce you to the basic idea of a percentage as a part of a whole.
Turning a number into a percentage is the same as dividing by 100. What I mean by this is that 35 percent or 35% is the same as 35/100 = 0.35. Another example is that 50 percent is 50/100 = 0.50. A simple trick to convert a number into a percentage is to move the decimal place two spots. This means that 35% becomes 0.35, 50% becomes 0.50 and 85% becomes 0.85. It’s worth noting that 100 percent or 100% is just 100/100 = 1. All of this might seem like a sort of random piece of trivia, but if you understand how to change numbers to percentages and vice versa, then you’ll already know the majority of what you need to know to take percentages.
If you want to find a certain percentage of a number, then you multiply by the decimal form of the percentage. For example, if you want to find 25 percent of 40, then you multiply 40 * 0.25 to get 10. Another example that you might see in a textbook or on an algebra test could be, “What is 35% of 60?” You just multiply 60 by the decimal form of 35% which is 0.35, and you get 60 * 0.35 = 21. This means that 35 percent of 60 is 21. You could also say that 21 is 35% of 60; these are just two different ways of saying the same exact thing.
You can use percentages in algebra to put some more advanced ideas into action. For example, if I asked you the question, “12 is 20% of what number?” To solve this problem, you’d need to use a small amount of algebra. To turn this question into an equation, we’re going to say 12 = 0.20 * x. Now that we have a basic linear equation, we can solve for x by dividing both sides by 0.20 to get 60.
I get a lot of enjoyment out of helping people who have trouble with math, especially non-traditional students who are learning algebra. As far as math subjects go, algebra is a sort of dividing line between what’s considered basic arithmetic and “smart people math” for the majority of these students, and it seems to be the same for students who are from other demographics as well. In general, I think that my favorite group of people to help with algebra are people who are intimidated by it and/or have a lot of anxiety when it comes to math and algebra overall. I’ve decided to make a blog post here outlining my approach to working with people who have a lot of psychological problems with math.
As I mentioned in my Psychology of Algebra series that you can find in the right-hand toolbar of this site, anxiety is one of the biggest obstacles that keep people from learning algebra quickly and easily. What’s really interesting about algebra in particular is that this dynamic doesn’t really exist for lower-level math like basic arithmetic, and it also does not apply to higher-level math like calculus or group theory. Basic arithmetic is concrete enough that people can easily relate it to the world around them, and I think this is what takes a lot of the sting out of it. Students who are taking higher-level math are usually the types who will need it for their jobs, or they could be people who actually enjoy the math. Both of these types of people won’t have to deal with anxiety as much with higher-level math because it’s something that’s already been addressed before in their lives.
That leaves us with algebra students who are scared. To start things off, I like to bring up the fact that they are scared and anxious about the material that we will be covering. I want them to get some of their feelings out there so that we can talk about things like being afraid to fail and how their anxiety can keep them from seeing success with algebra. I make a point to explain to them that a lot of how I approach teaching math is geared around lowering their anxiety levels and making it easier for them to learn the material without feeling like they are in the middle of a huge emotional grind. When I explain these ideas to them, I always feel like they see me as more than an instructor. Instead, they see me as someone who really cares about them as human beings. They appreciate that I’m not going to treat them like emotionless robots.
When we jump into the material, here’s how my lessons are normally structured. I’ll start talking to my students about some problem or issue. If it’s at the beginning of their algebra careers, then I might talk to them about how we need negative and positive numbers to be able to represent things like expenses and income. This is usually enough, at least in the beginning, to get their anxieties about math up and running. Once I feel like the level of anxiety is sufficient, then I ask them about it in a straight-forward way. I ask them if they feel anxious, if they are scared and what they are scared of. By getting all of these feelings out in the open in the beginning of the lesson, they are easier to deal with once we get on into the instruction.
After the psychological issues are brought out into the open, we’ll start off with a bit of theory regarding whatever the topic is that we are discussing. If we stick with the example of integers, then we might start off by looking at how to add numbers that have the same sign. After asking the students to complete a couple of examples, I point out any mistakes in a way that allows me to make sure that the students understand what went wrong and how things are supposed to be done. A bit of theory is followed by some examples, and then I bring up the anxiety question again. This time, I point out that they are learning the topic that they were so afraid of earlier, and I make a point to get them to agree to, or at least address, that it might not be as bad as they originally thought. The pattern of theory followed by examples and psychological discussion will continue until the lesson is finished.
I want to point out why the psychological checkpoints during the lesson are so important. Following this process and having them talk out their fears of algebra while they are learning really cuts down on how big of a hold anxiety has over them in the long run. After just a week or two of instruction in this way, most students see huge improvements in their ability to concentrate on their algebra work. Since algebra becomes less of an emotional torture device, students open up more than they would before. This is the key idea in how I teach math to students who have problems with anxiety and fear of failure.
One of the trickiest topics to learn is how to divide fractions. Because fractions themselves are a type of division with the numerator being divided by the denominator, you can end up with a very complicated scenario if you aren’t careful with what you’re doing. Here at algebra1help.org, we’re always trying to show you the easiest and most simple ways to do math in general. Along these lines, we’re going to show you the easiest way that there is for dividing fractions. However, you’ll need to know how to multiply fractions before you can use this easy trick for the division of fractions.
If you don’t know how to multiply fractions, then click the link above and read about how to do it. If you know how to multiply regular numbers, then you’ll be able to learn how to multiply fractions in about 90 seconds. Once you know how to do that, we’re going to show you how to divide fractions the easy way by just turning it into a multiplication program. Suppose we have the following division problem:
The simple way to divide fractions is to flip the second fraction and change the operation from division to multiplication.
Since you already know how to solve this from the link we mentioned above, you’re one step away from being done. Since 7 times 3 is 21 and 8 times 2 is 16, we get the following:
When I show people how easy it is to divide fractions using this trick, they can’t believe how insanely difficult it had been made for them before. These are the types of time-saving and sanity-saving tricks that I like to show people on this website.