After all of the Math Mondays I have done this year, this post is the last. Writing about math every Monday has not really helped me with math, but it has helped me learn some new things about math. That is because these topics come from the pre-algebra teachers, and I am in algebra so I don't know everything that is taught in pre-algebra. On some of the post topics I have had to do research such as on the post about Pi.
Next year we are starting a new thing called Common Core. This is a new system for how we test and all of that stuff. Common Core includes a lot more writing. This includes math, so we will have to answer more written problems. I think math Mondays should have prepared me for that a little bit, so maybe I did learn something from my math Monday blogs this year.
There are a lot of connections between math and science. In science there are a lot of formulas that you have to use to find out certain things. One formula that I remember using this year was when we were studying plants. We had to memorize the chemical formulas for respiration and photosynthesis. All of these formulas used in science are a type of math. You also have to use math when you are measuring things which you have to do a lot with chemistry, and pretty much everything.
One other thing that we used math for in science class was when we studied radioactive decay in rocks. We had to do a lot of addition and multiplication, and used percents when finding out how much radioactive isotope was in the rock. As you can seen, math and science are connected in many ways.
Negative numbers are numbers below zero. There are an infinite number of negative numbers just like there are positive. One interesting thing about negatives is that none of them have a square root! It is impossible for them to have a square root because a positive times a positive is a positive, and a negative times a negative is a positive.
There are a lot of ways that we use these numbers in real life. The way that we use them every day that really stands out to me is money. One way that we use them is money is when we owe someone money, or are in debt. Say that someone gives you money to buy something and you have to pay them back 10$; you owe that person 10$ or in other words they owe you -10$. There are a lot of ways that we use negative numbers in real life, but this is just one way I can think of when using money.
An equation like 2x-7=15 is very easy to solve using simple algebra. The goal is to get x by itself so you can know what its value is. The first step in solving this problem is to add seven to itself, to cancel itself out, and then add seven to fifteen to get twenty-two. You do this because in an equation you have to add a term to both sides to cancel it out. Now the equation is 2x=22. The next step is to divide both sides by two to get x by itself. You divide two by two to cancel itself out, then you divide twenty-two by two to get eleven. Now x is by itself and all that is left is x=11. This is how you find the value of x in a simple equation such as this one.
There is really only one way to convert decimals to fractions, and I think that is the way that most people use. The way I do it is to first just read the decimal in my head. Then you can just write that in fraction form. For example, lets say you have the fraction .9; you would read this as nine tenths. When you read that, it is pretty obvious that the fraction is 9/10. You can do this with any decimal no matter how long it is.
Here's another example of converting decimals to fractions: the decimal is .1329. How would you convert that? Well all you have to do is read it: one thousand three hundred twenty-nine ten-thousandths. It is kind of long and confusing, but still easy to understand that the fraction is 1329/10,000. Whenever you add another place to the decimal, you add a zero to the denominator of the fraction. That is how you convert decimals to fractions.
There are a few different ways to convert a fraction to a decimal, but there are two very common ones that I think of first. First there is the method where you just divide it, and then there is the method where you have to make the denominator one hundred, so it can be a percent in the hundredths place. When I am converting fractions to decimals, my favorite method is to just divide the numerator by the denominator. So if you had a fraction such as 1/4 all you do is divide 1 by 4 and get .25 as the answer. In my opinion, that is the easiest way to do it, and is how I do it every time. There is another way too, but I think it is more complicated and time consuming.
The other way to convert a fraction to a decimal is to make a ratio, and find the equivalent fraction over 100. For example, say you have the fraction 10/50- you can put that over 100 by multiplying the numerator and the denominator by whatever will get them to equal 100. In this case you multiply 50 by 2, which means that you also have to multiply 10 by 2. That would get you the fraction 20/100 or 20% which is .20 in decimal form. Those are the two ways to convert a fraction to a decimal.
If I was working in a restaurant trying to find the better deal on two items I would use ratio to do it. I personally think that ratio is maybe a longer way to solve, but it is simpler. It is laid out in a way that is simpler to solve in my opinion. Here is an example...
Let's say I work in a restaurant and we need to buy more salt. There are two choices: I could either buy 5 lb. containers of salt for $12.00 each, or I could buy 8 lb. containers of salt for $16.00 each. How do I figure out which is the better buy? Well I have to set it up as two ratios: the ratios are $12.00/5 and $16.00/8. I need to find out the price per pound of salt for each container, and to do that you just divide $12 by 5 lb. and $16 by 8lb. For the 5 pound container you get 2.4, which means that in that container, each pound of salt costs $2.40. In the 8 pound container you get exactly 2 by dividing 16 by 2, so the price per pound of that container is $2.00. Just by looking at those two prices you see that buying the 8 lb. containers is cheaper since it has a lower price per pound of salt. This is how you use ratio to solve a problem like that!
The formula for finding the area of a circle is pi times the radius squared. If you were given a circle and the only measurement you had was the radius, it would be enough to find the area. Lets say you have a circle with a radius of 3 feet. The first thing you have to is to square the radius, so you get 9 because 3 times 3 is 9. Next you multiply 9 by pi (3.14). 9 times 3.14 is 28.26, so the area of a circle with a radius of 3 inches is 28.26 square inches.
If you know the radius of a circle you can also use it to find the circumference of it. The first thing you need to do is find the diameter, which of course is 2 times the radius, equaling 6 feet in this case since the radius is 3 feet. Once you know what the diameter is all you have left to do is multiply it by Pi; so you would multiply 6 times 3.14 which equals 18.84 and that is the circumference. Now you should hopefully understand how to find the area and circumference of a circle.
Y=mx+b is a formula that you use to graph a linear function or just line. The "m" represents the slope of the line, so if m=2 then you would start at the starting point and go up two, and over one. The only problem is that you don't know where to start the line. You only know the slope. That is what "b" is for. "B" represents the starting point of the line, or the y-intercept, which is the point along the y-axis where the line crosses it. If you know the value of "m" and "b" you can graph the line.
Step 1: Example equation y=2x+1
Step 2: Y-intercept is 1 so graph a point on (0,1)
Step 3: From (0,1) go up two, over one to find the next point (3,1)
Step 4: Keep adding points, then connect them to create the line
As you can see it is really very simple to create at graphed line when using y=mx+b!
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