For today's math blog, we were to play this very interesting math game. In that math game, you were suppose to find the difference of the two numbers that was on that side the of the frame; there was a total of four numbers in each frame. There were also 3 levels: integers, fractions, and decimals. The one that was very easy for me to figure it out was the level with the integers. I think that was level was the easiest for me because I understand all the rules when adding, subtracting, mulitplying, and dividing integers. For example, the problem was -2 subtracted from 7. I knew the answer to that was 5 because 7 was the largest number and it was positive. The sign of the answer always comes from the largest number. I had no difficulties while playing that level. 
     I did have some problems with the other two levels, though. The most difficult one for me out of the three levels was the fractions. I think I had the most trouble with that one because some of the fractions did not have common denominators. I have yet to learn how to subtract fractions with unlike denominators in an easy and fast way. I eventually found out though because I looked online. The easiest way was to cross mulitply, and then add, and then add the denominators for the common denominator. I found that very easy and it also worked. I'm glad I learned how to do that because it is very helpful. 
    I didn't have much trouble with the decimals, expect that some numbers had me thinking for awhile. I think the reason why I had trouble was because there was more than one number and there was a decimal. But overall, I enjoyed playing that math game. 
     When graphing inequalities, there are two rules. The first rule is that if the sign is greater than or less than, it is always an open circle. If the sign has 'equal to', it always has a closed circle. The reason for these two rules are because it tells whether the number is or not apart of the solution.
     The sign that has 'equal to' is graphed with a closed circle because it's saying that that number is apart of the solution. That number including all the other numbers to the left or right is correct and it can be proven. So take 'm is greater than or  equal to 5' as an example. All the numbers to the right of 5, including 5 is a solution. That is why the sign that has 'equal to' needs a closed circle when it is being graphed. 
     The sign that is greater than or less than is graphed with a open circle because it's saying that the number is not apart of the solution. That number and all the other numbers that is either to its left or right is not a solution to that problem. Take "k is less than 6" as an example. All the numbers to the left of 6 with be graphed with a open circle because it is saying that all the numbers to the right of it is less than six. It is not that diffcult once you learn it. 
     The possiblities of math methods are endless. There is solving from left to right, using specific operations, doing opposite operations, etc. But sometimes there is that one math problem where you have to do it one specific way. I have some methods of solving math problems, all depending on the type of math problem. 
      The first thing I always do when a math problem is given is look at it and read the directions. That is a required method of course! Then depending on the problem, I figure out what to do. Honestly, I don't really have favorite methods. I just do what I have to. But if it's like, solving for x when it's on both sides of the equation, I drag the x that is on the right side of the equation to the left side and perform the opposite operation because I think that is more simple, even though if you do it the other way, you will still get the same answer. There are many math methods. So what are some of your favorites? 
     There is no such thing as division. You're probably wondering, "How is that possible?! I've learned division since I was in the 3rd grade!" Well, there are much more simpler ways than just dividing. Take 2x=16 for example. Instead of dividing both sides by 2, what else could you do to find x? Well, in this case, figuring out the answer to 2x=16 is pretty easy if you know your multiplication facts. But one way you could figure out this answer is adding 2 until it reaches the number 16. So you would add two eight times to get the answer 16. Another way is using the distributive property. These are much more difficult ways, so wouldn't you just stick to dividing by 2? I would!
    Why do you think there's an infinite amount of numbers between 0 and 1? Well, 0 is a starting point for all numbers. 1 is a whole number. So how do you get to 1 starting from 0 on a number line? There's parts in between 0 and 1. These parts are parts of a whole number. 
      These parts, or numbers, are usually written as fractions or decimals. The numbers that are between 0 and 1 go on forever because it is usually greater than 0 but less than 1. For example, the decimal .01 is greater than 0 but less than 1. If you keep adding 0's to the 1 or any other number, it will still be between 0 and 1. And there are an infinite amount of numbers for that. All these parts will make 1 whole. So then, between 1 and 2, there are also parts. It is also the same with 2 and 3, 3 and 4, 4 and 5, etc. The possiblities of numbers between 0 and 1 are endless, therefore the list goes on forever. The numbers that are infinite between 0 and 1 are parts of a whole, also known as fractions. This is my explaination for why there are an infinite amount of numbers between 0 and 1. 
     Why is it that when the denominator gets larger in a fraction, its value gets smaller? Well, if you look at it this way, it is like cutting a pie. First you have it as one whole. Then you could cut it into halves, thirds, fourths, etc. That one piece you have will remain the same, but the whole just gets smaller.  This analogy has help me understand this concept better. 
     When the denominator gets larger in a fraction, the value gets smaller because it is seperated into more smaller parts, such as 1/5, 1/6, 1/7, etc.  So 1/3 would be greater than 1/5 because the larger the denominator is, the smaller the value gets. 1/5 may seem larger but it's not. Because one out of five is not greater than one out of three. 
     Math is my 2nd favorite subject. We have reviewed and learned many things in math class. Today, we learned about rational and irrational numbers. 
     I thought I knew what it was all about, but I was wrong. It turned out to be something I haven't really learned in 6th grade. Rational and irrational numbers have to deal with converting fractions into decimals, identifying the decimal as a rational or irrational number, converting decimals into fractions, finding equivalent fractions, etc. The part that I was getting confused on was identifying the decimal as a rational or irrational number. I thought I knew the difference between rational and irrational numbers, but I was wrong again. A rational number is when a decimal terminates or repeats; a irrational number is when a decimal goes on forever. When Mrs.Pope, my math teacher, solved another problem and went through the steps, I was like "Ohhhhhh, I understand this now!" This concept wasn't so difficult after all. After that, I was doing all those problems like a boss! 
     I probably did not understand that concept at first because I haven't done it in so long or I'm not use to doing it all the time. Once I learned it, it was a piece of cake!