Solving Rational Expressions

HEY YOU. Time to be rational! LOL. So I am back again to write an entry that was due ages ago. A while back, when we were still doing rational expressions, Mr. Cheng gave us two equations and challenged us to solve one of them. That is what I will be doing/trying to do today.

Alrighty! So here goes nothing. At first glance, this question looks quite long and very difficult. But don't be scare! There is nothing afraid. You just need to break down this equation into little tiny pieces and it is as easy peasy, lemon squeezy. I will now give step-by-step instructions as to how I will solve it.

1. First, to make this equation a lot easier, I will move x^-2 to the bottom and y^-4 to the top, thus removing the negatives from the equation.

2. Next, I will multiply the exponent 5/2 to everything in the equation. So for 81, you would put the denominator 2 on the outside and you can square root 81 to get 9^5, which is 59049, a pretty big number.

3. Then you multiply y^4/1 by 5/2, making it y^20/2 or simplified y^10.

4. You repeat steps 2 and 3 with the bottom terms, and getting 16807 and x^5 as a result.

There you have it! Rational expressions in a nutshell. And if you still don't get it, feel free to ask me how. (NOT!) ;)

Problem Solving #2

This is one of my favorite questions from the second problem solving sheet that I got:

10. If x + y + z = 25 and y + z = 14, then x is:

A.) 8 B.) 11 C.) 6 D.) -6 E.) 31

This question was actually quite simple. Because you know that y and x are equal to 14, you can plug that into the first equation. You can replace (y+z) with 14 to get this equation:

x + 14 = 25

From there, you can easily solve the equation and get the answer B.) 11. One year ago, I wouldn't have been able to solve this question. But now that I have learned to use equations to solve equations, it is much easier. Another way you could solve this problem is guess and check, but that would take forever. I really enjoy problem solving because you never know what kind of problems you are going to get. There are thousands of problems out there just waiting for you to solve them. I especially like problems that you can apply in real life because they are very useful and the skills you pick up are essential. I hope to do more problem solving and get better at it!

Problem Solving #1

I love math(sort of). Math is cool. This is a math problem that I did:
3. The value of 2 1/10+ 3 11/100 + 4 111/1000 is

(A) 9. 321 (B) 9.111 (C) 9.123 (D) 9.111111 (E) 9.11081081

The first step in solving this equation is to make the three denominators the same. To do that, you should multiply 2 1/10 by 100 to make the denominator 1000, resulting in 2 100/1000. Secondly, you multiply 3 11/100 by 10 to make it 3 110/1000. After that, you can add the three numbers together and the answer will be 9 321/1000. Finally, you change the number into a decimal. The final answer is A- 9.321. :)

Tower of Hanoi

My strategy for this puzzle was to first move the biggest one to the right. Also, you have to work backwards before you can go forwards. You alternate between putting the first ring on the right and in the center. At the beginning, it was really easy and I had no problems solving it, but as the number of rings increased, it seemed to be more difficult. But basically, you just do the same thing over and over. I found it quite fun and tried to get the lowest number of moves possible.