quarter 2 math REFLECTION
This semester I learned that there is so much that I haven't mastered in math. I never understood the elimination method and would always forget the process. Now I can actually remember how to match two similar variables so that one cancels out the other to get one of the two points (see below for example). And when exponents were used as fractions it would always get very confusing, especially when negatives were added in. There was also when the exponents themselves were fractions. Also very tricky and difficult. Throughout this whole semester, I have to thank my very close friends Lea and, can't believe I'm saying this, Nicholas, two brilliant individuals who have helped me through my math problems this whole year.
Elimination Method
![Picture](/uploads/1/6/5/9/16591066/1079613.jpg)
The elimination method is used to find the point where these lines intersect.
Step one: Choose a way to make one of your variables (x and y) equal but opposite. We can do this by multiplying one of the lines below be negative one so that you will get x-2y=5 and -x+4y=4. *Keep in mind that you have to multiply the whole line by negative one, not just the variable you wish to change*
Step Two: cancel out the match variables and then solve for the remaining one. What this means is that you are going to take the x from one equation and the -x from the other, and add them together. This gets you zero. Now combined your y's. 4-2= 2. so that leaves you with 2y. Last for this step is to combined your regular numbers, after the equal sign and that gets you 5+4= 9. That means your new equation is 2y=9.
Step Three: Next you have to solve for y. This means you divide 2y by two, what ever you do to one side you do to the other, and you get y=9/2.
Step Four: Your final step is to plug in and solve for x. any equation is fine. x-4(9/2)=-4 ----> x-(36/2)=-4 ---->x-18=-4 --Add 18 to both sides--> x=14. Your point is now (14,9/2)
Step one: Choose a way to make one of your variables (x and y) equal but opposite. We can do this by multiplying one of the lines below be negative one so that you will get x-2y=5 and -x+4y=4. *Keep in mind that you have to multiply the whole line by negative one, not just the variable you wish to change*
Step Two: cancel out the match variables and then solve for the remaining one. What this means is that you are going to take the x from one equation and the -x from the other, and add them together. This gets you zero. Now combined your y's. 4-2= 2. so that leaves you with 2y. Last for this step is to combined your regular numbers, after the equal sign and that gets you 5+4= 9. That means your new equation is 2y=9.
Step Three: Next you have to solve for y. This means you divide 2y by two, what ever you do to one side you do to the other, and you get y=9/2.
Step Four: Your final step is to plug in and solve for x. any equation is fine. x-4(9/2)=-4 ----> x-(36/2)=-4 ---->x-18=-4 --Add 18 to both sides--> x=14. Your point is now (14,9/2)
Exponents in fractions *Warning: looks scarier than actually is*
![Picture](/uploads/1/6/5/9/16591066/7595064.jpg)
Step One: Check for negatives. Any exponent that is a negative is simply trying to tell you that it is on the wrong side of the fraction. so we'd take that x^-5 and z^-4 and add it to the top of the fraction and the x^-10 to the bottom. This now gives us (28x^5y^3z^12)/(7x^10y^6)
Step Two: Cancel out the matching bases. 28 and 7 are regular numbers and can be divided as such. 28/7= 4. but the variables we have to cancel out based on their exponents. x^10 on the bottom of the fraction cancels out x^5 on the top leaving x^5 on the bottom. do the same for all of them and you end up with ----> (4z^12)/(x^5y^3)
Step Two: Cancel out the matching bases. 28 and 7 are regular numbers and can be divided as such. 28/7= 4. but the variables we have to cancel out based on their exponents. x^10 on the bottom of the fraction cancels out x^5 on the top leaving x^5 on the bottom. do the same for all of them and you end up with ----> (4z^12)/(x^5y^3)
When exponents are fractions
![Picture](/uploads/1/6/5/9/16591066/9800628.jpg)
Step One: get rid of the extra exponent on the out side. We do this by multiplying the two ----> (-1/2)(-2/3)= 2/6. This leaves us with 27^(2/6).
Step Two: Take the denominator of the fraction. This is asking you to root your base number (in this case 27). You would treat it like your square rooting only this time, you're trying to find a number that when multiplied by itself six times, produces 27. The number in question is 1.732050807568877. Confusing now but just wait a sec.
Step Three: take your numerator used in your exponent, and that is what you will multiply your number by.... so when you multiply 1.732050807568877 times 2 you get...... 3! and that is your answer.
Step Two: Take the denominator of the fraction. This is asking you to root your base number (in this case 27). You would treat it like your square rooting only this time, you're trying to find a number that when multiplied by itself six times, produces 27. The number in question is 1.732050807568877. Confusing now but just wait a sec.
Step Three: take your numerator used in your exponent, and that is what you will multiply your number by.... so when you multiply 1.732050807568877 times 2 you get...... 3! and that is your answer.