Wednesday, May 31, 2006

Tears' Growing Post For May 30th!!!!

Question #1
What is the difference between an algebraic expression and an equation (hint:One contains this and the other doesn't)? Give an example of both an expression and an equation.

An algebraic expression is an expression when you could choose the value of the variable. For Example: 7+3N=. (Instead of N you could put 4 for example) 7+3x4. Like this: 7+3x4=
7+12=19

An algebraic equation is an equation when the value of the variable is given to you. For example: 7+3N= 16 N= 3 . Because if you multiply 3 by3 it givese 9 and add 7 it gives 16.
Solution:
7+3N= 16
7+3x3+16
7+9=16

The difference between them is about their variable. The algebraic equation gives the value of the variable but the algebraic expression lets you choose the value of the variable.

Question #2
What is a variable and why do we use one in algebra?

A variable is a symbol or a letter used to represent any number. We use variables in algebra to represent an unknown number. It doesn't matter if we know its value or not, still variables can help you solve things faster. In an algebraic expression, a variable is the number you can change the value. It should look like this : START+ CHANGE(VARIABLE)=. The one on the brackets you could change. In an algebraic equation, a variable is the number you need to find out. For example: 4+ 2N= 8 N= 2 .

Question #3
Solve for N


On the diagram above, I showed how I got 5 as the value of the triangle. If you look on the right side of the scale, You see 9 blue circles and each blue circles is worth 1 so the total value of the circles is 9 or 9 circles. On the left side of the scale you see 2 pink squares, each squares is worth 2 or 2 circles so the total value of the 2 squares is 4 or 4 circles. On the left side of the scale there's a triangle too. To get the value of the triangle you subtract the total value of the 2 squares from the total value of the 9 circles. Like this: 9 - 4 = 5. So the value of the triangle is 5 or 5 circles.

On the diagram above, I showed how I got the value of the N. I f yoou look on the right side of the scale. You see 6 squares and as we learned from the last diagram each square is worth 2 or 2 circles so the total value of the 6 squares is 12 (6 x 2). On the right side of the scale there's also 2 triangles and as wew learned from the last diagram each triangle is worth 5 or 5 circles so the total value of the 2 triangles is 10(5 + 5). To get the value of the 2 pink circles with the N inside on the left side of the scale, first you have to find out the total value of all the shapes on the right side of the scale. Like this: 10 ( total value of the 2 triangles) plus 12 ( total value of the 6 squares). 10 + 12 = 22. As you can see on the left side of the scale there are 2 pink circles with N inside. So you have to divide the total value of all the shapes from the right side of the square by 2. Like this : 22 / 2 = 11. N = 11

Question # 4
Solve the following equations. Show all of the steps that are needed.

a) 3n + 4n + 7 = 2n + 12
7n + 7 = 2n + 12
7n - 2n + 7 = 2n + 12 - 2n
5n + 7 = 12 5n + 7 - 7 = 12 - 7
5n = 5
5n /5 = 5 / 5
n = 1


b) 8n - ( 4 + 9 ) = 11
8n - 13 = 11
8n - 13 + 13 = 11 + 13
8n = 24
8n / 8 = 24 / 8
n = 3


c) (8 - 3) n + 7n + 8 = 4n + 40
5n + 7n + 8 = 4n + 40
12n + 8 = 4n + 40
12n - 4n + 8 = 4n + 40 - 4n
8n + 8 = 40
8n + 8 - 8 = 40 - 8
8n = 32
8n / 8 = 32 / 8
n = 4

Question #5
For this question you need to create a T-Chart and a graph to plot your data from this question onto.

You are having a race against your friend, except you are on foot and he is on his bike. You both know that if you are in your bike you will be faster so your friend gives you a head start of 3 minute. If you can run 400m per minute, and your friend can bike 700m per minute, who will be the first to make it to the finish line 2000m away?


Tearsamay's T-Chart (The Runner)



Tearsamay's friend's T-Chart (The Biker)
The Race's Graph
Who won the race?
Tearsamay Won by a minute!!!




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3 Comments:

At 7:27 PM, Blogger Mr. Reece said...

Tears you didn't include a graph for the question #5. Otherwise wow, I will be sharing this post with some highschool math teachers that I know because this is outstanding work.

Add the graph and this post will be added to the hall of fame

 
At 7:37 PM, Blogger tears_77 said...

Sorry, my graph was delayed . My computer froze but it's ok now..

 
At 1:33 PM, Blogger Mr. Reece said...

Your mark is 30/30. Amazing job Tears77

 

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