PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for...
-
Upload
doankhuong -
Category
Documents
-
view
214 -
download
2
Transcript of PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for...
![Page 1: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/1.jpg)
![Page 2: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/2.jpg)
A Question of BalanceThe two sides on a balanced scale must be equal to each other
What does the Egg weigh?
E + 6 = 11E = 5
![Page 3: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/3.jpg)
When you do something to one side of an equation,You have to do the same thing to the other side.
A Question of Balance
2(3) + 4 10
The two sides of an equation are equal to each otherThe left side and the right side must be balanced
![Page 4: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/4.jpg)
A Question of BalanceIf the two sides of an equation are not equal…
3(7) – 2 20 + 1
![Page 5: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/5.jpg)
A Question of BalanceIf the two sides of an equation are not equal…
3(7) – 220 + 1
Then it is not balanced!
![Page 6: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/6.jpg)
A Question of BalanceWhat happens if we change one of the sides of a
balanced equation?
Then it is not balanced!
8 + 3
11+ 18 + 3 + 1
![Page 7: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/7.jpg)
A Question of BalanceWhat happens if we change one of the sides of a
balanced equation?
Then it is not balanced!
8 + 3 + 1
11
We need to make the same change to the other side!
+ 1
![Page 8: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/8.jpg)
We need to make the same change to the other side!
What happens if we change one of the sides of a balanced equation?
A Question of Balance
8 + 3 + 1
11 + 1
We need to make the same change to the other side!Whatever thou dost unto the left, thou also must do unto the right.
The 11th Commandment (for equations):
![Page 9: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/9.jpg)
To solve an equation means to find every number that makes the equation true.
We do this by adding or subtracting to each side of the
equation … but always keep it balanced!
![Page 10: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/10.jpg)
In the equation, 157 x7 added to a number gives 15…
Solving the equation means, finding the value of the variable that makes the equation true.
Let’s go back to the balance
![Page 11: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/11.jpg)
x + 7 15
Whatever thou dost unto the left, thou also must do unto the right.
The 11th Commandment (for equations):
- 7 - 7
Subtract 7 from both sidesSimplify both sides
![Page 12: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/12.jpg)
Whatever thou dost unto the left, thou also must do unto the right.
The 11th Commandment (for equations):
x 8
Subtract 7 from both sidesSimplify both sidesNow we know the value of x
![Page 13: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/13.jpg)
x 8
Subtract 7 from both sides Simplify both sidesNow we know the value of x
Whatever thou dost unto the left, thou also must do unto the right.
The 11th Commandment (for equations):
So the solution goes like this…x + 7 = 15x + 7 – 7 = 15 – 7
x = 8
![Page 14: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/14.jpg)
In some equations, the solution is obvious.x – 7 = 12
x = 19 5n = 35
n = 7
20 + h = 41h = 21
8c
= 3
c = 24We can simply work the operation
backwards in our head to get the answer.
![Page 15: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/15.jpg)
But in other equations, the solution is not so obvious.
93127 x 08.12.3 w
43
52
p
We have to know what operation(s) must be done to solve it, and work it out carefully.
452.1 m
![Page 16: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/16.jpg)
But in other equations, the solution is not so obvious. 93-127 x 08.12.3 w
43
52
p 452.1 m
12793-127127 x220-x
2.308.12.32.3 w28.4w
43
25
52
25
p
815
p
2.145
2.12.1
m
75.3m
You have to do the inverse operation to both sides to get the variable by itself
The opposite of addition is subtraction
The opposite of subtraction is addition
The opposite of
multiplying by
is multiplying by52
25
The opposite of multiplication is division
![Page 17: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/17.jpg)
Multi-step equationsWhen and equation has more than one operation you still have to isolate the variable by doing the following:•Make sure variable terms are all on one side, and constant terms are on the other.•Simplify•Divide by the coefficient of the variable.
![Page 18: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/18.jpg)
3x + 5 12
How would we solve 3x + 5 = 12?Let’s take another look at the balance
– 5 – 5
Subtract 5 from both sides
![Page 19: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/19.jpg)
3x 7
How would we solve 3x + 5 = 12?Let’s take another look at the balance
Subtract 5 from both sidesSimplify
![Page 20: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/20.jpg)
3x 7
How would we solve 3x + 5 = 12?Let’s take another look at the balance
Subtract 5 from both sidesSimplify
33
Divide both sides by coefficient of the variable (3)
![Page 21: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/21.jpg)
7
How would we solve 3x + 5 = 12?Let’s take another look at the balance
Subtract 5 from both sidesSimplify
3x
Divide both sides by coefficient of the variable (3)
So the solution is: 37x
![Page 22: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/22.jpg)
Let’s try some more equationsRemember, we have to keep the equations balanced!
Solve:8m – 10 = 36
423
31176w
173117176w 8m – 10 + 10 = 36 + 10
8m = 468 8m =
146w
1466w6
w = 84
![Page 23: PowerPoint Presentation€¦ · PPT file · Web view · 2012-01-08The 11th Commandment (for equations): - 7 - 7 Subtract 7 from both ... is addition The opposite of multiplying](https://reader035.fdocuments.us/reader035/viewer/2022070609/5ad37db87f8b9a665f8dc3b7/html5/thumbnails/23.jpg)
5x 2 = x + 4 Solve:
5x 2 + 2 = x + 4 + 2
Notice that there are variables on both sides
5x = x + 6
Get rid of the -2 on the left side
Simplify
5x – x = x – x + 6 Get rid of the x on the right side
4x = 6 Get rid of the cofficient of x4 4
23x = Simplify
Simplify