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# AFS7 Math 3

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Math 1
1
• 2. Multiplying Integers
When multiplying two integers with the same sign (positive or negative) the product will always be positive.
Example: 4x3=12
-4x(-3)=12
When multiplying two integers with different signs the product will always be negative.
Example:
-4x3=-12
2
• 3. Negative
Or
Positive
Working with exponents
Example 1: (-2)3
-2 × (-2) × (-2)
4 × (-2)
-8
Rule: When multiplying a negative number in parenthesis with an exponent you must multiply the base by itself the number of times the exponent tells you.
Example 2: -23
2 × 2 × 2
4 ×2
8
-8
Rule: When multiplying a negative number with an exponent you must multiply the base by the exponent without the negative sign. When you are finish multiplying, add the negative sign.
3
• 4. Distributive Property
By, Jessica
The distributive property is a simplifying method.
5(4+2)
The first step to the distributive property is eliminating the parentheses.
5×4+5×2
You do this by multiplying each number in the parentheses by the number outside the parentheses ( as shown to the left )
20+10
Then you add or subtract the two products
30
30
• 5. Identity property of multiplication
If you multiply any number by 1 the product doesn’t change
The end
8×1=8
5×1=5
30×1=30
By, Jessica
• 6. Combining like terms
For Example
Here, we have a simple equation.
To do this equation, we must combine the variables together.
Instead of doing (2x-3+5x), we can convert this to (7x-3). This is combining like terms. Then, we can finish off this equation by using the distributive property.
By: Sean
3(2x-3+5x)
3(7x-3)
(21x-9)
You are now a master of the art of the distributive property!
When you have an equation with variables that represent the same value, their value can be combined.
• 7. Exponents
By Austin
22: When a positive number has a exponent you times the base by itself the amount of times the exponent.
The End
-22: When the base has a negative sign in front of it without parenthesis you do the problem as if there was no negative in front of it and once you have your product add your negative in front of it making the answer -4.
(-2)2 When the base is a negative number with parenthesis you do the problem like it shows. -2x-2. When the the exponent is even the answer will be positive but when the exponent is odd the answer will be negative
7
• 8. Adding and Subtracting Integers
BARK! BARK!
Step 3: To subtract integers, remember three words, “Add the Opposite”. Change the sign of the second number, then add the two numbers using the addition rules that I showed you.
Step 2. To add integers with different signs, you have to take the difference of the two numbers as if they were positive and take the sign of the larger integer.
Step 1. To add integers with the same sign, you have to add the numbers as if they were positive and keep the original sign.
I’ll Show you how!
By: Douglas
Example: 6 + 2 = 8
Example: 6 + (-2) = 4
Example: 6-(-2) = 8
GREAT! Now I know how to add and subtract integers!
How do you add and subtract integers?
8
• 9. The Rules of The IntegersBy Josh
_______________________________________
When adding integers, to find whether or not the answer is positive or negative you must figure out whether the positive numbers have the greatest number value or the negative numbers do. Think of adding negatives, as adding positive.
-12+3=(-9)
12+(-3)=9
Subtracting Integers
QUACK
When subtracting integers, subtracting positives makes a negative number farther from zero and subtracting negatives makes the number closer to zero. Subtracting a negative from a positive makes the number larger.
12-3=9
12-(-3)=15
-12-(-3)=(-9)
THE END!!!
9
Review
How to Solve
7(4+x)
7*4 7x
28+7x
State the problem.
Multiply the first factor (7) by each value in the parentheses.
Add or subtract the two products accordingly.
Multiply the first factor (8) by each value in the parentheses
Add or subtract the products accordingly
8(6-5)
The Distributive Property
State the problem
boom
8*6 8*5
48-40=8
By Dorian
10
• 11. Addition Property of Equality
By: Nina
The End
Right or Wrong?
Example:
The Addiction Property of Equality is when your problem can be solved by adding the same number to each side.
Wrong
x-197=-237
X=40
768 - x = -285
-X= 1,053
Right
X-197+197= -237+197
X-197+197= -237+197
768-x-768 = -285
768-x-768 = -285
This is done because it eliminates a number, so you are closer to narrowing down the variable. (Which is the awser)
The Golden Rule
Golden Rule: Do onto one side as you would the other
11
• 12. The Distributive Property ( For Algebra)
‘Multiplication “distributes” over addition.” (or subtraction.)
Step 1: Distribute the number you are multiplying with to both numbers
(multiply),
Ex. 4 (y+9)  (4 × y) + (4 × 9)
THE END
Step 2: Remove the parentheses
Ex. 4 × y + 4 × 9
By: Meara
Step 3: Multiply the numbers…and…voila!
Ex. 4 × y + 4 × 9  4y + 36
This problem cannot be simplified because it is an algebra problem.
For a subtraction problem, take out the addition sign and substitute
a subtraction sign.
Distributing rubber ducks!
12
• 13. Rules for Subtraction:
Change the second number of the problem to addition, and use the rules of addition
Ex: 2-6=2 + (-6) = -4
Rules for Subtraction