1. Seventh Grade Math
Math 3

2. Distributive Property
Explanation of Distributive Property
Distributive Property is a property of numbers that ties t he operation of addition ( Subtract) and multiplication together.
The Rules Of Distributive Property
It says that for any numbers 9, 13, C, A x ( B + C) = A x B + A x C.
For those used to multiplications without the multiplication sign
The same property applies when there is subtraction instead of addition
How It is Used
The Distributive property is used when something in parentheses is multiplied by something, or, in reverse, when you need to take a common multiplier but of the parentheses
Ex. X(2y-3) : 2 x y – 3x

3. Positive and Negative Integers
Subtracting negative integers are just like adding, except when using two different integers. When a smaller number is subtracted from a bigger number, the result is negative.
EXAMPLE: 5 – 10 = (-5)
When a positive number is subtracted from a negative number, the answer I decided whether the positive or negative number is bigger.
EXAMPLE: -20 – 10 = (-10) OR 20 – (-10) ‘
When using more than two integers, the larger amount decides the answer.
EXAMPLE: 10 – (-20) – 30 – (-40) = 0
As previously stated, negative numbers plus positive numbers are more complicated than positive plus positive. Using the hot and cold cube strategy can be helpful. When there are more hot cubes then cold cubes, the result will be positive,
EXAMPLE: = 10
This is similar to more cold cubes then hot
EXAMPLE: 10 + (-20) = (-10)
When using two negative integers, the sign stays the same.
EXAMPLE: (-20) = (-30)
Positive and Negative Integers
Think of adding integers like hot and cold cubes, with negative integers being cold. When you add two or more cold cubes together, you get an even colder tempeture and vice versa with hot cubes, but adding hot cubes to cold cubes is a bit more complicated.
Multiplying integers are pretty easy: when there are an even number of negative numbers, the answer is positive.
EXAMPLE: -10 x -10 = 20
When there is an odd number, the answer is negative.
EXAMPLE: -10 x 10 x -10 = -200
If done correctly, negative integers can be a lot like positive integers. The main thing to know about negative numbers is that not all equations using negative numbers are actually negative, they can be positive too!
THE END!!!!!!!!!!!!!
Use the same strategety used for multiplying for dividing.
EXAMPLE: -10 / -10 = 100
positive.
EXAMPLE: -10 x -10 =20
When multiplying an odd number of negative numbers, the answer is always negative.
EXAMPLE: -10 x (-10) x 10 = (-200)
EXAMPLE: 10 / (-10) / (-10) = (-200)
Everyone knows how to add, subtract, multiply, and divide positive integers, but what about negative inters?

4. BY: Ben Adding and Subtracting Integers Subtracting Adding Rule 1
When adding integers of the same sign, add their absolute value and give the same sign.
Example: -15+(-15)= -30
Rule 2
When adding integers if opposite signs, take their absolute values, subtract smaller from larger, and give the result with the sign that has a larger value.
15+(-17)=-2
Subtracting
Add the opposite!
4-7
4+(-7) -3

5. Adding And Subtracting Integers. BY: Abby
Adding integers having the same sign.
Rule #1
Add the numbers as if they were positive then add the sign of the numbers.
Example -5+(-3) or 5+3 then add the sign
Rule #2 Adding integers with different signs
Take the difference of the two numbers as if they were positive then give the result the sign of the absolute value or the bigger number.
Example -5+3 = 2 or 5-3 = 2.
Subtracting Integers
Rule#1
When we subtract Integers we would ADD THE OPOSITE!!! Then follow the steps of addition.
Example 5-(-3) becomes 5+3 or -5-(-3) becomes -5+(-3)= -2

6. Adding and Subtracting Integers
ADDITION
Subtraction
Rule #1- When adding integers having the same sign: Add the Numbers as if they are positive and then add the sign of the numbers.
Example: -4+(-8)=? -> 4+8=12 then add the negative… -4+(-8)= -12
Rule #2- When adding integers having different signs: Take the difference of the numbers as if they are positive, then give the result of the number with the greatest absolute value.
Example: 8+(-17)=? -> 17-8=9 ->
8+(-17)=-9
Rule- Add the opposite! (this rule applies to all subtraction) then, follow the rules to addition. Example: 3-(-12)=? -> 3+12=15 & -3-12=? -> -3+(-12)=9

7. The Distributive Property
The End
Look at the problem. 5(7+a-3)
Example:
Rewrite the problem by adding the opposite if needed. 5(7+a+[-3])
Add arrows if you want to.
Use the distributive property to make it say 5 times every term. 5x7+5xa+5x(-3)
Get the answer to each multiplication step. 35+5a+(-15)
Simplify the like terms. 20+5a
Rules:
DO add the opposite
DON’T add unlike terms
By: Courtney

8. Adding Integers ADD SUBTRACT MATH PROJECT AHMER
Examples: = = = -7
Rule: If you add two negative Integers you have a Negative Integer.
Rule: When you add a positive integer with a negative integer you get either a
Negative or positive because it depends on which number is bigger.
MULTIPLY
Examples: = (-12) =33
DIVIDE

9. Multiplying Integers By: Brian Rule#1
When multiplying an even number of negative integers the product will always be positive.
Example: -8(-5)=40
Rule#2
Example:-9(5)=45
When multiplying and odd number of integers the product will always be negative.

10. Adding and Subtracting Integers
Hailey
Adding Integers With The Same Sign
Rule: Add numbers as if they were positive, then add the sign of the numbers
Ex. (-3)+(-8) 3+8=11 (-11)
Adding Two Integers Having Different Signs
Rule: Take the difference of the two numbers as if they were positive then give the result the sign of the number with the greatest absolute value (dominant)
Ex =2 (-2)
Subtracting Integers
Rule: When we subtract integers, we “add the opposite” then use the rules for addition
Ex. 7-(-6) 7+6=13 13

11. By: Isabelle Distributive property
1.You take the first number/variable and multiply it by the second number/ variable
Example:
3(4+a)  3x4
3(4+a)  3xa
This is the distributive property.
3.Then finish the problem.
3x4 12 +
3xa  3a =
12 + 3a
By: Isabelle
3(4+a)  3x4 + 3xa
2. Then when you add or subtract depending on the sign in the problem. Do the same to the second number variable.
Example: 3x4 + 3xa

12. Subtracting Integers
Rule: Subtracting an integer is the same as adding it’s opposite.
By: Morgan
Note: The integer that goes first never changes.
Examples:
-6-3=-6+(-3)=9
-7-(-2)=-7+2=-5 8-(-9)=8+9=17
4-(-5)=4+5=9

13. Multiplying and Dividing Integers
By: Tatiana
1.When multiplying or dividing two integers with the same sign the answer to the
equation is always a positive number.
2.When multiplying or dividing two integers with different signs the answer to the
equation is always a negative number.
3.When multiplying or dividing more than two numbers that include a negative
number count how many negative numbers there are. If there is an even amount
of negative numbers then the answer is a positive number. If there is an odd
amount of negative numbers than the answer will be a negative number.
3 × 3 = 9
-3 (-3)= 9
4 ÷ 4= 1
-4 ÷ (-4)= 1
Examples:
3. -2(-2)-2)(-2)= 16
3(-9) (-8)= 216
3(-2) (-4) (-2)= -48
-2(-2)(-2)= -8
2. 2 (-5)= -10
6÷ (-3)= -2

14. Adding Integers By Will Malone
When adding integers of the same sign, we add their absolute values, and give the result the same sign.
2 + 5 = 7 (-7) + (-2) = -(7 + 2) = -9 (-80) + (-34) = -(80 + 34) = -114
When adding integers of the opposite signs, we take their absolute values, subtract the smaller from the larger, and give the result the sign of the integer with the larger absolute value.
8 + (-3) = ? The absolute values of 8 and -3 are 8 and 3. Subtracting the smaller from the larger gives 8 - 3 = 5, and since the larger absolute value was 8, we give the result the same sign as 8, so 8 + (-3) = 5.

15. Combining Like Terms
Combine like terms. Using the properties of real numbers and order of operations you should combine any like terms.
Isolate the terms that contain the variable you wish to solve for. Use the Properties of Addition, and/or Multiplication and their inverse operations to isolate the terms containing the variable you wish to solve for.
Isolate the variable you wish to solve for. Use the Properties of Addition and Subtraction, and/or Multiplication and Division to isolate the variable you wish to solve for on one side of the equation.
Substitute your answer into the original equation and check that it works. Every answer should be checked to be sure it is correct. After substituting the answer into the original equation, be sure the equality holds true.