The document provides explanations and examples for adding, subtracting, multiplying, and dividing integers. It begins by explaining the rules for adding integers with the same sign and integers with different signs, providing examples such as -6 + -2 = -8. It then explains that subtracting integers uses the rule of "adding the opposite" and provides examples like 7 - (-6) = 13. The document also covers multiplying and dividing integers, noting that an even number of negatives yields a positive result and an odd number yields a negative result. It provides examples such as -2(-2)(-2)= 16 and 2 (-5)= -10.

1. Seventh Grade MathMath 3

2. Distributive Property Explanation of Distributive PropertyDistributive Property is a property of numbers that ties t he operation of addition ( Subtract) and multiplication together.The Rules Of Distributive PropertyIt 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 signThe same property applies when there is subtraction instead of additionHow It is UsedThe 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 parenthesesEx. X(2y-3) : 2 x y – 3x2

3. Everyone knows how to add, subtract, multiply, and divide positive integers, but what about negative inters?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 + 20 = 10This is similar to more cold cubes then hotEXAMPLE: 10 + (-20) = (-10)When using two negative integers, the sign stays the same.EXAMPLE: -10 + (-20) = (-30)PositiveandNegativeIntegersMultiplying integers are pretty easy: when there are an even number of negative numbers, the answer is positive. EXAMPLE: -10 x -10 = 20When there is an odd number, the answer is negative.EXAMPLE: -10 x 10 x -10 = -200Think 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. 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!Use the same strategety used for multiplying for dividing.EXAMPLE: -10 / -10 = 100positive.EXAMPLE: -10 x -10 =20When multiplying an odd number of negative numbers, the answer is always negative.EXAMPLE: -10 x (-10) x 10 = (-200)EXAMPLE: 10 / (-10) / (-10) = (-200) THE END!!!!!!!!!!!!!3

4. BY: BenAdding and Subtracting IntegersAdding Rule 1When adding integers of the same sign, add their absolute value and give the same sign.Example: -15+(-15)= -30Rule 2When 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)=-2SubtractingAdd the opposite!4-74+(-7)-34

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 signRule #2 Adding integers with different signsTake 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 5

6. Adding and Subtracting IntegersADDITION 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)= -12Rule #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)=-9SubtractionRule- 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 6

7. The Distributive PropertyThe EndExample:Look at the problem. 5(7+a-3)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 oppositeDON’T add unlike termsBy: Courtney7

8. ADDSUBTRACT Adding Integers MATH PROJECTAHMER Examples: -6 + -2 = -8 -10 + -10 =-20 -2 + -5 = -7Rule: 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. MULTIPLYExamples: -20+10 = -10 45+(-12) =33DIVIDE

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

10. Adding and Subtracting IntegersHaileyAdding 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. -5+3 5-3=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. Distributive property1.You take the first number/variable and multiply it by the second number/ variableExample: 3(4+a)  3x4 3(4+a)  3xaThis is the distributive property.3.Then finish the problem.3x4 12+3xa  3a=12 + 3aBy: Isabelle3(4+a)  3x4 + 3xa2. 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 IntegersRule: Subtracting an integer is the same as adding it’s opposite. By: MorganNote: The integer that goes first never changes. Examples:-6-3=-6+(-3)=9-7-(-2)=-7+2=-5 8-(-9)=8+9=174-(-5)=4+5=9

13. Multiplying and Dividing IntegersBy: 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. Examples:3 × 3 = 9 -3 (-3)= 9 4 ÷ 4= 1 -4 ÷ (-4)= 1 3. -2(-2)-2)(-2)= 16 3(-9) (-8)= 216 3(-2) (-4) (-2)= -48 -2(-2)(-2)= -82. 2 (-5)= -10 6÷ (-3)= -2

14. 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. Adding IntegersBy Will Malone

15. Combining Like TermsCombine 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.