Math 2 1

Subtracting integers: 2 – (-8) Rule When we subtract we ADD THE OPPISITE! (never change the first number!) is the same as 2 – (-8)….. So, the answer is the same, = -6 The answer is positive because you always use the sign of the number with the highest absolute value. -8 is farther away from zero then 2 is. So - 8 has the highest absolute value. By: Claudia Vocab: Integers – the set of whole numbers and their opposites. Absolute Value – the distance the number is from zero on the number line. 2

How to Multiply Integers When multiplying integers with the same sign the product is always positive. When multiplying integers with different signs the answer will always be negative. If any of the integers is zero the result is always zero. 3

Adding Integers Ex: 5+3=8 Add the numbers as if they were positive, then add the sign of the numbers.  Adding Integers having the same sign= Ex: -5+(-3)= Adding two integers having signs: Ex: -5+3 Take the difference of the numbers as if they were positive, then add the sign of the number having absolute value. Ex: -5+3=-2 Subtracting Integers Ex: -5-(-3) =-5+3 When we subtract, we ADD THE OPPOSITE Rule: 2-1 then turns into 2+(-1) It helps us to get the right answer, too, and less confusing. 4

 Dividing Integers   If a pair of integers has the same sign, then the answer will have a positive sign. You must calculate the absolute value of each integer and then divide the first integer by the second integer.   Example: -10 / -2 = ?   Step 1: |-10| / |-2| = 10 / 2  Step 2: 10 / 2 = 5  Step 3: Since integers have same sign, answer is  positive: +5   If a pair of integers have different signs, then the answer will be negative. You must calculate the absolute value of each integer and then divide the first integer by the second integer.   Example: -10 / +2 = ?   Step 1: |-10| / |+2| = 10 / 2  Step 2: 10 / 2 = 5  Step 3: Since integers have different signs, answer is negative: -5   Multiplying Integers   When multiplying two integers having the same sign, the product is always positive   Example 1: -2 · (-5) = 10  Example 2: 2 · 5 = 10   When having two integers with different signs, the product is always negative   Example 1: -2 · 5 = (-2)+(-2)+(-2)+(-2)+(-2) = -10  Example 2: 2 · (-5) = (-5)+(-5) = -10   When multiplying more than two integers   Example 1: (-1) · (-2) · (-3) = ?   Step 1: group the first two numbers and use rules I and II above to calculate the intermediate step   (-1) · (-2) = +2 (used rule I)   Step 2: use result from intermediate step 1 and multiply by the third number.   2 · (-3) = -6 (used rule II)  5

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Subtracting Integers Convert the problem to addition. Ex. 12-(-36) to remember to change the last number of the sequence from negative to positive or positive negative. Add or subtract the problem like a regular math problem. Ex =48. Ex 126-(-176) =302 or (-176)=(-50) or -126-(-176) =50 (note) when you add integers remember that when you add integers with the same sign the answer is going to be the same as the sign, but if the absolute value of the negative number is higher than the positive than the numbers going to be a negative. 7

When the number in the equation is positive you add the opposite to the number. Then you add the opposite to the answer. That way, the variable is alone on the left side of the equation in this example, and the difference of the answer and the opposite number is on the other. Example X+13=26 X+13+(-13)=26+(-13) 26+(-13)=13 13+(-13)=0 X= =26 When the number in the equation is negative then you convert the number to a positive. Then you change the operation to its opposite. After that, you add the opposite to the number. Then you add the opposite to the answer. That way, the variable is alone on the one side of the equal sign, and the difference of the answer and the opposite number is on the other. Example X-(-13)=13 X+13+(-13)=26+(-13) 26+(-13)=13 13+(-13)=0 X=13 13-(-13)=26 8

Distributive Property For Algebra 9

How to Solve Equations Step 1 A legal move (you have to do the same thing to both sides) is very simple. Step 2 What you are trying to do here is; you want to get the variable alone. All you have to do is add the opposite to the constant Example: X + 5 = 12 X (-5) = 12 + (-5) Once the constant is gone, you add the same number you added to the sum, then whatever you get from that equation, is what the variable equals Step 3 Example: X (-5) = 12 + (-5) X = 7 Created By: Jonah 10

By: Cameron When subtracting integers you “add the opposite”. Example: 12-8=4 12+(-8)=4  Rule When Subtracting Integers you add the opposite. Example: 10-(-4)= =14 Do you want to know how this works~ click to find out. 11

Just draw a number line if it helps you more. Also when you have a subtraction sign next to a parenthesis. You change the sign to addition and the negative number to a positive. Example: -10-(-4)= =14 Example2: -10-(4)= =14 12

HOW TO COMBINE LIKE TERMS A.K.A. SIMPLIFYING ALGEBRAIC EXPRESSIONS Step 1  Y You begin with an Algebraic Expression to simplify 3x+y+2x+7=? and find………………….. The Surprise Expression Step 2  B Before we simplify, find the terms, like terms, coefficients, and constants.  Terms --- The algebraic expression separated between each plus or minus sign Ex. 3x, y, 2x, 7  Like terms --- Terms that conduct the same variables Ex. 3x & 2x  Coefficients --- The numbers that are involved with a variable Ex. 3, 2, 1  Constants --- Terms without an variable Ex. 7 Step 3  Begin simplifying Hint The only like terms are 3x & 2x 3x+2x=5x Final answer 5x+y+7 Congrats you can now simplify algebraic expressions!!!!!!!! 13

Solving an algebraic equation!!!! You solve an algebraic equation by doing different sets of legal moves. You do a legal move by adding or subtracting and in some cases multiplication and dividing what you do to one side to the other until you cant do anymore moves. example: =Y By Lennon Dresnin