Class Presentation Math 1
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This document contains notes from a 7th grade math class covering topics like subtracting integers, multiplying integers, and solving algebraic equations. Key points covered include: when subtracting integers, you add the opposite; when multiplying integers with the same sign the product is positive, and with different signs the product is negative; and to solve equations, you perform the same operation to both sides until the variable is isolated on one side.
Class Presentation Math 1
- 1. Seventh Grade MathMath 21
- 2. By: ClaudiaSubtracting Integers Subtracting integers:2 – (-8) Rule When we subtract we ADD THE OPPISITE! (never change the first number!)2 + 8 is the same as 2 – (-8)…..So, the answer is the same, 10 -8 + 2 = -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. Vocab:Integers – the set of whole numbers and their opposites. Absolute Value – the distance the number is from zero on the number line. 2
- 3. How to Multiply IntegersWhen 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
- 4. 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)= -82. 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=-2Subtracting IntegersAdding IntegersEx: -5-(-3) =-5+3 When we subtract, we ADD THE OPPOSITERule: 2-1 then turns into 2+(-1) It helps us to get the right answer, too, and less confusing.4
- 5. Multiplying and Dividing IntegersDividing 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 = 5Step 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
- 6. AddingandSubtractingIntegersWhen adding Integers with the same sign add them as if they were positive then add the sign. Example:6 + 3 = 9 -6 + (-3) = -9When adding integers with different signs, subtract them as if they were positive and add the sign of the number with greatest absolute value. Example:-6 + 3 = -3 When subtracting any integer you add the opposite.Example:-6 – 3 = -9 Change to-6 + (-3) = -9Hannah6
- 7. Subtracting IntegersEx126-(-176) 126+176=302 or126-176126+(-176)=(-50) or-126-(-176)-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 ishigher than the positive thanthenumbers going to be anegative.Convert the problem to addition. Ex. 12-(-36) to 12+36. 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. 12+36=48.7
- 8. Solving EquationsWhen 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.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.ExampleX+13=26X+13+(-13)=26+(-13)26+(-13)=1313+(-13)=0X=1313+13=26ExampleX-(-13)=13X+13+(-13)=26+(-13)26+(-13)=1313+(-13)=0X=1313-(-13)=268
- 9. Distributive Property For Algebra Take both numbers in the parentheses and multiply them separately to the number outside of the parentheses, still using the sign in between both numbers in parentheses.Ex. 1 : 5(Y+9) turns into 5y+59 = 5Y+45Ex. 2 : 5(-Y+9) turns into 5(-Y)+59 = 5(- Y)+45Ex. 3: -5(Y-9) turnsinto -5Y-(-59) = -5Y - (-45)9
- 10. How to Solve EquationsCreated By:JonahStep 1A legal move (you have to do the same thing to both sides) is very simple.Step 2Step 3What 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 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 equalsExample:X + 5 = 12X + 5 + (-5) = 12 + (-5)Example:X + 5 + (-5) = 12 + (-5) X = 710
- 11. Subtracting IntegersBy: CameronWhen subtracting integers you “add the opposite”.
- 12. Example: 12-8=4 12+(-8)=4 RuleWhen Subtracting Integers you add the opposite.Example: 10-(-4)=14 10+4=14 Do you want to know how this works~ click to find out.11
- 13. 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 toa positive. Example2: -10-(4)=6-10+-4=14Example: -10-(-4)=1410+4=1412
- 14. HOW TO COMBINE LIKE TERMSA.K.A. SIMPLIFYING ALGEBRAIC EXPRESSIONS Congrats you can now simplify algebraic expressions!!!!!!!!Terms --- The algebraic expression separated between each plus or minus signEx. 3x, y, 2x, 7 Like terms --- Terms that conduct the same variablesEx. 3x & 2x Coefficients --- The numbers that are involved with a variable Ex. 3, 2, 1 Constants --- Terms without an variable Ex. 7Step 1Step 3HintThe only like terms are 3x & 2xYou begin with an Algebraic Expression to simplify
- 15. Begin simplifying 3x+y+2x+7=?Step 23x+2x=5xFinal answer5x+y+7The Surprise Expressionand find…………………..Before we simplify, find the terms, like terms, coefficients, and constants.13
- 16. 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: 3+4+-4=Y+4+-4+3By Lennon Dresnin
- 17. (-2)2 ≠ -22ExponentsExponentsThis is where your journey into Exponents beginsBy LoghanIn (-2)2 You can tell (-2) is the base because it is in parenthesis, In -22 there are no parenthesis. Because of that 2 is the base not -2. Another way of doing the problem would be 0-22. In 0-22 you would start off by doing 2 to the second power, which is 2 times 2. The answer would be 4. But after you do that the equation would be 0-4. 0-4=(-4). The answer is different than (-2)2. In (-2)2 you can tell the base is (-2) because there are parenthesis. There is no chance of it being -2 or minus two. Now all we need to find out is what negative 2 multiplied by itself is. When you multiply a negative by a negative what do you get? A positive! So when you multiply -1 by -1 you get 1! Positive 1. So when you multiply -2 by -2[In other words (-2)2] you get… By LoghanI hope you enjoyed your journey into Exponents 22=(-2)222=-22So this will sum everything up:(-2)2 = 4Does it work?It WorksOH NO IT DOESN’T WORK-22 = -4