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# Algebra 1 chapter 2 notes

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### Algebra 1 chapter 2 notes

1. 1. Chapter 2 Notes Lesson 2.1 Lesson 2.4 Lesson 2.2 Lesson 2.5 Lesson 2.3 Lesson 2.6 Lesson 2.7
2. 2. 2.1 Adding Rational Numbers identity property of addition n+0=n additive inverse a when the opposite is added to a number the sum equals zero additive identity property a number plus its opposite equals zero x + (-x) = 0 adding numbers with same signs add numbers together the answer will have the same sign adding numbers with different signs subtract numbers; the answer will have the same sign as the larger number (not looking at sign)
3. 3. Examples -2 + (-6) -8 4 0 4 + (-8) 16 -9 + 9 9+7 The temperature falls 15 degrees and then rises 18 degrees. Use addition to find the change in temperature. Evaluate the expression n = -4 m=5 m+(-4) -n + 5 5 + (-4) = 1 -(-4)+5 = 9
4. 4. Matrix [ ] 4 6 Row 5 7 1 8 2 rows by 3 columns Column ] [ ] [ -2 5 4 -1 + 3 0 = 7 1 [ ] [ ] -2 + 4 5+(-1) = 2 4 7+3 1+0 10 1 End
5. 5. 2.2 Subtracting Rational numbers Subtracting numbers change the second number to its opposite and follow the addition rules Absolute value do all the operations inside the absolute value then take the positive of the answer
6. 6. Examples 2 - (-6) 4 - (-8) -4 - 5 9- 2 Evaluate: for n = -3 and m = 2 n-6 -m - 8
7. 7. Examples | -8 - 6| |6-2| ] [ ] [ -2 5 4 -1 7 1 - 3 0 [ ] [ ] -2 - 4 5-(-1) -6 6 = 7-3 1-0 4 1
8. 8. 2.3 Multiplying and Dividing Rational Numbers Identity Property of Multiplication n*1=n Multiplication Property of Zero n*0=0 Multiplication Property of -1 n * (-1) = -n Multiplying or Dividing Numbers with same sign Multiply or Divide numbers together; answer is POSITIVE Multiplying or Dividing Numbers with different signs Multiply or Dividing numbers together; answer is NEGATIVE
9. 9. Examples -5 * (-10) 7*8 -8 * 5 -50 2 -30 75 -3 25 Evaluate: for n = -2 and m = 8 8m -n2
10. 10. Matrix scalar multiplication ] [ ] [ 5(4) 5(-5) 5(-1) 5 4 -5 -1 = 5(3) 5(0) 5(-9) 3 0 -9 ] [ Pull 20 -25 -5 15 0 -45
11. 11. 2.4 The Distributive Property Distributive property a(b + c) = a(b) + a(c)
12. 12. Example 2(3 + 7) 2(3) + 2(7) 6 + 14 20 3(4x -9) 3(4x) - 3(9) 12x - 27 -(6n + 8) -1(6n + 8) -6n - 8
13. 13. Example Like Terms 5a2 - 9ab - 18 Constant coefficient 8x + 3(x + 4) 8x + 3x +12 11x + 12 End
14. 14. 2.5 Properties of numbers Commutative Property a+b=b+a a*b=b*a Associative Property (a + b) + c = a + (b + c) (a * b) * c = a * (b * c) Identity Property a+0=a a*1=a Inverse Property a + -a = 0 a * (1/a) = 1 Symmetric Property if a = b then b = a
15. 15. Distributive property a(b + c) = ab + ac a(b - c) = ab - ac Multiplication Property of Zero n*0=0 Mutliplication Property of -1 n * -1 = -n
16. 16. End
17. 17. 2.6 Theorectical and Experimental Probability Probability Favorable outcome total number of outcomes Outcome result of a single trial Sample Space all possible outcomes Event an outcome or group of outcomes Theoretical Probability how an event should turn out Compliment of an event the probability an event will not occur Experimental Probability how an event did turn out from a trial(s)
18. 18. Example P (green) = 1 5 = 20% P (Red) = 2 = 40% 5 P ( not red) = 3 = 60% 5 Red Pink Orange Blue
19. 19. 2.7 Probability of Compound events Independant Events events that do not effect each other P ( A and B) = P(A) * P(B) Dependant Event events that do effect each other P ( A and B) = P(A) * P(B after A) End
20. 20. You have a bag of marbles with 8 red marbles, 10 blue marbles, 7 yellow, and 5 black marbles. What are the following probabilities WITHOUT replacement? P( yellow and black) P(2 reds) P(purple) What are the following probabilities with replacement? P( yellow and black) P(2 reds) P(purple)