VC Ch 3 Notes

Algebra I Chapter 3 Mrs. Cataldo CLASS NOTES CHAPTER 3.1-3.7 3.1 The Integers Draw a number line and label with integers. Integers: whole numbers that are positive, ___________ and zero The sign, ___, can be used to show which number is greater than another. The large end always goes next to the __________ number. Any positive number is _________ than any negative number. Any number to the right of another number on the number line is ____________ than the first number. 8 _____0 -8 ______0 6 ____8 6 _____-1 -2 ____-5 -5____-3 The distance between two points on a number line is the difference between them. Lesson 3.2 An Expanded Coordinate Graph There are ________ quadrants on the coordinate graph. Label them. In quadrant I, x and y are both ________________. In quadrant _____, x is negative and y is positive. In quadrant III, x and y are both _______________. In quadrant _____, x is positive and y is negative. Example 1: Plot these points on a graph (attach graph paper). (6,3) (-2,5) (-1,-7) (4,-2) Example 2: Plot a graph of a function extending through all quadrants. Plot y = 4x + 1 Make a table: Plot the graph and extend into all x y quadrants (attach graph paper). -2 -1 0 1 2 3.3 Addition of Integers The opposite of a number is the integer you add to it to make a sum of ___. It is also called the ________________________ such that x + -x = 0 . The opposite of 2 is ____ since 2 + ____ = 0. What is the opposite of -2?___ There are two ways to think of adding positive and negative integers: a. Think of adding particles (positive numbers) to antiparticles (negative numbers) where the negative number cancels out the positive one. e.g. -2 + 1 = -1 oo + o = o b. Think of a number line. Adding 1 to -2 brings you to -1. A key strategy: Write all addition and subtraction problems as addition problems. eg. 2 – 4 = -2 should be written as 2 + -4 = -2 How should you write 6 – 3= 3? ________________ 3.4 Subtraction of Integers Example: 4-6 = ? First write as an addition problem. 4 + -6 = ? a. Use the particle drawing method to solve. oooo + oooooo = oo -2 -1 0 1 2 b. Use the number line method to solve. Start at 4, then go -6 to the left (left for negative, right for positive). Therefore, 4+ -6 = -2 NOTE: Two negatives next to each other make a positive. Example: 4 --6 = ? Write as an addition problem. 4 + -(-6) or 4 + 6 = 10 Write the following as addition problems: -5-6= __________________ -5 --6 =____________________ 3.5 Multiplication of Integers KEY CONCEPT: A negative • a positive = a negative A negative • a negative = a positive Make a chart at the top of your homework and tests: + -+ + ---+ -2 -1 0 1 2 3 4 If we graph the function y = 4x, we can see that this is true. Make a table: x y Draw a graph: 0 0 1 4 2 8 Extend the graph into the opposite quadrant. What does y equal if x = -2? _ If we graph the function y = -4x, we can see that a negative times a positive is a negative. X y Draw the graph and extend into the opposite quadrant to see 0 0 when x is neg, y is pos. and vice versa. 1 -4 2 -8 3.6 Division of Integers Simply ask the question, “What times the divisor is the dividend?” Example: -12 /4 = ? What times 4 is -12? You know that it has to be a negative number since a positive times a negative is a negative. So the answer would be -3. The quotient of a positive and a negative is always _________________. The quotient of two negative numbers is always ___________________. Practice: 6/-3 = ___ -10/-2 = _____ -24/8= ______ 3.7 Using Several Operations Remember: Please Excuse My Dear Aunt Sally, left to right Write as addition problems. Practice: 8 – 6(2) = (3-7) + 4= 8 – 6(-2) = (-4)² = 5(-4) – 10 = Velocity problems v(ft/sec) = 25 (ft/sec) – 32(ft/sec²) • t (sec) where v is the velocity of the ball being thrown up in the air and t is the time the ball is aloft. Draw a picture: For part of the trip, the velocity is positive. The ball is going up. For part of the trip the velocity is negative. The ball is falling. Example: When the ball is released, t = 0 sec. The velocity is 25 ft/sec upward (pos). At t = 1 sec, v = 25 ft/sec + -32 ft/sec² • (1sec) = -7 ft/sec, going down. What is the velocity and direction of the ball at t=0.5?