2.1. Graphing Integers on a Number Line

Transcription

1 Ch 2 Integers

2 2.1 Graphing Integers on a Number Line

3 Integers Number Line A line with equal distances marked off to represent numbers

4 Integers Positive Number A number greater than zero Negative Number A number less than zero Zero is neither positive or negative

5 Integers

6 Venn Diagram of Numbers Venn Diagram A diagram that uses circles to show relationships among sets of numbers or objects

7 Venn Diagram of Numbers Natural Numbers 1, 2, 3, 4 Whole Numbers 0, 1, 2, 3 Integers -3, -2, -1, 0, 1, 2, 3

8 Graphing on a Number Line To graph a set of integers, Locate number on number line Place dot ON THE number line Label point above number line Coordinate The number that corresponds to the point

9 Example Name the coordinates of G, H, and J. Graph points K, L, and M on a number line if K has coordinate -4, L has coordinate 2, and M has coordinate -1.

10 Example Name the coordinate of A, B, and C. Graph points X, Y, and Z on a number line if X has coordinate 4, Y has coordinate 0, and Z has coordinate -3.

11 Numbers on the Number Line Numbers increase as they go to the Right So numbers on the right are larger than numbers on the left Or greater than

12 Examples Replace each with < or > to make a true sentence

13 Absolute Value Distance is always positive

14 Example

15 Assignment 1 st Assignment due today P55: nd Assignment due next time P55: 18 26, 30 47, 49, 52, 54 60

16 2.2 The Coordinate Plane

17 Coordinate System Coordinate System Formed by the intersection of two number lines that meet at right angles at their zero points

18 Coordinate System Coordinate Plane The plane that contains the x- and y-axes X-axis The horizontal number line Y-axis The vertical number line Origin The point at which the number lines intersect

19 Ordered Pair Ordered Pair The coordinates of any point on a coordinate plane X-coordinate The first number in an ordered pair Corresponds to a number on the x-axis Y-coordinate The second number in an ordered pair Corresponds to a number on the y-axis Always in parentheses with a comma between the coordinates

20 Ordered Pair (3, 5)

21 Example Write the ordered pair that names each point.

22 Example Graph each ordered pair on the coordinate plane. V(2, 4) W(-4, -1) R(2, -4) S(-1, 4) T(0, -3)

23 Quadrants Each coordinate plane is separated into four regions, called quadrants Named with roman numerals The axes are not in the quadrants

24 Example Name the quadrants in which each point is located. C(-2, -7) D(-4, 9) E(0, -3) F(1, 0) G(3, -1)

25 Example The first zeppelin flown in 1900 flew at a speed of 18 mph. Let x represent the number of hours. Then 18x represents the total distance traveled in x hours. Evaluate the expression to find the distances traveled in 1, 2, and 3 hours. Then graph the ordered pairs (time, distance).

26 Assignments 1 st Assignment due today P61: nd Assignment due next time P62: 23 29, 31 33, Worksheet

27 2.3 Adding Integers

28 Think number line Adding Integers

29 Adding Integers with the Same Sign

30 Example (-8) (-4)

31 Adding Integers Zero Pair Two numbers that cancel each other when added together Ex: Opposite or Additive Inverses Zero pairs Ex:

32 Adding Integers

33 Examples (-8)

34 Example Traci opened a checking account with a deposit of $100. During the next week, she wrote checks for $45 and $65 and made a deposit of $28. Find the balance in her account.

35 Example Simplify: -7y + 6y -8y + 3y 6m + 4m + (-2m)

36 Assignment 1 st Assignment due today P68: 2, nd Assignment due next time P68: even, 57 60, 63 73

37 2.4 Subtracting Integers

38 Think number line

39 Subtracting Integers

40 Examples (-6) (-5)

41 Examples (-10) 5 (-1) -4 6

42 Examples -7 (-2) (-11) 9 3

43 Example Evaluate a b if a = -8 and b = -2. Evaluate m n if m = 5 and n = -3. Evaluate w x + y - z if w = -5, x = -7, y = 10 and z = -5.

44 Example During one school year, 23 new students moved into a school district and 52 students moved out of the school district. Find the change in the number of students resulting from these moves.

45 Assignment 1 st Assignment due today P73: nd Assignment due next time P73: 33 48, P694 (2-2): 1 16 Worksheet(s)

46 2.5 Multiplying Integers

47 Multiplying Integers

48 Example Find each product 4(-3) -2(7) -7(7) 10(-3) 15(-3) 10(4) -8(-6)

49 Find each product 7(-3)(-6) Example 4(-5)(-12)(-5) -2(-3)(4) (-1)(-5)(-2)(-3)

50 Example Evaluate 4ab if a = -3 and b = -5. Evaluate -5n if n = -7. Evaluate 2xy if x = -4 and y = -2.

51 Example Simplify (4m)(-7n). Simplify (2a)(-5b). Simplify 12(-3z).

52 Example The graphs of A(3, 5), B(-2, 4), and C(0, 1) are connected with line segments to form a triangle. Multiply each y-coordinate by -1 and redraw the triangle. Describe how the position of the triangle changed.

53 Assignment 1 st Assignment due today P77: nd Assignment due next time P78: 14 46, 49, Need graph paper for both!

54 2.6 Dividing Integers

55 Dividing Integers

56 Summary of Multiplying/Dividing X = X = = =

57 Examples (-10) (-4) 16 (-2)

58 Examples Evaluate (6x) y if x = -4 and y = 8. Evaluate -12 x if x = -3.

59 Example In the last 5 years at a high school, the number of students with no tardies during the entire school year dropped from 315 to 95. What was the average change in the number of students without a tardy for each of those 5 years?

60 Assignment 1 st Assignment due today P84: nd Assignment due next time P84: 13 42, 47 57