Integers The Number Line Number Lines 10 5

Integers & The Number Line

Number Lines -10 -5 0 5 • A number line is a line with marks on it that are placed at equal distances apart. • One mark on the number line is usually labeled zero and then each successive mark to the left or to the right of the zero represents a particular unit such as 1 or ½. • On the number line above, each small mark represents ½ unit and the larger marks represent 1 unit. 10

Number Lines -10 -5 0 5 Number lines can be used to represent: A. Whole numbers – the set {0, 1, 2, 3, …} B. Positive numbers – any number that is greater than zero C. Negative numbers – any number that is less than zero D. Integers – the set of numbers represented as {…, -3, -2, -1, 0, 1, 2, 3, …} The arrows at the ends of the number line show that the number line continues in both directions without ending. 10

Graphing on Number Lines -5 -10 0 5 A number can be graphed on a number line by placing a point at the appropriate position on the number line. Example a) {4} b) {integers between – 10 and – 5} (blue point) (purple) 10

Graphing on Number Lines -10 -5 0 5 • Name the set of numbers that is graphed. {-8, -4, 1, 5, 8} 10

Moving on Number Lines -10 -5 0 5 • Movement to the right on the number line is in the positive direction (increasing). Do this to add a positive #. • Movement to the left on the number line is in the negative direction (decreasing). Do this to add a negative #. • Make the following moves on the number line. Start at 5 and move left 7 integers. • Where did you stop? -2 How can we represent this mathematically? 5 + (-7) = -2 10

You Try It! 1) Graph these pairs of numbers on a number line. Write two inequalities comparing the two numbers. a) -2, 7 b) -9, -4 c) 3, 8 2) Find each sum using a number line. Place the 1 st # on a # line, then move to the right or left. a) 3 + 7 b) -1 + (-7) c) -4 + 12 d) -9 + 5 e) -6 + 6

Problems 1 & 2 -10 -5 0 5 10

Problems 3 & 4 -5 -10 0 5 10 Show 3 + 7 using the number line. Start at 3 and move 7 places to the right. 3 + 7 = 10 -5 0 Show -1 +(-7) using a number line. Start at -1 and move 7 places to the left. -1 + (-7) = -8

Problems 5 & 6 -5 -10 0 5 10 Show – 9 + 5 using the number line. Start at – 9 and move 5 places to the right. – 9 + 5 = – 4 -5 -10 0 Show -6 + 6 using a number line. Start at -6 and move 6 places to the left. -6 + 6 = 0