1. Slide #1 Introduction to Signed Numbers

2. Slide #2 Introduction to Signed Numbers 1.Write positive and negative numbers used in everyday situations. 2.Graph signed numbers on a number line. 3.Use the symbols to compare integers. 4.Find the absolute value of integers. Objectives:

3. Slide #3 Introduction to Signed Numbers Negative Signs and Subtraction Signs NOTE To write a negative number, put a negative sign (a dash) in front of it: – 12. Notice that the negative sign looks exactly like the subtraction sign, as in 7 – 2 = 5. The negative sign and subtraction sign do not mean the same thing (more on that in the next section). To avoid confusion for now, we will write negative signs in red and put them up higher than subtraction signs. – 12 means negative 12 15 – 6 means 15 minus 6 Raised dashNot raised

4. Slide #4 Introduction to Signed Numbers EXAMPLE 1 Writing Positive and Negative Numbers (a)Andy improved his test score by 10 points. + 10 points or 10 points Write each positive number in two ways. Raised positive sign No sign (b)Lauren lost $20. – $20 Raised negative sign Write each negative number with a raised negative sign.

5. Slide #5 012345 -5-5 -4-4 -3-3 -2-2 -1 Negative numbersPositive numbers Zero is neither positive nor negative Introduction to Signed Numbers The Number Line

6. Slide #6 Introduction to Signed Numbers EXAMPLE 2 Graphing Numbers on a Number Line (a) – 3 (a) Graph each number on the number line. 012345 -5-5 -4-4 -3-3 -2-2 -1 (b) 4 1 2 4 (d) – (c) 1 2 2 (b)(c)(d)

7. Slide #7 Introduction to Signed Numbers Integers NOTE A list of integers can be written like this: …, – 3, – 2, – 1, 0, 1, 2, 3, … The dots show that the list goes on forever in both directions.

8. Slide #8 Introduction to Signed Numbers Relational (or Comparison) Operators NOTE Relational (or comparison) operators can be used to compare numbers. The < symbol is called the “less than” symbol, and the > symbol is called the “greater than” symbol.

9. Slide #9 Introduction to Signed Numbers Comparing Two Integers Using a Number Line Using the symbols, we can compare two integers. 012345 -5-5 -4-4 -3-3 -2-2 -1 – 1 is to the left of 4. – 1 is less than 4. Use < to mean “is less than.” – 1 < 4 – 1 is less than 4 4 is to the right of – 1. 4 is greater than – 1. Use > to mean “is greater than.” 4 > – 1 4 is greater than – 1

10. Slide #10 Introduction to Signed Numbers The “Less Than” and “Greater Than” Symbols NOTE One way to remember which symbol to use is that the “smaller end of the symbol” points to the “smaller number” (the number that is less). 3 – 2 Smaller number Smaller end of symbol Smaller number

11. Slide #11 Introduction to Signed Numbers EXAMPLE 3 Comparing Integers,Using the Symbols (a) 4 _____ 0 Write between each pair of numbers to make a true statement. (b) – 5 _____ 12 (c) – 7 _____ – 2 4 is to the right of 0 on the number line, so 4 is greater than 0. > – 5 is to the left of 12 on the number line, so – 5 is less than 12. – 7 is to the left of – 2 on the number line, so – 7 is less than – 2. < <

12. Slide #12 Introduction to Signed Numbers Absolute Value The absolute value of a number is its distance from 0 on the number line. Absolute value is indicated by two vertical bars. For example, | 3 | is read “the absolute value of 3.” Two vertical bars

13. Slide #13 Introduction to Signed Numbers EXAMPLE 4 Finding Absolute Values (a)| 5 | Find each absolute value. The distance from 0 to 5 on the number line is 5 spaces. So, | 5 | = 5. 012345 -5-5 -4-4 -3-3 -2-2 -1 5 spaces

14. Slide #14 Introduction to Signed Numbers EXAMPLE 4 Finding Absolute Values (b)| – 2 | Find each absolute value. The distance from 0 to – 2 on the number line is 2 spaces. So, | – 2 | = 2. 012345 -5-5 -4-4 -3-3 -2-2 -1 2 spaces