1. Objective 2 Add and subtract integers © 2002 by R. Villar All Rights Reserved

2. Add and subtract integers How do you add using a number line? When you add a positive number… move to the right. When you add a negative number… move to the left.

3. Example: 3 + (–5) 1. Start at the first number.

4. Example: 3 + (–5) 1. Start at the first number.3

5. Example: 3 + (–5) 1. Start at the first number.3 2. Move the number of spaces and the direction of the second number.

6. Example: 3 + (–5) 1. Start at the first number.3 2. Move the number of spaces5 left and the direction of the second number.

7. Example: 3 + (–5) 1. Start at the first number.3 2. Move the number of spaces5 left and the direction of the second number. 3. The sum is the number you end at.

8. Example: 3 + (–5) 1. Start at the first number.3 2. Move the number of spaces5 left and the direction of the second number. 3. The sum is the number–2 you end at.

9. Example: –2 + 6 1. Start at the first number.

10. Example: –2 + 6 1. Start at the first number.–2

11. Example: –2 + 6 1. Start at the first number.–2 2. Move the number of spaces and the direction of the second number.

12. Example: –2 + 6 1. Start at the first number.–2 2. Move the number of spaces6 right and the direction of the second number.

13. Example: –2 + 6 1. Start at the first number.–2 2. Move the number of spaces6 right and the direction of the second number. 3. The sum is the number you end at.

14. Example: –2 + 6 1. Start at the first number.–2 2. Move the number of spaces6 right and the direction of the second number. 3. The sum is the number4 you end at.

15. Rules of Addition Sometimes, it’s not practical to use a number line to add. Here are some to add without a number line. Example –28 + (–22) Adding with the same sign: 1. add up the numbers (absolute value) 2. keep the sign –50 Ex. a. –10 + (–33) b. –6 + (–12) –43 –18

16. Example: 28 + (–22) Adding different signs: 1. Subtract the numbers. 2. Keep the dominant sign. 6 Ex. a. 24 + (–40) b. –12.1 + 3.8 –16 –8.3

17. Example: 8.1 + (–2.3) + (–1.5) + 4 Get all the positives together, get all the negatives together, then add. 12.1 + (–3.8) 8.3

18. Is this statement true? (1 + 2) + 3 = 1 + (2 + 3) Yes, changing the grouping (parentheses) does not change the sum. The property that allows this is called the... Associative Properties for addition: (a + b) + c = a + (b + c)

19. Subtraction of Real Numbers Adding the opposite of a number is the same as subtracting the number. Definition of subtraction: a – b = a + (–b) Example: 25 – 47 =25 + (–47) add the opposite Now, use the rules for addition = –22

20. Example: 7 – (–2) = 7 + 2 add the opposite = 9 Hint: When you have 2 negatives in a row, cross them both. Example: 2 – (–5) – 5 + 3 2 + 5 + (–5) + 3 add the opposite 7 + (–5) + 3 2 + 3 5