2. The set of all numbers that can be represented on a number line are called real numbers. You can use a number line to help you with addition and subtraction of real numbers. Addition To add a number, always move to the right. Subtraction To subtract a number, always move to the left. BUT: If adding or subtracting a NEGATIVE number, switch directions.

3. Add or subtract using a number line. –3 + 7 Start at 0. Move left to –3. To add 7, move right 7 units. -3 -2 01234 5 6 7 89 –3 +7 –3 + 7 = 4

4. Add or subtract using a number line. Start at 0. Move left to –4. 1110 98 7 654321 0 + (–7) –4 + (–7) = –11 To add –7, move left 7 units. –4 –4 + (–7)

5. Add or subtract using a number line. Start at 0. Move right to 3. To subtract –6, move right 6 units. -3-20123456 7 89 + 3 3 – (–6) = 9 3 – (–6) – ( – 6)

6. Add or subtract using a number line. –3 – 7 Start at 0. Move left to –3. To subtract 7, move left 7 units. –3–3 –7–7 11 10 987 6 54 3210 –3 – 7 = –10

7. Subtracting can be thought of as the “opposite of”. 5 – ( – 4) 5 − (–4) = 5 + 4 To subtract –4, add 4. (5 + 4 = 9)5 − 4 = 5 + 4 (– ) = 9

8. Add or subtract using a number line. –5 – (–6.5) Start at 0. Move left to –5. To subtract –6.5, move right 6.5 units. 87 65 43 210 –5 –5 – (–6.5) = 1.5 1 2 – ( – 6.5)

9. Another way to look at it: a) b) c) d) e) –2 – 9 6 – ( – 8) –5 + 8 7 + 12So, try some now: 1) 2) 3) 4) –13 – 4 10 – (-9) –11 + 6 2 +(-13) 5 - 14

10. When you multiply or divide two numbers, the signs of the numbers determine whether the result is positive or negative. NumbersProduct/Quotient Both positive One negative Both negative Positive Negative Positive Chapter 2.3 and 2.4 – Multiplying and Dividing Rational Numbers

12. Find the value of each expression. –5–5 A. 12 B. C.

13. a.) 4(-3y) – 15yb.) 13x + (-6)(4x) -12y – 15y -27y 13x + (-24x) -11x

14. Stock Market Example 500,000 (1.25) = $625,000 DROP!!

15. Two numbers are reciprocals if their product is 1. A number and its reciprocal are called multiplicative inverses. To divide by a number, you can multiply by its multiplicative inverse.

16. Example 2 Dividing by Fractions Evaluate the expression.

17. You can write the reciprocal of a number by switching the numerator and denominator. A number written without a denominator has a denominator of 1. Helpful Hint

18. Evaluate the expression

19. a.) b.) 3a + 2– 12x + 8

20. a. -8 + 13 b. 7 – 19 c. -12 – (-15) d. -10 + (-36) Lesson Review Simplify. e. f. g. h.

21.  2-2, 2-3 & 2-4 Study Guide/Skills Practice Worksheets (In-Class) Homework  Pages 823 – Lesson 2-2 Odds  Pages 823 – Lesson 2-3 Odds  Pages 824 – Lesson 2-4 Odds  Quiz on Sections 1-1, 1-2, 1-5, 2-2, 2-3, and 2-4 on Friday, September 18th!!!