1. BELL RINGER Four 4’s Order of Operations Use what you know about the order of operations to insert the correct symbol in each blank to make the statement true. You may use +, -, x, ÷, and parentheses ( ) to fill in the blanks. 1.4444=1 2.4444=12 3.4444=3

2. THE NUMBER LINE Integers = {…, -2, -1, 0, 1, 2, …} Whole Numbers = {0, 1, 2, …} Natural Numbers = {1, 2, 3, …} -505

3. TO GRAPH A SET OF NUMBERS MEANS TO LOCATE AND MARK THE POINTS ON THE NUMBER LINE. Graph {-1, 0, 2}. Be sure to put the dots on the line - not above or below. 05 -5

4. EXAMPLES: USE THE NUMBER LINE IF NECESSARY. 4 2) (-1) + (-3) = -4 3) 5 + (-7) = -2 1) (-4) + 8 =

5. REAL NUMBERS: 1-5: ADDING & SUBTRACTING 1-6: MULTIPLYING & DIVIDING I CAN FIND THE SUM & DIFFERENCE OF REAL NUMBERS. I CAN FIND THE PRODUCT AND DIFFERENCE OF REAL NUMBERS. Ms. K.M. Showers August 23, 2015

6. ABSOLUTE VALUE of a number is the distance from zero. Distance can NEVER be negative! The symbol is |a|, where a is any number.

7. ABSOLUTE VALUE

8. Examples  7  = 7 10 100  10  =  -100  =  5 - 8  =  -3  = 3

9. ADDITION RULE: SAME SIGN 1) When the signs are the same, ADD and keep the sign. (-2) + (-4) = -6 2 + 4 = 6

10. ADDITION RULE: DIFFERENT SIGN 2) When the signs are different, SUBTRACT and use the sign of the larger number. (-2) + 4 = 2 2 + (-4) = -2

11. EVALUATE -16 + (-18) = -11 + 9 = 9 + (-11) = -6 + (-2) =

12. INVERSE PROPERTY OF ADDITION For every real number, a, there is an additive inverse (-a) such that a + (-a) = (-a) + a = 0

13. INVERSE PROPERTY OF ADDITION The additive inverses (or opposites) of two numbers add to equal zero. Opposites are two numbers that are the same distance from zero on the number line. (-3) & 3 are opposites

14. -3 Proof: 3 + (-3) = 0 We will use the additive inverses for subtraction problems. Example: The additive inverse of 3 is

15. INVERSE PROPERTY OF ADDITION 14 + (-14) = (-14) + 14 =

16. SUBTRACTING REAL NUMBERS To subtract a real number, add its opposite. a – b = a + (-b) 3 – 5 = 3 + (-5) = -2 3 – (-5) = 3 + 5 = 8

17. SOLVE 4.8 – (-8.7) = 3.5 – 12.4 =

18. 1-6: MULTIPLYING REAL NUMBERS The product of two real numbers with different signs is negative. (2) (-3) = -6 (-2) (3) = -6

19. 1-6: MULTIPLYING REAL NUMBERS The product of two real numbers with the same signs is positive. (2) (3) = 6 (-2) (-3) = 6

20. 1-6: DIVIDING REAL NUMBERS The quotient of two real numbers with different signs is negative. -20 ÷ 5 = -4 20 ÷ 5 = -4

21. 1-6: DIVIDING REAL NUMBERS The quotient of two real numbers with the same signs is positive. 20 ÷ 5 = 4 -20 ÷ (-5) = -4

22. DIVISION INVOLVING ZERO The quotient of zero & any real number is zero. The quotient of any real number & zero is undefined. 0 ÷ 8 = 0 8 ÷ 0 = undefined

23. RECIPROCAL The reciprocal of a non-zero real number of the form a/b = b/a.  12/a reciprocal is a/12.  4 reciprocal is ¼.

24. RECIPROCAL The product of a number and its reciprocal is 1. The reciprocal of a number is called its multiplicative inverse.

25. INVERSE PROPERTY OF MULTIPLICATION For every non-zero real number, a, there is a multiplicative inverse (1/a). a (1/a) = 1 -4 (-1/4) = 1

26. DIVIDING FRACTIONS When dividing fractions, you have to multiply the second term by its reciprocal.

27. HERE’S WHY: To get the fraction ½ out of the denominator, we must multiply by its reciprocal (2/1) or its multiplicative inverse. Remember: whatever you do to the denominator, you must also do to the numerator! This leaves you with 1 in the denominator & (4/5)(2/1) in the numerator.

28. NEGATIVE SQUARE ROOTS Negative square roots are represented by - √

29. B -√25 = -5 because (-5) (-5) = 25

30. POSITIVE/NEGATIVE SYMBOL NOTE: Every positive real number has both a positive & negative square root.