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# Integers, roots, powers, order of operations

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### Integers, roots, powers, order of operations

1. 1. Nicknamed “Signed Numbers”INTEGERS
2. 2. What are Integers • Integers are positive and negative numbers and zero-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
3. 3. Comparing Integers• Each positive number has an opposite negative number.• Positive numbers are larger than negative numbers• To compare integers, a less than sign (<), a greater than sign (>) or an equal sign is used.  Think of an alligator.• Examples:  -5 < 2  9 > -3  -7 < -5 • You can think about it this way: if you spend \$7, you will have less money left over than if you spent only \$5.
4. 4. Absolute Value• Absolute Value is the distance an integer is from zero on a number line  The absolute value is always a positive• Expressed with bars on both sides of the number – Example: |5|=5 – Example: |-7|=7-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
5. 5. Absolute Value Check my work:1. |9|=92. |-3|= -33. |-2|=24. |25|= -25-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
6. 6. Why Learn Integers? Some word problems require integers.  At 8:00 a.m. it was 10 degrees below zero. By 3:00 p.m., the temperature had risen 35 degrees. What was the temperature at 3:00 p.m.?  -10 + 35 = +25 degrees above zero. Most importantly, Algebra requires knowing integers.
7. 7. Integer Rule Handout
8. 8. Multiplying and Dividing have thesame rules If SAME signs = Positive Answer +2 x +3 = +6 + + + -2 x - 3 = +6 - - If Different signs = Negative Answer +2 x-3 = -6 + - - - 2 x +3 = -6 - +
9. 9. Multiplying/Dividing - Practice1) 5 x -2 = -10 DIFFERENT signs2) 12 4 + 3 or 3 SAME signs3) 20 10 -2 DIFFERENT signs
10. 10. Multiplying/Dividing Tabe D. pg. 77
11. 11. Adding Integers Rule Add/Subtract Same signs = 1+3= 4 add numbers - 1 +-3 = - 4 Different signs = -3+4= 1 take the difference 3 +- 4 = -1 When adding, always keep sign of the largest absolute value
12. 12. Adding Integers - Practice1) 5 + 2- = 3 DIFFERENT signs Take the difference2) -12 + - 3 = - 15 SAME signs Add numbers3) -7 + 4 = -3 DIFFERENT signs Take the difference
13. 13. Adding Integers Tabe D. pg 75
14. 14. Subtracting Integers Rule Add/Subtract Change it! -1 - 3 = subtraction sign - 1 +3 = to plus sign Switch it! sign of 2nd number - 1 + -3 = Solve it! using adding rules - 1 +-3 = -4Another way to say this: Rewrite the subtraction problem as an additionproblem in which you add the opposite of the number being subtracted.
15. 15. Subtracting Integers - Practice
16. 16. Subtracting Integers Tabe. D. pg 76
17. 17. Assignment -- Integers IXL.com -- Integers Get a Smart Score of 100 on all of these! Level H. I.6 (Adding) I.8 (Subtracting) Level J. C.3 (Add/Subtract) C.7 (Mult/Division) Level H. X.3 (All Integers)
18. 18. INTEGER JEOPARDY
19. 19. Powers
20. 20. Properties of Powers
21. 21. Opposite Operations• Addition and Subtraction• Multiplication and Division• Exponents and …
22. 22. Square Roots
23. 23. Common Square Roots
24. 24. Order of Operations Please Excuse My Dear Aunt Sally1. Parenthesis (4-2)2. Exponent 4³[3.4. Multiply Divide 4(3) or 4x3 4÷2 or 4/2[5.6. Add Subtract 4+2 4-2
25. 25. Left to Right• 3x6÷2 – Multiply First 18 ÷2 =9 – Divide First 3x3=9• 4 – 5 +6 – Add First 4+1=5 – Subtract First -1 + 6 = 5
26. 26. (8-3)² =PE[MD[AS
27. 27. (6-4)² - 2 =PE[MD[AS
28. 28. (6x2)(8÷2)² =PE[MD[AS
29. 29. 50 ÷2+1²-3²=PE[MD[AS
30. 30. 3 x 4 + 6 ÷ 2 + 5 – 1=No Parenthesis- No ProblemE[MD[AS
31. 31. PEMDAS – Guided Practice 21) (2 + 1) - 7 = 2 22) 4 - (6 + 2) = 83) (8 x 2) + (7 x 3) = 374) 8 x 2 – 10 – 3 = 3 25) 24 ÷ 2 + 6 =12
32. 32. IXL.com• Order of Operations Practice – Level K. B. 2