Teachers: Kalis, Teixeira, Tober Course: Algebra Readiness Periods: all Assignment: Week 3 Integer Review Chapter 5 Integers INTEGERS In elementary school, you learned to use whole numbers. Whole numbers = { 0, 1, 2, 3, 4, 5 . .} For most things in life, whole numbers are all we need to use. However, when a checking account falls below zero or the temperature falls below zero, we need a way to express that. Mathematicians have decided that a negative sign, which looks exactly like a subtraction sign, would be used in front of a number to show that the number is below zero. All the negative whole numbers and positive whole numbers plus zero make up the set of integers. Integers = { -4, -3, -2, -1, 0, 1, 2, 3, 4 ...} ABSOLUTE VALUE The absolute value of a number is the distance the number is from zero on the numberline. -6 -5 -4 -3 2 1 0 1 2 3 4 5 6 The absolute value of 6 iswritten] 6]. 16]=6 The absolute value of -6 is written ] -6 ]. 1-61=6 Both 6 and -6 are the same distance, 6 spaces, from zero So their absolute value is the same, 6. EXAMPLES: 1-41=4 -1-41=-4 1-91+5=9+5=14 191-181=9-8=1 161-1-61=6-6=0 1-51+1-21=5+2=7 Simplify the following absolute value problems. 1. 191= 6. 1-2]= 11. 1-21+161= 2. -151= 7. -1-3]= 12. 1101+18]=. 3. 1-25= 8. 1-41-131= 13. 1-21+141= 4. -1-121= 9. 1-81-1-41= 14. 1-31+1-41= 5. -1641= 10. 151+1-4]= 15. 171-1-51= 73 ADDING INTEGERS First, we will see how to add integers on the number line; then, we will learn rules for working the problems without using a number line. EXAMPLE 1: Add: (-3) + 7 Step 1: The first integer in the problem tells us where to start. Find the first integer, -3, on the number line. -3 Step 2: (-3) + 7 The second integer in the problem, +7, tells us the direction to go, positive (toward positive numbers), andhow far, 7 places. (-3) +7=4 EXAMPLE 2: Add: (-2) + (-3) Step 1: Find the first integer, (-2), on the number line. Step 2: (-2) + (-3) The second integer in the problem, (-3), tells us the direction to go, negative (toward the negative numbers), and how far, 3 places. (-2) + (-3) = (-5) Solve the problems below using this number line. 1. 2 + (-3) = 9. 3 + (-7)= 17. (-2) + 6 = 2. 4 + (-2) = 10. (-2) + (-2)= 18. (-4) + 8 = 3. (-3) + 7 = 11. 6 + (-7) = 19. (-7) +4= 4. (-4) +4 = 12. 2 + (-5)= 20. (-5) + 8 = 5. (-1) + 5 = 13. (-5) +3 = 21. - (-2) = 6. (-1) + (-4) = 14. (-6)+7= 22. 8+ (-6) = 7. 3 + 2 = 15. (-3) + (-3) = 23. 5 + (-3) = 8. (-5) + 8 = 16. (-8) + 6= 24. + (-8)= 74 SUBTRACTING INTEGERS The easiest way to subtract integers is to changethe problem to an addition problem and follow the rules you already know. RULES FOR SUBTRACTING INTEGERS 1. Change the subtraction sign to addition. 2. Changethe sign of the second number to the opposite sign. EXAMPLE 1: -6 - (-2) = Change the subtraction sign to addition and -2 to 2. -6-(-2)=(-6+2 (-6)+2= (-4) EXAMPLE 2: 5 - 6 = Change the subtraction sign to addition and 6 to -6. 5-6=5 + (-6) 5 + (-6)=(-1) Solve the problems usingthe rules above. 1. (-3) - 8= 7. (-5) - (-13) = 13. (-7) -4= 2. 5 - (-9) = 8. 6- (-7)= 14. 1- (-9) = 3. 8- (-5) = 9. 8- (-6)= 15. (-5) - 12 = 4. (-2) - (-6) = 10. (-2) - (-2) = 16. (-1) -9= 5. 8 - (-9) = 11. (-3)-7= 17. 6- (-7) = 6. (-4) - (-1)= 12. (4) - 8 = 18. (-8) - (-12) = Solve the addition and subtraction problems below. 19. 4- (-2) = 27. (-5) + 3 = 35. 30 + (-15) = 20. (-3) +7= 28. (-6) + 7 = 36. -40 - (-5) = 21. (-4) + 14 = 29. (-4) + 8 = 37. 25 - 50 = 22. (-1) - 5 = 30. (-4) - 11 = 38. -13 + 12= 23. (-1) + (-4) = 31. (-5) + 8 = 39. (-21) - (-1) = 24. (-12) + (-2) = 32. 2- (-2) = 40. 62 - (-3) = 25. 0 - (-6) = 33. (-8) +9 = 41. (-16) + (-2) = 26. 2 - (-5) = 34. 0 + (-10) = 42. (-25) + 5 = 77 MULTIPLYING INTEGERS You are probably used to seeing multiplication written with a "X" sign, but multiplication can be written two other ways. A "4" between numbers means the same as "X", and parentheses () around a number without a "X33 or a "t." also means to multiply. EXAMPLES: 2 X 3 = 6 or 2 •3 = 6 or (2)(3) = 6 All of these mean the same thing, multiply. DIVIDING INTEGERS Division is commonly indicated two ways: with a "4" or in the form of a fraction. EXAMPLES: 6 + 3 = 2 means the same thing as 5 =2 RULES FOR MULTIPLYING AND DIVIDING INTEGERS If the numbers have the same sign, the answer is positive. 2. If the numbers have different signs, the answer is negative. EXAMPLES: 6 X 8 = 48 (-6) X 8 = (-48) (-6) X (-8) = 48 48 + 6 = 8 (-48) + 6 = (-8) (-48) + (-6) = 8 Solve the problems below using the rules of adding integers with opposite signs. 1. (-4) + 2 = 8. 2 (-5) = 15. (-5) x 8 = 2. 12 (-3) = 9. 3 X (-7) = 16. -12 (-14) 3. 10. (-2) (-12) • (-2) = _ 17. 8 (-4) = (-18) 4. -15 + 3 = 11. (-6) 18. 1 • (-8) = 5. (-3) x (-7) = 12. 21 + (-7) = 19. (-7) • (-4) = 6. (-1) • (5) = 13. -5 X 3 = 20. (-2) + (-2) = 7. -1 X 18 (-4) = 14. (-6) (7) = 21. (-6) 78.