1 signed numbers 125s
- 2. Signed Numbers We track the “directions” of measurements by giving them positive (+) or negative (-) sign.
- 3. Signed Numbers We track the “directions” of measurements by giving them positive (+) or negative (-) sign. Signed measurements represent amounts of increases versus decreases, surpluses versus deficiencies, credits versus debits and so on.
- 4. Signed Numbers We track the “directions” of measurements by giving them positive (+) or negative (-) sign. Signed measurements represent amounts of increases versus decreases, surpluses versus deficiencies, credits versus debits and so on. Numbers with signs are called signed numbers.
- 5. Signed Numbers Example A. a. We deposited $400 into a bank account then withdrew $350 from the account, write the transactions using signed numbers. How much is left in the account? We track the “directions” of measurements by giving them positive (+) or negative (-) sign. Signed measurements represent amounts of increases versus decreases, surpluses versus deficiencies, credits versus debits and so on. Numbers with signs are called signed numbers.
- 6. Signed Numbers Example A. a. We deposited $400 into a bank account then withdrew $350 from the account, write the transactions using signed numbers. How much is left in the account? Using “+” for deposit or having surplus in the account and “–” for withdraw or debit from the account, the transactions may be listed as: +400, –350. (In this section we will use red color for negative numbers for emphasis.) We track the “directions” of measurements by giving them positive (+) or negative (-) sign. Signed measurements represent amounts of increases versus decreases, surpluses versus deficiencies, credits versus debits and so on. Numbers with signs are called signed numbers.
- 7. Signed Numbers Example A. a. We deposited $400 into a bank account then withdrew $350 from the account, write the transactions using signed numbers. How much is left in the account? Using “+” for deposit or having surplus in the account and “–” for withdraw or debit from the account, the transactions may be listed as: +400, –350. (In this section we will use red color for negative numbers for emphasis.) The balance of the account is a surplus of $50 or +50. We track the “directions” of measurements by giving them positive (+) or negative (-) sign. Signed measurements represent amounts of increases versus decreases, surpluses versus deficiencies, credits versus debits and so on. Numbers with signs are called signed numbers.
- 8. Signed Numbers Example A. a. We deposited $400 into a bank account then withdrew $350 from the account, write the transactions using signed numbers. How much is left in the account? Using “+” for deposit or having surplus in the account and “–” for withdraw or debit from the account, the transactions may be listed as: +400, –350. (In this section we will use red color for negative numbers for emphasis.) The balance of the account is a surplus of $50 or +50. We write the entire transactions as +400 – 350 = +50. We track the “directions” of measurements by giving them positive (+) or negative (-) sign. Signed measurements represent amounts of increases versus decreases, surpluses versus deficiencies, credits versus debits and so on. Numbers with signs are called signed numbers.
- 9. Signed Numbers b. We deposited $400 into the account then withdrew $600 from the account, write the transactions using signed numbers. How much is left in the account?
- 10. Signed Numbers b. We deposited $400 into the account then withdrew $600 from the account, write the transactions using signed numbers. How much is left in the account? The transactions may be listed as: +400, –600.
- 11. Signed Numbers b. We deposited $400 into the account then withdrew $600 from the account, write the transactions using signed numbers. How much is left in the account? The transactions may be listed as: +400, –600. The account is short by $200.
- 12. Signed Numbers b. We deposited $400 into the account then withdrew $600 from the account, write the transactions using signed numbers. How much is left in the account? The transactions may be listed as: +400, –600. The account is short by $200. This is a deficiency so its –200.
- 13. Signed Numbers b. We deposited $400 into the account then withdrew $600 from the account, write the transactions using signed numbers. How much is left in the account? The transactions may be listed as: +400, –600. The account is short by $200. This is a deficiency so its –200. We write the entire transactions as +400 – 600 = –200
- 14. Signed Numbers b. We deposited $400 into the account then withdrew $600 from the account, write the transactions using signed numbers. How much is left in the account? The transactions may be listed as: +400, –600. The account is short by $200. This is a deficiency so its –200. We write the entire transactions as +400 – 600 = –200 c. We deposited $400 in a bank account, later deposited another $200, then withdrew $350, then deposited $250, then withdrew $600, make a list of the transactions using signed numbers. How much is left?
- 15. Signed Numbers b. We deposited $400 into the account then withdrew $600 from the account, write the transactions using signed numbers. How much is left in the account? The transactions may be listed as: +400, –600. The account is short by $200. This is a deficiency so its –200. We write the entire transactions as +400 – 600 = –200 c. We deposited $400 in a bank account, later deposited another $200, then withdrew $350, then deposited $250, then withdrew $600, make a list of the transactions using signed numbers. How much is left? The transactions are listed as +400, +200, –350, +250, –600.
- 16. Signed Numbers b. We deposited $400 into the account then withdrew $600 from the account, write the transactions using signed numbers. How much is left in the account? The transactions may be listed as: +400, –600. The account is short by $200. This is a deficiency so its –200. We write the entire transactions as +400 – 600 = –200 c. We deposited $400 in a bank account, later deposited another $200, then withdrew $350, then deposited $250, then withdrew $600, make a list of the transactions using signed numbers. How much is left? The transactions are listed as +400, +200, –350, +250, –600. To find the final balance in the account, we note that the total of the deposits is +850
- 17. Signed Numbers b. We deposited $400 into the account then withdrew $600 from the account, write the transactions using signed numbers. How much is left in the account? The transactions may be listed as: +400, –600. The account is short by $200. This is a deficiency so its –200. We write the entire transactions as +400 – 600 = –200 c. We deposited $400 in a bank account, later deposited another $200, then withdrew $350, then deposited $250, then withdrew $600, make a list of the transactions using signed numbers. How much is left? The transactions are listed as +400, +200, –350, +250, –600. To find the final balance in the account, we note that the total of the deposits is +850 and the total of the withdrawals is –950,
- 18. Signed Numbers b. We deposited $400 into the account then withdrew $600 from the account, write the transactions using signed numbers. How much is left in the account? The transactions may be listed as: +400, –600. The account is short by $200. This is a deficiency so its –200. We write the entire transactions as +400 – 600 = –200 c. We deposited $400 in a bank account, later deposited another $200, then withdrew $350, then deposited $250, then withdrew $600, make a list of the transactions using signed numbers. How much is left? The transactions are listed as +400, +200, –350, +250, –600. To find the final balance in the account, we note that the total of the deposits is +850 and the total of the withdrawals is –950, so the account is short of $100, or there is “–100” left in the account.
- 19. Signed Numbers b. We deposited $400 into the account then withdrew $600 from the account, write the transactions using signed numbers. How much is left in the account? The transactions may be listed as: +400, –600. The account is short by $200. This is a deficiency so its –200. We write the entire transactions as +400 – 600 = –200 c. We deposited $400 in a bank account, later deposited another $200, then withdrew $350, then deposited $250, then withdrew $600, make a list of the transactions using signed numbers. How much is left? The transactions are listed as +400, +200, –350, +250, –600. To find the final balance in the account, we note that the total of the deposits is +850 and the total of the withdrawals is –950, so the account is short of $100, or there is “–100” left in the account. We write these transactions as +400 + 200 – 350 + 250 – 600 = –100.
- 20. Signed Numbers The above operation of totaling two or more signed numbers into a single signed number is called the combining operation.
- 21. Signed Numbers Example B. +100 + 200 = +300, The above operation of totaling two or more signed numbers into a single signed number is called the combining operation.
- 22. Signed Numbers Example B. +100 + 200 = +300, –100 – 200 = –300 The above operation of totaling two or more signed numbers into a single signed number is called the combining operation.
- 23. Signed Numbers Example B. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, The above operation of totaling two or more signed numbers into a single signed number is called the combining operation.
- 24. Signed Numbers Example B. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 The above operation of totaling two or more signed numbers into a single signed number is called the combining operation.
- 25. The above operation of totaling two or more signed numbers into a single signed number is called the combining operation. Signed Numbers Example B. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 A number written without a sign is treated as a positive number.
- 26. Signed Numbers Example B. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 A number written without a sign is treated as a positive number. Therefore, 100 + 200 is the same as +100 + 200 and both combined to 300. The above operation of totaling two or more signed numbers into a single signed number is called the combining operation.
- 27. Signed Numbers Example B. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 A number written without a sign is treated as a positive number. Therefore, 100 + 200 is the same as +100 + 200 and both combined to 300. In order to state precisely the rules for combining signed numbers, we introduce the notion of absolute values. The above operation of totaling two or more signed numbers into a single signed number is called the combining operation.
- 28. Signed Numbers Example B. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 A number written without a sign is treated as a positive number. Therefore, 100 + 200 is the same as +100 + 200 and both combined to 300. In order to state precisely the rules for combining signed numbers, we introduce the notion of absolute values. In example A of the bank account, if we are only interested in the amount of the transactions but not the type of transactions, this amount is called the absolute value. The above operation of totaling two or more signed numbers into a single signed number is called the combining operation.
- 29. Signed Numbers Example B. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 A number written without a sign is treated as a positive number. Therefore, 100 + 200 is the same as +100 + 200 and both combined to 300. In order to state precisely the rules for combining signed numbers, we introduce the notion of absolute values. In example A of the bank account, if we are only interested in the amount of the transactions but not the type of transactions, this amount is called the absolute value. The absolute value of a number x is written as |x|. The above operation of totaling two or more signed numbers into a single signed number is called the combining operation.
- 30. Signed Numbers Example B. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 A number written without a sign is treated as a positive number. Therefore, 100 + 200 is the same as +100 + 200 and both combined to 300. In order to state precisely the rules for combining signed numbers, we introduce the notion of absolute values. In example A of the bank account, if we are only interested in the amount of the transactions but not the type of transactions, this amount is called the absolute value. The absolute value of a number x is written as |x|. Hence, |500| = 500, The above operation of totaling two or more signed numbers into a single signed number is called the combining operation.
- 31. Signed Numbers Example B. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 A number written without a sign is treated as a positive number. Therefore, 100 + 200 is the same as +100 + 200 and both combined to 300. In order to state precisely the rules for combining signed numbers, we introduce the notion of absolute values. In example A of the bank account, if we are only interested in the amount of the transactions but not the type of transactions, this amount is called the absolute value. The absolute value of a number x is written as |x|. Hence, |500| = 500, |-350| = 350, The above operation of totaling two or more signed numbers into a single signed number is called the combining operation.
- 32. Signed Numbers Example B. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 A number written without a sign is treated as a positive number. Therefore, 100 + 200 is the same as +100 + 200 and both combined to 300. In order to state precisely the rules for combining signed numbers, we introduce the notion of absolute values. In example A of the bank account, if we are only interested in the amount of the transactions but not the type of transactions, this amount is called the absolute value. The absolute value of a number x is written as |x|. Hence, |500| = 500, |–350| = 350, |–600| = 600, etc.. The above operation of totaling two or more signed numbers into a single signed number is called the combining operation.
- 33. Signed Numbers Rules for Combining Signed Numbers
- 34. Signed Numbers Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, +100 + 200 = +300, –100 – 200 = –300
- 35. Signed Numbers Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300
- 36. Signed Numbers Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300
- 37. Signed Numbers Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300
- 38. Signed Numbers Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 II. To combine two numbers of different signs,
- 39. Signed Numbers Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 II. To combine two numbers of different signs, keep the sign of the number with larger absolute value, take the difference of the absolute values of the numbers.
- 40. Signed Numbers Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 II. To combine two numbers of different signs, keep the sign of the number with larger absolute value, take the difference of the absolute values of the numbers.
- 41. Signed Numbers Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 II. To combine two numbers of different signs, keep the sign of the number with larger absolute value, take the difference of the absolute values of the numbers.
- 42. Signed Numbers Example C. 8 – 9 + 11 There are different ways to combine multiple signed numbers. We may combine them from left to right. Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 II. To combine two numbers of different signs, keep the sign of the number with larger absolute value, take the difference of the absolute values of the numbers.
- 43. Signed Numbers Example C. 8 – 9 + 11 = –1 + 11 There are different ways to combine multiple signed numbers. We may combine them from left to right. Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 II. To combine two numbers of different signs, keep the sign of the number with larger absolute value, take the difference of the absolute values of the numbers.
- 44. Signed Numbers Example C. 8 – 9 + 11 = –1 + 11 = 10 There are different ways to combine multiple signed numbers. We may combine them from left to right. Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 II. To combine two numbers of different signs, keep the sign of the number with larger absolute value, take the difference of the absolute values of the numbers.
- 45. Signed Numbers Example C. 8 – 9 + 11 = –1 + 11 = 10 To combine many numbers, an alternative way is to do it as in example A of the bank transactions. There are different ways to combine multiple signed numbers. We may combine them from left to right. Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 II. To combine two numbers of different signs, keep the sign of the number with larger absolute value, take the difference of the absolute values of the numbers.
- 46. Signed Numbers Example C. 8 – 9 + 11 = –1 + 11 = 10 To combine many numbers, an alternative way is to do it as in example A of the bank transactions. That is, we combined all the positive ones (deposits) first, There are different ways to combine multiple signed numbers. We may combine them from left to right. Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 II. To combine two numbers of different signs, keep the sign of the number with larger absolute value, take the difference of the absolute values of the numbers.
- 47. Signed Numbers Example C. 8 – 9 + 11 = –1 + 11 = 10 To combine many numbers, an alternative way is to do it as in example A of the bank transactions. That is, we combined all the positive ones (deposits) first, then combine all the negative ones (withdrawals), There are different ways to combine multiple signed numbers. We may combine them from left to right. Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 II. To combine two numbers of different signs, keep the sign of the number with larger absolute value, take the difference of the absolute values of the numbers.
- 48. Signed Numbers Example C. 8 – 9 + 11 = –1 + 11 = 10 To combine many numbers, an alternative way is to do it as in example A of the bank transactions. That is, we combined all the positive ones (deposits) first, then combine all the negative ones (withdrawals), then combine the two results. There are different ways to combine multiple signed numbers. We may combine them from left to right. Rules for Combining Signed Numbers I. To combine two or more numbers of the same signs, keep the sign, sum of the absolute values of the numbers. +100 + 200 = +300, –100 – 200 = –300 +500 – 300 = +200, –500 + 300 = –200 II. To combine two numbers of different signs, keep the sign of the number with larger absolute value, take the difference of the absolute values of the numbers.
- 49. * The above method is easier when summing many numbers. Signed Numbers
- 50. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers
- 51. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11
- 52. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front
- 53. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front = 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11
- 54. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front = 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11
- 55. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front = 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11 = 36
- 56. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front = 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11 = 36 – 61 = –25
- 57. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front = 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11 = 36 – 61 = –25 Another method for combining many signed numbers is to do two in groups of two’s.
- 58. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front = 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11 = 36 – 61 = –25 Another method for combining many signed numbers is to do two in groups of two’s. Hence 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs
- 59. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front = 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11 = 36 – 61 = –25 Another method for combining many signed numbers is to do two in groups of two’s. Hence 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs = –4
- 60. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front = 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11 = 36 – 61 = –25 Another method for combining many signed numbers is to do two in groups of two’s. Hence 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs = –4 +2
- 61. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front = 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11 = 36 – 61 = –25 Another method for combining many signed numbers is to do two in groups of two’s. Hence 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs = –4 +2 –4 –19
- 62. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front = 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11 = 36 – 61 = –25 Another method for combining many signed numbers is to do two in groups of two’s. Hence 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs = –4 +2 –4 –19 in pairs again
- 63. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front = 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11 = 36 – 61 = –25 Another method for combining many signed numbers is to do two in groups of two’s. Hence 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs = –4 +2 –4 –19 in pairs again = –2 – 23 = –25
- 64. * The above method is easier when summing many numbers. * When doing this, it helps to move all the positive ones to the front and the negative ones to the back. Signed Numbers Example D. 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 positive ones to the front = 7 + 14 + 15 – 11 – 12 – 19 – 8 – 11 = 36 – 61 = –25 Another method for combining many signed numbers is to do two in groups of two’s. Hence 7 – 11 + 14 – 12 + 15 – 19 – 8 – 11 group them in pairs = –4 +2 –4 –19 in pairs again = –2 – 23 = –25 (Two Method Strategy) Do it two ways to double check the answer when combining multiple signed numbers.
- 65. Exercise A. Combine 1. 2 + 3 2. 10 + 6 3. 34 + 21 + 4 + 17 4. –6 –2 5. –11 – 5 6. –14 –15 7. –26 –15 – 5 –14 8. –3 + 2 9. 5 –11 10. –14 + 15 11. 26 –15 12. 12 – 13 13. –23 +18 B. Combine by moving the positive numbers to the front first. Combine the positive numbers, the negative numbers separately then then combine the two results. 14. 23 – 18 +7 –12 15. –6 –2 + 10 + 6 16. –14 + 23 –15 – 3 +12 17. –26 + 15 –5 –14 + 9 18. 19 – 13 – 9 – 3 + 15 19. –6 + 19 – 15 + 5 – 9 20. – 4 + 7 – 23 + 8 + 17 – 8 + 6 + 9 – 22 – 2 21. Try to get the same answer for #20 by combining two numbers at a time without separating the positive numbers from the negative numbers. Signed Numbers