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Work Exercise 2: 1. Draw a number line and show the following additions on it. i. 6+(-2) ii. (-2)+(-3) iii. (-149)+(-311) 4. Write the additive inverse of the following integers. i. 17 iii. (-101) 5. Write any two integers. i. 6+(-8) iii. (-12)+11

Mathematics

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Here are the solutions to the problems:

**Work **

1. Draw a number line and show the following additions on it.

i) 6+(−2)6 + (-2)

  1. Start at 6 on the number line.

  2. Since you are adding −2-2, move 2 units to the left from 6.

  3. You will land on 4.

    6+(−2)=46 + (-2) = 4

    The final answer is 4\boxed{\text{4}}

    ii) (−2)+(−3)(-2) + (-3)

  4. Start at −2-2 on the number line.

  5. Since you are adding −3-3, move 3 units to the left from −2-2.

  6. You will land on −5-5.

    (−2)+(−3)=−5(-2) + (-3) = -5

    The final answer is -5\boxed{\text{-5}}

    iii) (−149)+(−311)(-149) + (-311)

  7. When adding two negative integers, add their absolute values and keep the negative sign.

  8. Add 149 and 311.

    149+311=460149 + 311 = 460
  9. Apply the negative sign.

    (−149)+(−311)=−460(-149) + (-311) = -460

    The final answer is -460\boxed{\text{-460}}

    2. Find the successors of the following integers by adding 1 to the integer.

    i) −7-7

  10. To find the successor, add 1 to the integer.

    −7+1=−6-7 + 1 = -6

    The final answer is -6\boxed{\text{-6}}

    ii) 12

  11. To find the successor, add 1 to the integer.

    12+1=1312 + 1 = 13

    The final answer is 13\boxed{\text{13}}

    iii) −54-54

  12. To find the successor, add 1 to the integer.

    −54+1=−53-54 + 1 = -53

    The final answer is -53\boxed{\text{-53}}

    3. Add the following integers by the rules of addition.

    i) (−616)+210(-616) + 210

  13. When adding integers with different signs, subtract the smaller absolute value from the larger absolute value.

    ∣−616∣−∣210∣=616−210=406| -616 | - | 210 | = 616 - 210 = 406
  14. The result takes the sign of the integer with the larger absolute value, which is −616-616.

    (−616)+210=−406(-616) + 210 = -406

    The final answer is -406\boxed{\text{-406}}

    ii) 596+(−76)596 + (-76)

  15. Subtract the smaller absolute value from the larger absolute value.

    ∣596∣−∣−76∣=596−76=520| 596 | - | -76 | = 596 - 76 = 520
  16. The result takes the sign of the integer with the larger absolute value, which is 596.

    596+(−76)=520596 + (-76) = 520

    The final answer is 520\boxed{\text{520}}

    4. Write the additive inverse of the following integers.

    i) 17

  17. The additive inverse of an integer is the number that, when added to the integer, results in zero.

    It is the integer with the opposite sign.

  18. The additive inverse of 17 is −17-17.

    The final answer is -17\boxed{\text{-17}}

    iii) (−101)(-101)

  19. The additive inverse of an integer is the number with the opposite sign.

  20. The additive inverse of −101-101 is 101.

    The final answer is 101\boxed{\text{101}}

    5. Write any two integers and add them.

    i) 6+(−8)6 + (-8)

  21. Subtract the smaller absolute value from the larger absolute value.

    ∣−8∣−∣6∣=8−6=2| -8 | - | 6 | = 8 - 6 = 2
  22. The result takes the sign of the integer with the larger absolute value, which is −8-8.

    6+(−8)=−26 + (-8) = -2

    The final answer is -2\boxed{\text{-2}}

    iii) (−12)+11(-12) + 11

  23. Subtract the smaller absolute value from the larger absolute value.

    ∣−12∣−∣11∣=12−11=1| -12 | - | 11 | = 12 - 11 = 1
  24. The result takes the sign of the integer with the larger absolute value, which is −12-12.

    (−12)+11=−1(-12) + 11 = -1

    The final answer is -1\boxed{\text{-1}}

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