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1.1E: Exercises

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    104795

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    Practice Makes Perfect

    Add and Subtract IntegersIn the following exercises, simplify each expression.

    Add and Subtract

    Compute the following

    1. \(1+4\)
    2. \(3+9\)
    3. \(9-6\)
    4. \(8-3\)
    5. \(9-14\)
    6. \(1-8\)
    7. \(−17−42\)
    8. \(−58−(−67)\)
    9. \(64+(−17)−9\)
    10. \(48+(−16)\)
    11. \(34+(−19)\)
    12. \(−14+(−12)+4\)
    13. \(−17+(−18)+6\)
    14. \(19+2(−3+8)\)
    15. \(24+3(−5+9)\)
    16. \((2−7)−(3−8)\)
    17. \(32−[5−(15−20)]\)
    Answer
    1. 5
    2. 12
    3. 3
    4. 5
    5. -5
    6. -7
    7. \(-59\)
    8. \(9\)
    9. \(38\)
    10. 32
    11. 15
    12. \(-22\)
    13. \(-29\)
    14. \(29\)
    15. \(36\)
    16. 0
    17. 22
    Multiply and Divide

    multiply or divide:

    1. \(−4 \cdot 8\)
    2. \(13(−5)\)
    3. \(−24÷6\)
    4. \(−52÷(−4)\)
    5. \(−3 \cdot 9\)
    6. \(9(−7)\)
    7. \(35÷(−7)\)
    8. \(−84÷(−6)\)
    9. \(−3(−5)(6)\)
    10. \(−4(−6)(3)\)
    11. \((8−11)(9−12)\)
    12. \((6−11)(8−13)\)
    13. \(26−3(2−7)\)
    14. \(23−2(4−6)\)
    15. \(65÷(−5)+(−28)÷(−7)\)
    16. \(52÷(−4)+(−32)÷(−8)\)
    17. \(9−2[3−8(−2)]\)
    18. \(11−3[7−4(−2)]\)
    Answer
    1. \(−32\)
    2. \(−65\)
    3. \(−4\)
    4. \(13\)
    5. \(−27\)
    6. \(−63\)
    7. \(−5\)
    8. \(14\)
    9. \(90\)
    10. \(72\)
    11. \(9\)
    12. \(25\)
    13. \(41\)
    14. \(27\)
    15. \(-9\)
    16. \(-9\)
    17. \(-29\)
    18. \(-34\)

     

    Inequalities with Absolute Values

    For each of the expressions below, identify the appropriate inequality or equality that makes the statement true.

    1. \(-8\_\_−|8|\)
    2. \(13\_\_−13\)
    3. \(−(−1)\_\_|−1|\)
    4. \(-(−10)\_\_−|-10|\)
    5. \(-2 \_\_|−2|\)
    6. \(0 \_\_|0|\)
    7. \(−9 \_\_|−9|\)
    Answer
    1. =
    2. >
    3. =
    4. >
    5. <
    6. =
    7. <

     

     

    Order of Operations with Parentheses and Absolute Values

    Simplify the following expressions:

    1. \(2−|10+2(6−5)|\)
    2. \(−2|7+5(-3 + 5)|+3(4)\)
    3. \(4+4|1+8(−5+4)|\)
    4. \(3|4 - 12| - 2(4 + 7)\)
    5. \(−|1+3(6−7) + (9 - 2)|\)
    6. \(−2|3+(6−7) + (9 - 10)|\)
    7. \(3|1+4(-2 + 1)|-3(5)\)
    8. \(-|3 - 4| + |4 - 5| - |5 - 6|\)
    9. \(| 3 - 6| - |6 - 9| + |9 - 12|\)
    10. \((3 - 4)|4 + 9|\)
    11. \((7 - 2)|- 11 + 3|\)

     

    Answer

     

    1. -10
    2. -22
    3. 32
    4. 2
    5. -5
    6. -2
    7. -6
    8. -1
    9. 3
    10. -13
    11. 40

     

     

     

    Writing Exercises
    1. Explain why the sum of −8 and 2 is negative, but the sum of 8 and −2 is positive.
    2. Give an example from your life experience of adding two negative numbers.
    Answer

    Answers will vary


    This page titled 1.1E: Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Stanislav A. Trunov and Elizabeth J. Hale via source content that was edited to the style and standards of the LibreTexts platform.