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Understanding Additive Inverse Property in Integers

Learn what additive inverse means, how it relates to integers, and practice solving related problems with examples included. Explore how this property can help in adding integers correctly. Understand commutative property and adding integers with different signs. Workbook practice included.

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Understanding Additive Inverse Property in Integers

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  1. 7.NS.1 a. Understand that the additive inverse of a number is its opposite and their sum is equal to zero.

  2. Question? • Can you think of any number you can add to 4 to get 0?

  3. Additive Inverse Property • What do you think this property means? • Let’s look at the words individually. • 1st what does additive mean? • 2nd what is inverse? • Can you figure out what this property does?

  4. Additive Inverse Property

  5. Additive inverse examples

  6. More examples of additive inverse

  7. Let’s practice • 1. What is the additive inverse of 8? • 2. Solve: (-9) + 9 = • 3. What is the additive inverse of (-2)? • 4. Solve: (-66) + 66 = • 5. What is the additive inverse of 8,964? • 6. Solve: (-771) + x = 0 • 7. What is the additive inverse of (-9,276)? • 8. Solve: 27 + (-27) = • 9. What is the additive inverse of (-12)? • 10. Solve: 0 + 9,276 =

  8. Practice answers • 1. (-8)   • 2. 0   • 3. 2   • 4. 0   • 5. (-8,964)   • 6. 771   • 7. 9,276   • 8.  0   • 9.  12   • 10. 9,276 

  9. How can we use this property? • What if you see this problem. Could it help if you knew this property? -3 + 5 + (-5) Or 20 + (-20) + (8)

  10. Adding integers • When adding integers with the same sign just add and keep the sign: • Examples: 6 + 3 = 9 is the same as (+6)+ (+3)= +9 and -4 + (-7) = -11 or -7 + (-4) = -11 (Do you recognize this property?)

  11. Commutative property • Commutative property says that you can swap the order of two numbers when adding or multiplying and still get the same answer.

  12. Adding integers with different signs • When adding integers with different signs REMEMBER THIS… Adding a negative is the same as subtracting a positive and Subtracting a negative is like adding a positive

  13. Let’s examine this closer • Adding a negative is like subtracting a positive 11 + (-6) is the same as 11 – (6) 2 + (-3) is the same as 2 – (3) 5 + (-5) is the same as 5 - 5

  14. Let’s examine this… • Subtracting a negative is like adding a positive 3 – (-4) is the same as 3 + (4) 8 – (-6) is the same as 8 + (6) 9 – (-10) is the same as 9 + (10)

  15. Workbook practice • Volume 1 p. 204 p. 207 (1-10)

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