3.4+“Undoing”+with+Addition+And+Subtraction+0910

S. Z. 11 Apr 2010 Big Idea: Negative numbers help us to model many real world situations. E. Q. #3: How do I find the difference between integers?
 * __Problem 3.4: “Undoing” with Addition and Subtraction__**

Answer: (-17) + 13 = (-4). Answer: (-4) – 13 = (-17).
 * A) 1. Complete the addition sentence (-17) + 13 = ?.**
 * 2. Write a subtraction sentence that “undoes” the addition sentence you found in part 1.**

Answer: (-4) + (-18) = (-22). Answer: (-22) – (-18) = (-4).
 * B) 1. Complete the addition sentence (-4) + -18 = ?.**
 * 2. Write a subtraction sentence that “undoes” the addition sentence you found in part 1.**

Answer: 6 - (-18) = 24. Answer: (-3.2) – 6.1 = (-9.3). Answer: (-41) - (-13) = 54. Answer: 1/3 - (-1/3) = 2/3.
 * C) Write a subtraction sentence that solves each problem.**
 * 1. ? + (-18) = 6**
 * 2. ? + 6.1 = (-3.2)**
 * 3. ? + (-13) = (-41)**
 * 4. ? + (-1/3) = 1/3**

Answer: (-6) + (-6) = (-12). Answer: (-7.1) + 5.3 = (-1.8). Answer: (-3.2) + 6.1 = 2.8. Answer: (-3/4) + (-1/4) = (-1).
 * D) Write an addition sentence that solves each problem.**
 * 1. ? – (-6) = (-6)**
 * 2. ? – 5.3 = (-7.1)**
 * 3. ? - 6.1 = (-3.2)**
 * 4. ? – (-1/4) = (-3/4)**

Answer: 14 – 11 = 3.
 * __Problem 3.4 Follow-Up__**
 * 1. In the introduction to this problem, we wrote the number sentence 11 = 14 – 3 from the sentence 11 + 3 = 14. We could also write 3 + 11 = 14. Can you write a different subtraction sentence to go with this addition sentence?**

Answer: 3.8 + (-2.6) = 1.2 Answer: 1.2 - (-2.6) = 3.8; 3.8 – 1.2 = (-2.6)
 * 2. a) Complete the addition sentence 3.8 + (-2.6) = ?.**
 * b) Write all the addition sentences you can that are related to the subtraction sentence you found in part a.**

Answer: (-11) – 6 = (-17). Answer: (-17) + 6 = (-11); 6 + (-17) = (-11).
 * 3. a) Complete the subtraction sentence (-11) – 6 = ?.**
 * b) Write all the addition sentences you can that are related to the subtraction sentence you found in part a.**

Answer: Yes, but only when you subtract a positive from a positive, or a negative from a negative. If you subtract a positive from a negative, the result will always be a negative. Likewise, if you subtract a negative from a positive, the result will always be positive. In the first case, for example, 2 – 1 is 1, but 1 – 2 is (-1). Likewise, in the second case, (-1) – (-2) is 1, but (-2) – (-1) is (-1). Yet, for the last two cases, (-1) – 2 is (-3) (negative), and 2 – (-1) is 3 (positive). Therefore, it is possible to get both positive and negative integers when subtracting them.
 * 4. When you add positive and negative integers, sometimes you get a positive sum and sometimes you get a negative sum. Is the same true when you subtract positive and negative integers? Explain.**