1. Slide #1 An Alternative Method for Adding & Subtracting Integers

2. Slide #2 Alternative Method for Adding & Subtracting Integers 1.Add and subtract integers. 2.Identify properties of addition. 3.Combine adding and subtracting of integers. 4.Identify properties of addition. Objectives:

3. Slide #3 Alternative Method for Adding & Subtracting Integers The following slides will explain how to add and subtract signed numbers. We will be using an alternative approach. You can decide which method works best for you. In our explanation here, we will learn how to eliminate “double signs” in order to simplify mathematical expressions. We will use this method throughout the rest of this course.

4. Slide #4 Alternative Method for Adding & Subtracting Integers In our explanation, we will recognize the following: The “+” symbol can be used for two different purposes. “+” can identify the addition operator “+” can identify the positive sign of a number The “–” symbol can be used for two different purposes. “–” can identify the subtraction operator “–” can identify the negative sign of a number

5. Slide #5 Here’s what we mean by the symbols looking the same. + 3 – + 4 + – 2 Here’s what we mean by the symbols looking the same. + 3 – + 4 + – 2 Operators Signs Notice the “signs” and the “operators” look the same. We will refer to the highlighted areas as “double signs”. Alternative Method for Adding & Subtracting Integers

6. Slide #6 Eliminating “Double Signs” We can demonstrate how to eliminate “double signs” using the following examples. With Double Signs + 3 + + 4 Without Double Signs + 3 + – 4 + 3 – + 4 + 3 – – 4 3 + 4 3 – 4 3 + 4 match don’t match match Alternative Method for Adding & Subtracting Integers

7. Slide #7 Not a double sign – 2 + + 3 + 1 – – 9 – + 7 Eliminate all double signs. Do not simplify the expressions. You try… With Double SignsWithout Double Signs -8 – 5 + 2 – 8 – + 5 – – 2 15 + – 3 – 20 + – 215 – 3 – 20 – 2 – 2 + 3 + 1 + 9 – 7 Not a double sign Alternative Method for Adding & Subtracting Integers 1) 2) 3)

8. Slide #8 012345-5-4-3-2 a)2 + 3= 5 b)1 + 2= 3 c)-4 + 3= -1 d)-5 + 8= 3 Question: Without double signs, adding moves us which direction on the number line? Alternative Method for Adding & Subtracting Integers Addition Using a Number Line

9. Slide #9 012345-5-4-3-2 a)5 – 1= 4 b)4 – 2= 2 c)5 – 8= -3 d)-3 – 2= -5 Question: Without double signs, subtracting moves us which direction on the number line? Alternative Method for Adding & Subtracting Integers Subtraction Using a Number Line

10. Slide #10 012345-5-4-3-2 a)3 – 7 + 6 -4 + 6 2 Alternative Method for Adding & Subtracting Integers Use the number line to simplify the following expression.

11. Slide #11 012345-5-4-3-2 b) -1 – 4 + 8 -5 + 8 3 Alternative Method for Adding & Subtracting Integers Use the number line to simplify the following expression.

12. Slide #12 012345-5-4-3-2 1 c) -3 + 7 – 5 – 4 + 6 4 – 5 – 4 + 6 -1 – 4 + 6 -5 + 6 Alternative Method for Adding & Subtracting Integers Use the number line to simplify the following expression.

13. Slide #13 $195 Total Cost $30 Allowance Now, add his expenses and his money.First, organize the expenses and Johnny’s money.Does he have enough money? $155 Savings $30 Allowance $120 Boots $75 Helmet $155 Savings $120 Boots $75 Helmet $185 Total Money Addition & Subtraction Using Money Does Johnny have enough money to buy his motorcycle supplies? No. $195 – $185 = $10 (He needs $10) Alternative Method for Adding & Subtracting Integers

14. Slide #14 First, organize the bills and the income.Now add the total bills and the total income. $50 Gift $900 Paycheck $30 Rebate Check $40 Gas Bill $650 Rent $60 Electric Bill $30 Water Bill $20 Life Insurance $60 Auto Insurance $50 Gift $900 Paycheck $30 Rebate Check $40 Gas Bill $650 Rent $60 Electric Bill $30 Water Bill $20 Life Insurance $60 Auto Insurance $860 Total Bills $980 Total Income Determine if the income will “cover” the bills.Yes. $980 – $860 = $120 (left over) Addition & Subtraction Using Money Does Edward have enough money to pay his bills? Alternative Method for Adding & Subtracting Integers

15. Slide #15 Now, organize the positive and negative terms.Add each type of term (positive and negative).Lastly, determine the result. –3 + 7 – 5 – 4 + 6 –3 – 5 – 4 + 7 + 6 –12 + 13 1 First, identify the positive and negative terms. The positive term is “larger than” the negative term by 1. Alternative Method for Adding & Subtracting Integers Addition & Subtraction by Organizing Terms

16. Slide #16 First, identify the positive and negative terms.Now, organize the positive and negative terms.Add each type of term (positive and negative).Lastly, determine the result. 1 – 8 + 15 – 10 + 24 – 30 1 + 15 + 24 – 8 – 10 – 30 40 – 48 –8 Assumed positive The negative term is “larger than” the positive term by 8. Alternative Method for Adding & Subtracting Integers Addition & Subtraction by Organizing Terms

17. Slide #17 Now, organize the positive and negative terms.Add each type of term (positive and negative).Lastly, determine the result.First, identify the positive and negative terms. –12 + 4 + 6 – 15 + 17 – 24 –12 – 24 – 15 + 4 + 6 + 17 –51 + 27 –24 The negative term is “larger than” the positive term by 24. Alternative Method for Adding & Subtracting Integers Addition & Subtraction by Organizing Terms

18. Slide #18 Now, identify the positive and negative terms.Organize the positive and negative terms.Add each type of term (positive and negative).Lastly, determine the result.First, eliminate all double signs. – 3 + 15 + – 5 – – 9 + + 8 – + 1 – 7 – 3 + 15 – 5 + 9 + 8 – 1 – 7 – 16 + 32 16 The positive term is “larger than” the negative term by 16. – 3 – 5 – 1 – 7 + 15 + 9 + 8 Alternative Method for Adding & Subtracting Integers

19. Slide #19 Lastly, determine the result.First, eliminate all double signs.Now, identify the positive and negative terms.Organize the positive and negative terms.Add each type of term (positive and negative). 5 – 10 – – 15 + 20 – 30 + – 35 – + 40 5 – 10 + 15 + 20 – 30 – 35 – 40 40 – 115 –75 The negative term is “larger than” the positive term by 75. 5 + 15 + 20 – 10 – 30 – 35 – 40 Alternative Method for Adding & Subtracting Integers

20. Slide #20 Lastly, determine the result.First, eliminate all double signs.Now, identify the positive and negative terms.Organize the positive and negative terms.Add each type of term (positive and negative). – 12 – – 7 + – 6 + 9 – + 1 – 8 + + 20 – 12 + 7 – 6 + 9 – 1 – 8 + 20 – 27 + 36 9 The positive term is “larger than” the negative term by 9. – 12 – 6 – 1 – 8 + 7 + 9 + 20 Alternative Method for Adding & Subtracting Integers

21. Slide #21 Alternative Method for Adding & Subtracting Integers Addition Property of 0 Adding 0 to any number leaves the number unchanged. Some examples are shown below. 0 + 9 = 9 – 75 + 0 = – 75 18,345 + 0 = 18,345

22. Slide #22 Alternative Method for Adding & Subtracting Integers Commutative Property of Addition Changing the order of two addends does not change the sum. Here are some examples. 14 + 26 = 26 + 14Both sums are 40. – 24 + 8 = 8 + – 24Both sums are – 16.

23. Slide #23 Alternative Method for Adding & Subtracting Integers Associative Property of Addition Changing the grouping of addends does not change the sum. Here are some examples. (3 + 2) + 8 = 3 + (2 + 8) 5 + 8 13 ( – 1 + – 9) + 5 = – 1 + ( – 9 + 5) – 10 + 5 –5–5 3 + 10 13 = = = = –5–5 – 1 + – 4

24. Slide #24 Alternative Method for Adding & Subtracting Integers NOTE: Using the Associate Property of Addition When using the associative property to make the addition of a group of numbers easier: 1.Look for two numbers whose sum is 0. 2.Look for two numbers whose sum is a multiple of 10 (the sum ends in 0, such as 10, 20, 30, or – 100, – 200, etc.). If neither of these occurs, look for two numbers that are easier for you to add. For example, in 39 + 18 + 6, you may find that adding 18 + 6 is easier than adding 39 + 18.