Columbus State Community College

1. Columbus State Community College Chapter 1 Section 3 Adding Integers

2. Adding Integers • Add integers. • Identify properties of addition.

3. Using a Number Line to Add Integers EXAMPLE 1 Using a Number Line to Add Integers Use a number line to find –3 + –2. Think of the number line as a thermometer. Let’s say the temperature is currently 0 degrees Fahrenheit. 0º F 3º F ↓ –3º F On our first observation, the temperature has fallen by 3 degrees. 2º F ↓ –5º F On our second observation, it has fallen by an additional 2 degrees. The total decline in temperature is 5 degrees.

4. Adding Two Integers with the Same Sign Adding Two Integers with the Same Sign Step 1 Add the absolute values of the numbers. Step 2 Use the common sign as the sign of the sum. If both numbers are positive, the sum is positive. If both numbers are negative, the sum is negative.

5. Adding Two Integers with the Same Sign EXAMPLE 2 Adding Two Integers with the Same Sign Add. (a)–6 + –15 Step 1 Add the absolute values. | –6 | = 6 and | –15 | = 15 Add 6 + 15 to get 21. Step 2 Use the common sign as the sign of the sum. Both numbers are negative, so the sum is negative. –6 + –15 = –21

6. Adding Two Integers with the Same Sign EXAMPLE 2 Adding Two Integers with the Same Sign Add. (b) 3 + 28 In Step 1, when both numbers are positive, their absolute values are also positive, so we only need to show Step 2. 3 + 28 = 31 Both positive Sum is positive

7. Adding Two Integers with Unlike Signs Adding Two Integers with the Unlike Signs Step 1 Subtract the smaller absolute value from the larger absolute value. Step 2 Use the sign of the number with the larger absolute value as the sign of the sum.

8. Adding Two Integers with Unlike Signs EXAMPLE 3 Adding Two Integers with Unlike Signs Add. (a)–12 + 8 Step 1 | –12 | = 12 and | 8 | = 8 Subtract 12 – 8 to get 4. Step 2–12 has the larger absolute value and is negative, so the sum is also negative. –12 + 8 = –4

9. Adding Two Integers with the Unlike Signs EXAMPLE 3 Adding Two Integers with the Unlike Signs Add. (b)–9 + 27 Step 1 | –9 | = 9 and | 27 | = 27 Subtract 27 – 9 to get 18. Step 2 27 has the larger absolute value and is positive, so the sum is also positive. –9 + 27 = +18 or 18

10. Adding Several Integers EXAMPLE 4 Adding Several Integers Jernice is a competitive golfer. She lost 2 matches her first week, won 5 matches the second week, lost 1 match the third week, lost 3 matches the fourth week, and won 4 matches the fifth week. What can be said about Jernice’s wins and losses? –2 + 5 + –1 + –3 + 4 3 + –1 + –3 + 4 Since the result is positive, Jernice won 3 more matches than she lost. 2 + –3 + 4 –1 + 4 3

11. Adding Several Integers EXAMPLE 4 Adding Several Integers (Another Method) Jernice is a competitive golfer. She lost 2 matches her first week, won 5 matches the second week, lost 1 match the third week, lost 3 matches the fourth week, and won 4 matches the fifth week. What can be said about Jernice’s wins and losses? Total Losses: 6Total Wins: 9 Using either method, we can see that Jernice won 3 more matches than she lost. –6 + 9 = 3 or 9 + –6 = 3

12. Addition Property of 0 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

13. Commutative Property of Addition Commutative Property of Addition Changing the order of two addends does not change the sum. Here are some examples. 14 + 26 = 26 + 14 Both sums are 40. –24 + 8 = 8 + –24 Both sums are –16.

14. Using the Commutative Property of Addition EXAMPLE 5 Using the Commutative Property of Addition Rewrite each sum using the commutative property of addition. Check that the sum is unchanged. (a) 35 + –24 35 + –24 = –24 + 35 11 = 11 (b)–15 + 12 –15 + 12 = 12 + –15 –3 = –3

15. Associative Property of Addition Associative Property of Addition Changing the grouping of addends does not change the sum. Here are some examples. (3 + 2) + 8 = 3 + (2 + 8) (–1 + –9) + 5 = –1 + (–9 + 5) = = 5 + 8 3 + 10 –10 + 5 –1 + –4 13 13 –5 –5 = =

16. Using the Associative Property of Addition EXAMPLE 6 Using the Associative Property of Addition In each addition problem, pick out the two addends that would be easiest to add. Write parentheses around those addends. Then find the sum. (a) 7 + –5 + 5 Group –5 + 5 because the sum is 0. 7 + (–5 + 5) 7 + 0 7

17. Using the Associative Property of Addition EXAMPLE 6 Using the Associative Property of Addition In each addition problem, pick out the two addends that would be easiest to add. Write parentheses around those addends. Then find the sum. (b)–6 + –34 + 4 Group –6 + –34 because the sum is –40, which is a multiple of 10. (–6 + –34) + 4 –40 + 4 –36

18. Note on Using the Associative Property of Addition NOTE When using the associative property to make the addition of a group of numbers easier: • Look for two numbers whose sum is 0. • 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.

19. Adding Integers Chapter 1 Section 3 – End Written by John T. Wallace