1. Adding and Subtracting Integers Unit 1: The Number System

2. Part 1 Adding and Subtracting Integers

3. Common Core Standards CCSS.Math.Content.7.NS.A.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. CCSS.Math.Content.7.NS.A.1c CCSS.Math.Content.7.NS.A.1d Apply properties of operations as strategies to add and subtract rational numbers. CCSS.Math.Content.7.NS.A.1d

4. Vocabulary additive identity property – the sum of a number and it’s additive identity is the number (ex. 9 + 0 = 9) opposite – two numbers are opposites if they have the same absolute values but different signs (ex. 9 and -9) inverse property – the sum of a number and it’s additive inverse is zero (9 + -9 = 0)

5. Example 1A: Using a Number Line to Add Integers Use a number line to find the sum. (–6) + 2 2 –6 You finish at –4, so (–6) + 2 = –4. –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 Start at 0. Move left 6 units. From –6, move right 2 units.

6. To add a positive number move to the right on the number line. Helpful Hint –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 To add a negative number move to the left on the number line. –6 –5 –4 –3 –2 –1 0 1 2 3 4 5

7. Example 1B: Using a Number Line to Add Integers Use a number line to find the sum. –3 + (–6) –3–6 You finish at –9, so –3 + (–6) = –9. –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 Start at 0. Move left 3 units. From –3, move left 6 units.

8. Now You Try! Use a number line to find the sum. (–3) + 7 7 –3 You finish at 4, so (–3) + 7 = 4. –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 Start at 0. Move left 3 units. From –3, move right 7 units.

9. Example 2A: Using Absolute Value to Add Integers A. 1 + (–2) Add. 1 + (–2) 2 > 1; use the sign of 2. –1 B. (–8) + 5 (–8) + 5 8 > 5; use the sign of 8. –3 Think: Find the difference of 1 and –2. Think: Find the difference of –8 and 5.

11. Example 2B: Using Absolute Value to Add Integers C. (–2) + (–4) Add. (–2) + (–4) Same sign; use the sign of the integers. –6 Think: Find the sum of –2 and –4.

12. A. 3 + (–6) Add. 3 + (–6) 6 > 3; use the sign of 6. –3 B. (–4) + 1 (–4) + 1 4 > 1; use the sign of 4. –3 Think: Find the difference of 3 and –6. Think: Find the difference of –4 and 1. Now You Try!

13. C. (–6) + (–7) Add. (–6) + (–7) Same sign; use the sign of the integers. –13 Think: Find the sum of –6 and –7. Try One More!

14. Example 3A: Using Addition Properties Find the sum using the order of operations. Inverse property of addition () +7 – 7 () 8 – + () 5 – + = () 8 – + 0 () 5 – + = 8 – () 5 – + Identity property of addition = 13 – Same sign, so sum has common sign

15. Example 4: Application Meka opened a new bank account. Find her account balance after the first four transactions listed below. Deposits: $200, $20 Withdrawals: $166, $38 Use a positive sign for deposits and a negative sign for withdrawals. 200 + 20 + (–166) + (–38) Group integers with the same signs. (200 + 20) + (–166 + –38) Add integers within each group. 220 + (–204) 220 > 204; use the sign of 220. 16 Meka’s account balance after the first four transactions is $16.

16. Michael opened a new bank account. Find his account balance after the first four transactions listed below. Deposits: $175, $95 Withdrawals: $133, $65 Use a positive sign for deposits and a negative sign for withdrawals. 175 + 95 + (–133) + (–65) Group integers with the same signs. (175 + 95) + (–133 + –65) Add integers within each group. 270 + (–198) 270 > 198; use the sign of 270. 72 Michael’s account balance after the first four transactions is $72. Now You Try!

17. You can also subtract an integer by adding its opposite. You can then use the rules for addition of integers. Remember SAND BAGS & GAS! Take away sand bags (balloon goes UP) Take away gas (balloon goes DOWN)

18. Example 1: Subtracting Integers A. –7 – 4 –7 – 4 = –7 + (–4) B. 8 – (–5) 8 – (–5) = 8 + 5 C. –6 – (–3) –6 – (–3) = –6 + 3 = –11 = 13 = –3 Add the opposite of 4. Add the opposite of –5. Add the opposite of –3. Same sign; use the sign of the integers. 6 > 3; use the sign of 6. Subtract.

19. A. 3 – (–6) 3 – (–6) = 3 + 6 B. –4 – 1 –4 – 1 = –4 + (–1) C. –7 – (–8) –7 – (–8) = –7 + 8 = 9 = –5 = 1 Add the opposite of –6. Add the opposite of 1. Add the opposite of –8. Same signs; use the sign of the integers. Same sign; use the sign of the integers. 8 > 7; use the sign of 8. Subtract. Now You Try!

20. How about a rhyme to help you remember? To the tune of “Row, Row, Row Your Boat Same sign find the sum Different sign subtract Keep the sign of the larger number Then you’ll be exact

21. Part 2 Tomorrow Debits and Credits Activity

22. The top of the Willis Tower (aka Sears Tower), in Chicago, is 1454 feet above street level, while the lowest level is 43 feet below street level. How far is it from the lowest level to the top? Warm Up 1454 – (–43) 1454 + 43 1497 It is 1497 feet from the lowest level to the top.

23. The distance from the high dive to the swimming pool is 10 feet. The pool is 12 feet deep. What is the total distance from the high dive to the bottom of the pool? Warm Up 10 – (–12) Subtract the depth of the pool from the height of the high dive. 10 + 12Add the opposite of –12. 22Same sign; use the sign of the integers. It is 22 feet from the diving board to the bottom of the pool.