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Adding Integers •Workbook pgs. 19-26 •On-line textbook: Chapter 1 (lesson 2) The integers are the set of whole numbers and their opposites. Including zero. Remember! The whole numbers are the counting numbers and zero: 0, 1, 2, 3, . . . . The opposite of a number is the same distance from 0 on a number line as the original number. Zero is its own opposite. –4 and 4 are opposites –4 4 • • –5–4–3–2–1 0 1 2 3 4 5 Negative integers Positive integers 0 is neither positive nor negative A number’s absolute value is its distance from 0 on a number line. They are always positive or zero. Reading Math The symbol is read as “the absolute value of.” For example -3 is the absolute value of -3. Ex # 1: Modeling Integer Addition on the Number Line Use a number line to find each sum. –7 + (–4) –14 –12 –7 +(–4) –10 –8 –6 –4 –2 0 2 Start at 0. Move left 7 spaces. Then move left 4 more spaces. –7 + (–4) = –11 Course 2 Example # 2: Modeling Integer Addition on the Number Line Use a number line to find each sum. –12 + 19 19 –12 –12 –10 –8 –6 –4 –2 0 2 4 6 Start at 0. Move left 12 spaces. Then move right 19 spaces. –12 + 19 = 7 Course 2 8 Ex # 3: Modeling Integer Addition on the Number Line Use a number line to find each sum. –4 + (–5) –14 –12 –10 –4 +(–5) –8 –6 –4 –2 0 2 Start at 0. Move left 4 spaces. Then move left 5 more spaces. –4 + (–5) = –9 Course 2 Insert Lesson Title Here Ex # 4: Modeling addition integers on the number line Use a number line to find each sum. –7 + 12 12 –7 –12 –10 –8 –6 –4 –2 0 2 4 6 Start at 0. Move left 7 spaces. Then move right 12 spaces. –7 + 12 = 5 Course 2 8 Adding Integers Adding Integers (OMG) To add two integers with the same sign, find the sum of their absolute values. Use the sign of the two integers. To add two integers with different signs, find the difference of their absolute values. Use the sign of the integer with the greater absolute value. Course 2 Adding Integers Ex # 5: Adding Integers Using Absolute Values Find each sum. –4 + 8 The signs are different. Find the difference of the absolute values. –4 + 8 4 Course 2 Think: 8 – 4 = 4. Use the sign of the integer with the greater absolute value. Ex # 6: Adding Integers Using Absolute Values Find each sum. 23 + (–35) The signs are different. Find the difference of the absolute values. 23 + (–35) –12 Course 2 Think: 35 – 23 = 12. Use the sign of the integer with the greater absolute value. Ex # 7: Adding Integers using absolute values Find each sum. –5 + 3 The signs are different. Find the difference of the absolute values. –5 + 3 –2 Course 2 Think: 5 – 3 = 2. Use the sign of the integer with the greater absolute value. Ex # 8: Adding integers using absolute values Find each sum. –13 + (–24) The signs are the same. Find the sum of the absolute values. –13 + (–24) Think: 13 + 24 = 37. –37 Course 2 Use the sign of the two integers. Ex # 9 : Evaluating Expressions with Integers Evaluate x + y for x = –42, y = 71. x+y –42 + 71 29 Substitute for x and y. The signs are different. Think 71- 42 = 29 Use the sign of the integer with the greater absolute value (positive). Helpful Hint When adding integers, think: if the signs are the same, find the sum. If the signs are different, find the difference. Course 2 Ex # 10: Adding integers using absolute values Evaluate x + y for x = –24, y = 17. x+y –24 + 17 –7 Course 2 Substitute for x and y. The signs are different. Think: 24 – 17 = 7. Use the sign of the integer with the greater absolute value (negative). Ex # 11 (Word Problems: Adding Integers) “Application” A roller coaster starts at point A. It goes up 20 feet, down 32 feet, and then up 16 feet to point B. Write an addition sentence to find the height at point B in relation to point A. Find the sum and explain its meaning. . 20 + (-32) + 16 = 36 + (-32) = 4 Add positive integers Find the differences of the absolute values. The answer is positive. Point B is 4 feet higher than point A. Course 2 Ex # 12 (Word Problems: Adding Integers) “Application” Max owes his brother $20. He gives his brother $ 10 one week and then the next week he gives $5. Write an addition sentence to describe this situation. Then find the sum and explain its meaning. . (-20) + 10 + 5 = 15 + (-20) = -5 Add positive integers Find the differences of the absolute values. The answer is negative. Max still owes his brother $5. Course 2 Ex # 13 (Word Problems: Adding Integers) “Application” The jazz band’s income from a bake sale was $286. Expenses were $21. Use integer addition to find the band’s total profit or loss. 286 + (–21) 286 – 21 265 Use negative for the expenses. Find the differences of the absolute values. The answer is positive. The band earned $265. Course 2 Ex # 14 (Word Problems: Adding Integers) “Application” The French Club was raising money for a trip to Washington D.C. Their car wash raised $730. They had expenses of $52. Use integer addition to find the club’s total profit or loss. 730 + (–52) 730 – 52 678 Use negative for the expenses. Find the differences of the absolute values. The answer is positive. The club earned $678. Course 2 Adding Insert Lesson Integers Title Here Now you try a few problems (summary) pg. 1 Use a number line to find the sum. 1. –7 + (–6) –14 –12 –13 –10 –8 –6 –4 –2 0 2 Find each sum. 2. –15 + 24 + (–9) 3. –24 + 7 + (–3) 0 –20 4. Evaluate x + y for x = –2 and y = –15. Course 2 –17 Homework (differentiated) Tues 8-11 •If you got 4 problems correct, complete pg. 23-24 in workbook #’s 11-18 •If you got 3 problems correct, complete pg. 23-24 in workbook #’s 11-14 & # 18 •If you 1 or 2 problems correct, complete pg. 23-24 in workbook #’s 1-11, 13,14,18 •HINT…….Use the properties on pg. 21 to help you answer question # 14. Adding Insert Lesson Integers Title Here Now you try a few problems (summary) pg. 2 5. The math club’s income from a bake sale was $217. Advertising expenses were $32. Use integer addition to find the club’s total profit or loss? $185 profit Course 2