1.2 Adding Integers - Big Ideas Learning
English1.2SpanishAdding IntegersIs the sum of two integers positive, negative,or zero? How can you tell?1EXAMPLE: Adding Integers with the Same SignUse integer counters to find 4 ( 3).Combine 4 negative countersand 3 negative counters. Find the total numberof counters. 4 3 7So, 4 ( 3) 7.2ACTIVITY: Adding Integers with Different SignsWork with a partner. Use integer counters to find 3 2.Remove anyzero pairs.Combine 3 negative countersand 2 positive counters. 3 2So, 3 2 3 What is the totalnumber of counters? 3 2 .EXAMPLE: Adding Integers with Different SignsUse a number line to find 5 ( 3).Add 3.Start at 0. Move 5units to the right. 8 6So, 5 ( 3) 2.8Chapter 1Operations with Integers 4 2Then move 3 unitsleft to end at 2.502468
EnglishSpanish4ACTIVITY: Adding Integers with Different SignsWork with a partner. Write the addition expression shown.Then find the sum.Start at 0. Move 7units to the right. 8 6Then move 10 unitsleft to end at 3.Add 107 4 202468Inductive ReasoningWork with a partner. Use integer counters or a number line to complete the table.ExerciseType of SumSum15. 4 ( 3)Integers with the same sign26. 3 237. 5 ( 3)48. 7 ( 10)Sum: Positive,Negative, or ZeroNegative2Integers with different signs9. 2 410. 6 ( 2)11. 5 912. 15 ( 9)13. 10 1014. 6 ( 6)15. 12 ( 12)16. IN YOUR OWN WORDS Is the sum of two integers positive, negative, or zero?How can you tell?17. Write general rules for adding (a) two integers with the same sign, (b) twointegers with different signs, and (c) an integer and its opposite.Use what you learned about adding integers to completeExercises 8 –15 on page 12.Section 1.2Adding Integers9
English1.2SpanishLessonLesson TutorialsKey VocabularyAdding Integers with the Same Signopposites, p. 10additive inverse, p. 10WordsAdd the absolute values of the integers. Then use thecommon sign.2 5 7NumbersEXAMPLE1 2 ( 5) 7Adding Integers with the Same SignFind 2 ( 4). Use a number line to check your answer.Add 2 and 4 . 2 ( 4) 6Use the common sign.The sum is 6. 4 2Check 7 6 5 4 3 2 101 Add.OppositeWhen you sit acrossfrom your friend at thelunch table, you sitopposite your friend.1. 7 132. 8 ( 5)3. 20 ( 15)Two numbers that are the same distance from 0, but on opposite sides of 0,are called opposites. For example, 3 and 3 are opposites.Adding Integers with Different SignsWordsSubtract the lesser absolute value from the greater absolutevalue. Then use the sign of the integer with the greaterabsolute value.Numbers8 ( 10) 2 13 17 4Additive Inverse PropertyWordsThe sum of an integer and its additive inverse, or opposite,is 0.Numbers10Chapter 16 ( 6) 0Operations with Integers 25 25 0
EnglishSpanishEXAMPLE2Adding Integers with Different Signsa. Find 5 ( 10). 10 5 . So, subtract 5 from 10 .5 ( 10) 5Use the sign of 10.The sum is 5.b. Find 3 7. 7 3 . So, subtract 3 from 7 . 3 7 4Use the sign of 7.The sum is 4.c. Find 12 12. 12 12 0The sum is 0 by the Additive Inverse Property. 12 and 12 are opposites.The sum is 0.Add.Exercises 8–23EXAMPLE34. 2 115. 13 ( 8)6. 9 ( 10)7. 8 48. 7 ( 7)9. 31 31Adding More than Two IntegersThe list shows four bank account transactions in July. Find the changeC in the account balance.JULY TRANSACTIONSFind the sum of the four transactions.C 50 ( 40) 75 ( 50)Write the sum. 10 75 ( 50)Add 50 and 40. 85 ( 50)Add 10 and 75. 35Add 85 and 50.Because C 35, the account balance increased 35 in July.Exercises 28–3310. WHAT IF? In Example 3, the deposit amounts are 30 and 55. Findthe change C in the account balance.Section 1.2Adding Integers11
EnglishSpanishExercises1.2Help with Homework1. WRITING How do you find the additive inverse of an integer?2. NUMBER SENSE Is 3 ( 4) the same as 4 3? Explain.Tell whether the sum is positive, negative, or zero without adding. Explainyour reasoning.3. 8 204. 50 ( 50)5. 10 ( 18)Tell whether the statement is true or false. Explain your reasoning.6. The sum of two negative integers is always negative.7. An integer and its absolute value are always opposites.6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Add.128. 6 49. 4 ( 6)10. 2 ( 3)11. 5 1212. 5 ( 7)13. 8 ( 8)14. 9 ( 11)15. 3 1316. 4 ( 16)17. 3 ( 4)18. 14 ( 5)19. 0 ( 11)20. 10 ( 15)21. 13 922. 18 ( 18)23. 25 ( 9)ERROR ANALYSIS Describe and correct the error in finding the sum.24. 25.9 ( 6) 3 10 ( 10) 026. TEMPERATURE The temperature is 3 F at 7 a.m. During the next four hours,the temperature increases 21 F. What is the temperature at 11 a.m.?27. BANKING Your bank account has a balance of 12. You deposit 60.What is your new balance?Add.3 28. 13 ( 21) 1631. 19 26 1429. 22 ( 14) ( 35)30. 13 27 ( 18)32. 32 ( 17) 4233. 41 ( 15) ( 29)Tell how the Commutative and Associative Properties of Addition can help youfind the sum mentally. Then find the sum.1234. 9 6 ( 6)35. 8 13 ( 13)36. 9 ( 17) ( 9)37. 7 ( 12) ( 7)38. 12 25 ( 15)39. 6 ( 9) 14Chapter 1Operations with Integers
EnglishSpanishALGEBRA Evaluate the expression when a 4, b 5, and c 8.40. a b42. a b c 41. b c43. OPEN-ENDED Write two integers with different signs that have a sum of 25.Write two integers with the same sign that have a sum of 25.MENTAL MATH Use mental math to solve the equation.44. d 12 245. b ( 2) 046. 8 m 1547. FIRST DOWN In football, a team must gain 10 yards to get a first down.The team gains 6 yards on the first play, loses 3 yards on the second play,and gains 8 yards on the third play. Which expression can be used to decidewhether the team gets a first down?10 6 3 86 ( 3) 86 ( 3) ( 8)48. DOLPHIN Starting at point A, the path of a dolphin jumping out of the wateris shown.a. Is the dolphin deeper at point C or point E ? Explain your reasoning.b. Is the dolphin higher at point B or point D ? Explain your reasoning.B 24D 18 13 15ECA49.According to a legend, the Chinese EmperorYu-Huang saw a magic square on the back of a turtle. In amagic square, the numbers in each row and in each columnhave the same sum. This sum is called the magic sum. 1 3Copy and complete the magic square so that each rowand each column has a magic sum of 0. Use each integerfrom 4 to 4 exactly once.1Subtract. SKILLS REVIEW HANDBOOK50. 69 3851. 82 7452. 177 6354. MULTIPLE CHOICE What is the range of the numbers below?53. 451 268SKILLS REVIEW HANDBOOK12, 8, 17, 12, 15, 18, 30A 12 B 15 C 18 Section 1.2D 22 Adding Integers13
Write general rules for adding (a) two integers with the same sign, (b) two integers with different signs, and (c) an integer and its opposite. Use what you learned about adding integers to complete Exercises 8 –15 on page 12. 1.2 Lesson 10 Chapter 1 Operations with Integers Adding Integers with the Same Sign
2 Integers and Introduction to Solving Equations 98 2.1 Introduction to Integers 99 2.2 Adding Integers 108 2.3 Subtracting Integers 116 2.4 Multiplying and Dividing Integers 124 Integrated Review—Integers 133 2.5 Order of Operations 135 2.6 Solving Equations: The Addition and Multiplication Properties 142 Group Activity 151 ocabulary CheckV 152
of Integers using the chips. After using the number line to aid in adding integers, have students write general rules for adding and subtracting integers too large or too small to fit on the sample number line, for example, -14 35. Ask the students who are interested in football to describe how a football field is
Substituting Variable Values in Program Understand how real numbers and integers are treated by the CNC control Real numbers are any number rational or irrational Real numbers include integers 1.25, -.3765, 5, -10 are all real numbers Integers are whole numbers 2500, 3, 20 Numbers with decimals are not integers i.e. 1.25 Some NC words only allow integers
students have mastered addition of integers, subtraction of integers may be introduced. 4 Subtraction of Integers In a subtraction equation, a b c,a is called the minuend ,b is the subtrahend , and c is the difference . Example 5 involves subtracting integers with same signs and Example 6 involves subtracting integers
Inverse property of addition: The sum of a number and its opposite is 0. a 1 (2a) 5 0 2a 1 a 5 0 LESSON 3-7 Gr. 5 NS 2.1: Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results. Gr. 6 NS 2.3: Solve
Positive and Negative Integers 8 Day 2 Objectives: Students will 1. Subtract negative and positive integers 2. Create word problems and scenarios to describe problems with negative and positive integers 3. Explain why pairs of positive and negative chips can be added to help sol
Welcome and Introduction 1 Chapter 1: INTEGERS AND INTEGER OPERATIONS Activity Set 1.1: Modeling Integers with Black and Red Tiles 5 1.1 Homework Questions 7 Activity Set 1.2: Adding Integers with Black and Red Tiles 9 1.2 Homework Questions 13 Activity Set 1.3: Subtracting Integers with Black and Red Tiles 15 1.3 Homework Questions 19
Divis ADVANCED ENGINEERING MATHEMATICS 2130002 – 5th Edition Darshan Institute of Engineering and Technology Name : Roll No. : ion :
