LESSON Absolute Value
LESSON8Absolute ValuePlug InUnderstanding Absolute ValueThe absolute value of a numberis its distance from 0 on anumber line. 25 means “the absolute valueof 25.”You can use a number line tohelp you find the absolute valueof a number.5 4 3 2 10The distance from 25 to 0 is 5units. That means the absolutevalue of 25 is 5.1I can think ofabsolute value as adistance.Wordsto1 25 5 5I get it! Since a distanceis always positive, theabsolute value of a numberis always positive.Count the numberof units from thepoint to 0.absolute valuea number’s distance from 0 on a number lineKnow05 4 3 2 1The point is on 25 on thenumber line.number linea line that shows numbers placed in order4 3 2 1DISCU S S012348910Can an absolute value be 0? Explain.A You can find the absolute value of a positive number.DO1Plot the number 7 on anumber line.2Count the number ofunits to 0.374Find 7 .This distance is theabsolute value.7Think: I need to find the absolute value of1There are 7 501234units from 0 to 7.567.Duplicating any part of this book is prohibited by law. 2014 Triumph Learning, LLC 23 means “the absolute value of 23.”L e ss o n 8CC13 Mth G6 SE Final.indd 7421/05/13 11:37 AM
8 Absolute ValueB You can find the absolute value of a negative number.DOFind 210 .1Draw a point on a numberline for 210.2Count the number of unitsto 0.3This distance is theabsolute value.Think: I need to find the absolute value of 210 .10 9There are876 210 5232011I get it! Taking the absolutevalue of a positive numberdoesn’t change the number.Taking the absolute valueof a negative numbermakes it positive.keeping or changing its sign.14units from 210 to 0.C You can find the absolute value of a number byDO5Find 12 and 250 .positiveThe absolute value of a number is always.Think about the meaningof absolute value.Since 12 is already positive, to find 12 remove the absolute valueWrite the absolute values.symbols andits sign.Since 250 is negative, to find 250 remove the absolute valuesymbols and change its sign from 12 5to.and 250 5PRACTICEDuplicating any part of this book is prohibited by law. 2014 Triumph Learning, LLCDraw a point on a number line to show the integer and find its absolute value.12 4 55 4 3 2 1012345 22 55 4 3 2 1012345Find the absolute value of the integer.3 28 54 15 55 2126 575CC13 Mth G6 SE Final.indd 7521/05/13 11:37 AM
POWER UPFinding Opposites on a Number LineNegative numbers are to the left of 0 andpositive numbers are to the right of 0.The numbers 5 and 25 both have an absolutevalue of 5. They are both 5 units away from 0.25 and 5 are opposites. 25 5 5 5 5 5012345Numbers are opposites when theyhave the same absolute value butare on different sides of 0.Positive and negativenumbers are on oppositesides of zero on the numberline.WordstoKnowpositive numbera number greater than zero1512345I get it! The numbers 5and 25 are both 5 unitsfrom 0 on the number line,but have opposite signs.negative numbera number less than zerooppositesnumbers that have the sameabsolute value but differentsigns215read as “negative fifteen”CU S SDIS05 4 3 2 115 and 215 are opposites.Does every whole number, fraction, integer, and decimal except 0 have an opposite?Explain.A You can use a number line to find the opposite of a positive number.DO76Find the opposite of 7.1Determine which side of0 the given number is on.Draw a point.2Count the same numberof units in the oppositedirection from 0 anddraw a point.3Write the answer.The number 7 is7units to the8 7 6 5 4 3 2 1To find its opposite, countThe opposite of 7 is0of 0.123units to the.45678of 0.Duplicating any part of this book is prohibited by law. 2014 Triumph Learning, LLC5 4 3 2 1L e ss o n 8CC13 Mth G6 SE Final.indd 7621/05/13 11:37 AM
8 Absolute ValueThe opposite of apositive numberis negative, andthe opposite of anegative numberis positive.B You can use a number line to find the opposite of a negative number.DO123Find the opposite of 24.to theCount the samenumber of units in theopposite direction from0 and draw a point.unitsof 0.06 5 4 3 2 1To find its opposite, count123456units to theThe opposite of 24 isWrite the answer.CU S SDIS4The number 24 isDetermine which sideof 0 the given numberis on. Draw a point.of 0.On the number line below, locate a number (other than 0) and its opposite. What is theopposite of the opposite of your original number? Explain.8 7 6 5 4 3 20112345678PRACTICEFind the opposite of the number shown on the number line.125 4 3 2 101Duplicating any part of this book is prohibited by law. 2014 Triumph Learning, LLCThe opposite of 23 is23455 4 3 2 1.01The opposite of 2 is2345.Plot the number on the number line. Then, find its opposite and plot it on the number line.328The opposite of 28 is.10 9 8 7 6 5 4 3 2 146The opposite of 6 is0123456789100123456789101011.10 9 8 7 6 5 4 3 2 1Use the number line to find the opposite of the opposite of the given number.5The opposite of the opposite of 12 is.15 14 13 12 11 10 9 8 7 6 5 4 3 2 1012345678912 13 14 1577CC13 Mth G6 SE Final.indd 7721/05/13 11:37 AM
READY TO GOAbsolute ValueYou can find the absolute valuesof all rational numbers, whichinclude integers.You can use absolute value tofind and compare distances froma reference point.The numbers you work with inthe real world are often rationalnumbers.The elevation 35.5 feet is35.5 feet above sea level.The elevation 235.5 feet is35.5 feet below sea level.You can use the absolute valueof a number to describe its size,or its distance from a referencepoint.35.5 feet and 235.5 feet areboth 35.5 feet from sea level,but in opposite directions.The reference point is 0 feet,or sea level.The absolutevalue of a rationalnumber is itsdistance from 0!WordstoKnowI get it! I can use the absolutevalue of a real-world quantityto describe it in real terms.rational numbera number that can be written as a ratio of two integers170.75, 215, 0, 7 2 , 22.5, 9 CU S SDescribe the temperature 24 F, using its absolute value. What is the reference point inthis case?lesSon linkPlug InPOWER UPA number line can help youfind the absolute value of anumber.A number line can help youfind opposite numbers.3 2 13 2 101 22 5 2782301222 and 2 are opposites.3GO!I see! I can useabsolute value todescribe positiveand negative rationalnumbers in real-worldsituations!Duplicating any part of this book is prohibited by law. 2014 Triumph Learning, LLCDISL e ss o n 8CC13 Mth G6 SE Final.indd 7821/05/13 11:37 AM
8 Absolute ValueThe absolute valueof the negativebalance describesthe size of her debt!work togetherYou can describe a real-worldsituation using absolute value. A balance of 2 35.23 meansnegative 35 dollars and 23cents.Jeanne spent more money than she had in herbank account, and her balance is now 2 35.23.How much does Jeanne owe the bank? The absolute value of 235.23 is35.23. 235. 23 5 35. 23 The reference point is a balanceof 0, where Jeanne would haveno money in her account and notowe the bank any money, either.A negative balance means money owed. The balance of 2 35.23means that Jeanne owes the bank 35.23. Jeanne has a debt of 35.23.A Use absolute value to describe the situation.DOA treasure chest is buried at 225 feet. How many feet below the ground is the treasure chest?.1Determine the reference point.The reference point is2Find the distance from thereference point.The distance from the reference point is the absolute valueof 225.3Describe the situation. 225 5The treasure chest is.Duplicating any part of this book is prohibited by law. 2014 Triumph Learning, LLCB Write a positive or negative number for the situation described.DOBjorn wrote a check for 45.85 to the electric company. Write a number to represent thechange in Bjorn’s checking account.1Determine the reference point.2Determine the distance from thereference point.3Determine whether the distance isin a positive or negative direction.4Write a number., which would representThe reference point is no change to Bjorn’s account.The distance from the reference point isThe amount on the check will be taken from Bjorn’schecking account and given to the electric company.So, Bjorn’s account is losing the money. The number.should beThe number to describe the situation isCU S SDIS.When dealing with a bank account, a credit is money added to the account and a debit ismoney taken out. For the terms credit and debit, which would be described by a positivenumber and which would be described by a negative number?79CC13 Mth G6 SE Final.indd 7921/05/13 11:37 AM
Ready to GopracticeFind the absolute value of the number represented by the point on the number line.101123The absolute value is456789105432101.210987The absolute value is6.Find the absolute value of the number.34 45.2 5 12124 2 5REMEMBERThe absolutevalue of a numberis always positive.Determine the reference point. Use absolute value to describe the situation.A kite flies up 30 feet. How far is the kite from the ground?HINTThe distanceis the absolutevalue of thenumber.The reference point is 30 5The kite is6feet from the ground.A giant squid swims at 2800 feet. How far is the squid from thesurface of the ocean?.The reference point is 2800 5The squid isfeet from the surface.Determine the reference point. Describe the situation.7Hafid agrees to pay his neighbor 25 for mowing his lawn.The reference point is8Janna bakes a cake in an oven that is 350 F.The reference point is80.Duplicating any part of this book is prohibited by law. 2014 Triumph Learning, LLC5L e ss o n 8CC13 Mth G6 SE Final.indd 8021/05/13 11:37 AM
8 Absolute ValueWrite a positive or negative number for the situation described.9The temperature is 12 F below zero.The temperature is10 A hot-air balloon is 150 feet in the air. F.The hot-air balloon’s elevation isfeet.Write a positive or negative number to describe each person’s account balance.11 Cole owes the bank 21.15.12 Dominic opened a bank accountby depositing a check for 250.I know! A depositmeans puttingmoney intothe bank.Use absolute value to represent each situation. Then solve.13 Gail’s checking account shows a balanceof 265.34. How much debt does Gailshow in her checking account?14 The depth of a lake was written as 228 21 feet.Duplicating any part of this book is prohibited by law. 2014 Triumph Learning, LLCHow many feet below the surface is thebottom of the lake?CU S SDISPutting It TogetherA hiker and a scuba diver both start at sea level. After an hour, the hiker is at an elevation of 67.5 feet,and the scuba diver is at an elevation of 288.1 feet. How can you use absolute value to explain whetherthe hiker or diver is farther from sea level?81CC13 Mth G6 SE Final.indd 8121/05/13 11:37 AM
Ready to GoProblem solvingDEBIT OR CREDIT?READTamila had 75.80 in her bank account. The bank creditedher account 35.45 and then debited the account 40.Does her account have less than or more than 75.80after these transactions?PLAN What is the problem asking you to find?If Tamila’s account hasthan orthan now What do you need to know to solve this problem?The reference point is.A credit is anumber and a debit is anumber.If the credit is more than the debit , then the account has more thanthe reference point. If the credit is less than the debit , then the accounthas less than the reference point. How can you solve this problem?Compare the absolute values of theThe credit can be described by the numberThe debit can be described by the number.Find the absolute values. 35.45 5 240 5Compare the absolute values.The credit isTamila’s account hasCHECKthan the debit .than the reference point now.Check the problem by using addition and subtraction. 75.80 1 35.45 52 40 5.Does Tamila’s account have more than or less than 75.80?82.If I compare theabsolute valuesof the credit anddebit, I can solvethe problem withmental math!Duplicating any part of this book is prohibited by law. 2014 Triumph Learning, LLCSOLVEandL e ss o n 8CC13 Mth G6 SE Final.indd 8221/05/13 11:37 AM
8 Absolute ValuepracticeUse the problem-solving steps to help you.12The ground floor of a building is floor 0. Jeremy got intothe elevator and pushed the button marked 3. Alana wentdown one flight of stairs to the basement. Write a numberto describe each person’s position in the building, relativeto the ground floor.CHECKLISTReadPlanJeremy’s position can be described by the number.SolveAlana’s position can be described by the number.CheckTalia and Robert opened accounts at the same bank on thesame day. After the first week, Talia’s balance was 55.67and Robert’s balance was 2 2.17. Use absolute value todescribe each person’s account balance.CHECKLISTReadPlanSolveDuplicating any part of this book is prohibited by law. 2014 Triumph Learning, LLCCheck3A football coach uses negative numbers for yards awayfrom the other team’s goal line. He uses positive numbersfor yards closer to the other team’s goal line. After the firstplay, the coach says that the ball’s position is positive 12.What does that mean?CHECKLISTReadPlanSolveCheck83CC13 Mth G6 SE Final.indd 8321/05/13 11:37 AM
22 and 2 are opposites . The absolute value of a rational number is its distance from 0! I get it! I can use the absolute value of a real-world quantity to describe it in real terms. I see! I can use absolute value to describe positive and negative rational numbers in real-world s
Absolute Value Functions Lesson 4-7 Today’s Vocabulary absolute value function vertex Learn Graphing Absolute Value Functions The absolute value function is a type of piecewise-linear function. An absolute value function is written as f(x) a x-h k, where a, h, and k
4 Step Phonics Quiz Scores Step 1 Step 2 Step 3 Step 4 Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 . Zoo zoo Zoo zoo Yoyo yoyo Yoyo yoyo You you You you
1.1 Lesson 4 Chapter 1 Operations with Integers Key Vocabulary integer, p. 4 absolute value, p. 4 Absolute Value Words The absolute value of an integer is the distance between the number and 0 on a number line. The absolute value of a number a is written as a . 01 4 units 4 units 52 4 3 2 1 34 5
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The mean absolute deviation of a set of data is the average distance between each data value and the mean. 1. Find the mean. 2. Find the distance between each data value and the mean. . Sixth Grade Seventh Grade 88 116 94 108 112 124 144 91 97 122 128 132 9.The table shows the lengths of the longest bridges in the United BRIDGES States and in .File Size: 2MBPage Count: 6Explore furtherMean Absolute Deviation Worksheet 1.pdfdocs.google.comMean Absolute Deviation Worksheetswww.mathworksheets4kids.comMean Absolute Deviation Calculatorwww.alcula.comGrade 6 McGraw Hill Glencoe - Answer Keys Answer keys .www.mathpractice101.comMean Absolute Deviation Worksheet - Houston ISDwww.houstonisd.orgRecommended to you b
De nition 1.18. An absolute value kkthat satis es the stronger triangle inequality kx yk max(kxk;kyk) is called nonarchimedean (otherwise it is archimedean). The trivial absolute value is nonar-chimedean, as are all p-adic absolute values on Q. In fact, the absolute value jjis essentially the only archimedean absolute value on Q (as we shall see).
Participant's Workbook Financial Management for Managers Institute of Child Nutrition iii Table of Contents Introduction Intro—1 Lesson 1: Financial Management Lesson 1—1 Lesson 2: Production Records Lesson 2—1 Lesson 3: Forecasting Lesson 3—1 Lesson 4: Menu Item Costs Lesson 4—1 Lesson 5: Product Screening Lesson 5—1 Lesson 6: Inventory Control Lesson 6—1
Nutrition is an integral aspect of animal husbandry and the pet food trade now makes up a substantial proportion of the animal care industry. Providing animals with the appropriate feeds in the correct quantities, taking into account factors such as species, breed, activity level and age, requires an understanding of the fundamentals of animal nutrition. A balanced diet is vital to the .
