Section 1 Rational Numbers And Order Of Operations

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Foundations of Math 9Updated June 2019Section 1 – Rational Numbers and Order of OperationsThis book belongs to:SectionDue DateDate Handed InBlock:Level of CompletionCorrections Madeand Understood𝟏. 𝟏𝟏. 𝟐𝟏. πŸ‘πŸ. πŸ’πŸ. πŸ“Self-Assessment erging)321.51DescriptionWork meets the objectives; is clear, error free, anddemonstrates a mastery of the Learning TargetsWork meets the objectives; is clear, with someminor errors, and demonstrates a clearunderstanding of the Learning TargetsWork almost meets the objectives; contains errors,and demonstrates sound reasoning and thoughtconcerning the Learning TargetsWork is in progress; contains errors, anddemonstrates a partial understanding of theLearning TargetsWork does not meet the objectives; frequenterrors, and minimal understanding of the LearningTargets is demonstratedWork does not meet the objectives; there is no orminimal effort, and no understanding of theLearning Targetsβ€œYou could teach this!β€β€œAlmost Perfect, onelittle error.β€β€œGood understandingwith a few errors.β€β€œYou are on the righttrack, but key conceptsare missing.β€β€œYou have achieved thebare minimum to meetthe learning outcome.β€β€œLearning Outcomes notmet at this time.”Learning Targets and Self-EvaluationL–T𝟏 𝟏𝟏 𝟐𝟏 πŸ‘Description MarkAccurately perform operations with Integers (Add/Subtract/Multiply/Divide)Estimate and discuss sign of solutions without computingApplying the correct order of operationsIdentifying fractions relationships to decimalsUnderstand the need for a common denominatorApplying concepts of equivalence, simplification, and reciprocal fractionsCorrectly perform addition and subtraction of multiple type of fractionsCorrectly perform multiplication and division of multiple types of fractionsComments:Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Competency EvaluationA valuable aspect to the learning process involves self-reflection and efficacy. Research has shown that authenticself-reflection helps improve performance and effort, and can have a direct impact on the growth mindset of theindividual. In order to grow and be a life-long learner we need to develop the capacity to monitor, evaluate, andknow what and where we need to focus on improvement. Read the following list of Core Competency Outcomesand reflect on your behaviour, attitude, effort, and actions throughout this unit. Rank yourself on the left of each column: 4 (Excellent), 3 (Good), 2 (Satisfactory), 1 (Needs Improvement)I will rank your Competency Evaluation on the right half of each column4PersonalResponsibility Self-Regulation I keep track of my Learning TargetsI take ownership over my goals, learning, and behaviourI can solve problems myself and know when to ask for helpI can persevere in challenging tasksI am actively engaged in lessons and discussionsI only use my phone for school tasks Classroom Responsibility and Communication I am focused on the discussion and lessonsI ask questions during the lesson and classI give my best effort and encourage others to work wellI am polite and communicate questions and concerns with mypeers and teacher in a timely mannerI clean up after myself and leave the classroom tidy when I leaveCollaborativeActions 321I listen during instruction and come ready to ask questionsI am on time for classI am fully prepared for the class, with all the required suppliesI am fully prepared for TestsI follow instructions keep my Workbook organized and tidyI am on task during work blocksI complete assignments on timeI can work with others to achieve a common goalI make contributions to my groupI am kind to others, can work collaboratively and buildrelationships with my peersI can identify when others need support and provide it Communication Skills I present informative clearly, in an organized wayI ask and respond to simple direct questionsI am an active listener, I support and encourage the speakerI recognize that there are different points of view and candisagree respectfully I do not interrupt or speak over othersOverallGoal for next Unit – refer to the above criteria. Please select (underline/highlight) two areas you want to focus on1Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Section 1.1 - IntegersAdding and Subtracting Integers They represents all the countable numbers, both positive and negative( 3, 2, 1,0,1,2,3, ) A great place to start is to understand that subtraction can be shown as adding negatives7 4 7 ( 4)Example:This may seem weird now, but it will come in handy laterIf this helps, think of positive and negatives as:Positive – good thingsNegative – bad things This way when we are adding and subtracting just think of adding good and bad thingsor taking good or bad things awayAll you need to consider then is which did you have more of in the beginningExample: So 6– 2 45 ( 3) 2 4 – 8 1212 14 2 7 4 3 7 ( 2) 9When we subtract negatives don’t think β€˜subtract’, but think – take away5 ( 3)You have 5 good things and you take away 3 bad things Since you don’t have bad things to begin with introduce some in equilibrium (zero) Now you can take away the bad, but it leaves the good you brought.DIAGRAM 5 positives This is 0π‘π‘œπ‘€ π‘¦π‘œπ‘’ π‘π‘Žπ‘› π‘‘π‘Žπ‘˜π‘’ π‘Žπ‘€π‘Žπ‘¦ π‘‘β„Žπ‘’ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘£π‘’π‘ . What are you left with?2Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Example: 4 – ( 3)Use diagrams to solve the following:This situation is easier since we have what weneed to take away. Just take 3 negatives away. π‘π‘œπ‘€ π‘¦π‘œπ‘’ π‘π‘Žπ‘› π‘‘π‘Žπ‘˜π‘’ π‘Žπ‘€π‘Žπ‘¦ π‘‘β„Žπ‘’ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘£π‘’π‘ .4 negativesWhat are you left with?5 – ( 2) 1 negativeπ‘π‘œπ‘€ π‘¦π‘œπ‘’ π‘π‘Žπ‘› π‘‘π‘Žπ‘˜π‘’ π‘Žπ‘€π‘Žπ‘¦ π‘‘β„Žπ‘’ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘£π‘’π‘ . 4 – ( 3) 15 – ( 2) 7What are you left with? 5 positives 6 – (4) This is 08 positivesπ‘π‘œπ‘€ π‘¦π‘œπ‘’ π‘π‘Žπ‘› π‘‘π‘Žπ‘˜π‘’ π‘Žπ‘€π‘Žπ‘¦ π‘‘β„Žπ‘’ π‘π‘œπ‘ π‘–π‘‘π‘–π‘£π‘’π‘ . 6 negativesThis is 015 – ( 15) What are you left with? 6 – (4) 10 10 negativesπ‘π‘œπ‘€ π‘¦π‘œπ‘’ π‘π‘Žπ‘› π‘‘π‘Žπ‘˜π‘’ π‘Žπ‘€π‘Žπ‘¦ π‘‘β„Žπ‘’ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘£π‘’π‘ .15 – ( 15) 30What are you left with? 15 positive This is 030 positives3Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Multiplying and Dividing Integers When multiplying and dividing integers, two wrongs make a right and two rights make a right Same Same is always positiveOpposites are always negative Examples:5 ( 4) 2012 3 4 2 ( 3) 6 18 2 95 ( 4) 20( 7) ( 4) 282 ( 4) 8 ( 4) ( 3) 1215 ( 5) 34Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Section 1.1 – Practice ProblemsExecute the following operations by displaying diagrams of the situation (same as examples above)1.3 ( 2)2.( 5) ( 7)3.3 ( 5)4.12 75. 7 4Add the following Integers without a calculator6.4 77.4 ( 7)8.( 4) ( 7)9. 4 710.4 3 611.4 ( 3) 612.10 5 ( 12)13.4 ( 5) 1214. 4 ( 5) 715. 7 3 ( 5)5Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Subtract the following Integers without a calculator16.18 517. 18 718. 4 ( 7)19.4 720. 13 8 ( 4)21. 15 6 322. 7 ( 4) ( 6)23. 12 ( 15) 424.14 ( 5) 925.21 ( 7) 10Add and Subtract the following decimal integers without a calculator26. 4.06 1.8327. 5.637 ( 3.71)28.4.06 1.8329. 5.637 ( 3.711)30.7.204 ( 1.8)31. 7.204 ( 1.8)Multiply and Divide the following integers without a calculator32. 4 733. 4 ( 7)34.2 ( 9)35. 4 736.4 3 637.4 ( 3) 638.10 5 ( 12)39.4 ( 5) 1240. 40 ( 5)41. 72 342. 112 243. 200 544. 70 2 ( 1)45.28 ( 4) ( 3)46. 56 ( 8) ( 6)47.720 3 ( 3)6Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Section 1.2 - FractionsFractions – A Closer Look What are they? They are rational numbers, which means they can be written as aterminating (stops) or repeating decimal Everything we do with fractions is dependent on if we know what a fraction is to begin with.What is a Fraction? Piece of a wholePiece of somethingSomething broken into piecesAnd this is the representation:Number of Pieces you Have712Number of Pieces that Make a WholeConsider this: If you have 5 pieces and they are all one fifth in size, you have a whole.5Think about a Kit Kat bar, 5 pieces all the same size, makes 1 bar!5The whole that is broken in to pieces is always the same size, namely:1If you have 4 pieces of size 4 and 24 pieces of size 24, the whole they create is the same size.Example:SAME size WHOLE, DIFFERENT size PIECES7Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9 So now let’s estimate some fractions on a number line:Put these numbers on the line, why did you choose where you did?13551112780 1The distinguishing thing about fractions is that every fraction is either a terminating(ends) or repeating decimal number. Numbers that neither terminate nor repeat cannot be expressed as fractions, 𝑃𝑖 (πœ‹)being the most famous example, but there are an infinite number of themConverting from a Fraction to a Decimalo We can figure out the decimal expansion of any fraction, using good old fashion longdivisionExample:Write57as a decimal numberWe’ve seen this number before,this is the repeat pointThis reads 5 divided by 70.71428577So,πŸ“πŸ• 𝟎. πŸ•πŸπŸ’πŸπŸ–πŸ“50540000000 09107302820146056403550We’ve seen this number before8Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9EquivalenceEquivalence is a term that means β€˜the same value’ Two or more fractions can be equivalent, which means they have the same value, butthey look differentExample:12is the same as2341546830etc.The question is now do we get there?We multiply the original fraction by 1. The catch is that anything divided by itself is one.So by multiplying by 1, we use a fraction instead, that will give us the desired denominator.1 3 5 21 4 156 𝑒𝑑𝑐3 5 21 4 156So to make equivalent fractions we multiply the original fraction by 1, in the form of afraction.Example:135794 ?615?16 1357942226315321436416 9Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Comparing Fractions In order to accurately compare two or more fractions we need to make sure all thepieces are the same size. That means we need a common denominator.2Example:and32348412 Since3491236473,4bigger thanis bigger than3963127 8848856 Since12and4956273878,78749756 bigger thanis bigger than485667Mixed vs Improper FractionsImproper fractions: are fractions where the numerator (top number) is bigger than thedenominator (bottom number)Example:135,113Mixed fractions: are fractions with a whole number and a proper fractionExample:13 ,427 ,325610Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Converting from Mixed to Improper and Vice-Versa Again, think about your pieces (size and number)So, 114means that you have 11 pieces and 4 make a wholeLet’s break that down then,4 4 3 11 4So we can have44344 We still have 11 pieces of size 4.And since44is 13We can write it as 1 1 4114 23or 2 434Vice Versa235means we haveWe can say we have,21 1 1 555but since we can write 1 as55217555525 35517511Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Section 1.2 – Practice QuestionsPlace the following fractions on the number line below, add markings to justify your reasoning21.310Why:32.810Why:73.1210Why:Convert the following two fractions to decimals, show all the division steps4.55.84712Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9What makes two fractions equivalent? Why does changing to another form not changethe value of the original fraction? Give me an example.6.Convert the following fractions to equivalent fractions with the given denominator.7.10.13.16.34 416445100 121314319.8. 41694611.14.17.2439 17 911187 41449.12.15.99418.28121567 44542124936 58 432When attempting to compare two fractions, what makes it very easy?13Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Compare the following fractions using , , . Justify your reasoning.20.23.26.2345373 21.48 24.105 27.81225 502233 6622.25.13 28.136 712138811 971267Convert the following fractions from MIXED to IMPROPER or VICE VERSE229.3 32. 535.38.7173 311 236 130. 4 33.2 36. 39.456194235 6 34. 437. 331.40.5187 310 3310 14Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Section 1.3 – Fractions Cont. The Simplified Form of a fraction is when it is reduced down so the numerator anddenominator have no common factors The process is the same as finding equivalent fractions, but instead of multiplying, we divide The best way to understand this is to understand the prime factors of each number.28Example: this is not simplified54Right away I see that both numbers have a factor of 2 in common, but let’s go further.Break both numbers down into prime factors. The Prime Factors of 28 are:2, 2, π‘Žπ‘›π‘‘ 7 The Prime Factors of 54 are:2, 3, 3, 3, So, when you see factors that they have in common, divide out those common factors2854214227 - The only factors left aren’t common, so it’s simplified This concept of division is where the idea of cancelling out factors comes fromWhat this means is we can rewrite2854as2 2 72 3 3 3 Then when you have the same factor on the top and the bottom, they divide to give 1.And 1 multiplied by anything is doesn’t change it. We can therefore say that when you have the same factor on top and bottom theycancel out.2 2 72 2 72 714 2 3 3 3 2 3 3 3 3 3 3 27 The outcome of canceling out the factors is the Same as the division of the common factors Both work!15Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Adding and Subtracting Fractions There is often a lot of stress and frustration when we get to operations with fractionsOnce you can grasp what a fraction is and how to make equivalent fractions the rest isactually quite straightforwardIn order to accurately add or subtract fractions what do we need? Remember, the numerator: pieces we have and denominator: number of pieces in a whole.Naturally what is required is that the pieces that make up the whole are the same sizeSo what do we need?We need a COMMON DENOMINATOR (Same sized pieces), we get that using equivalent fractionsLet’s do some examples:Example:135173 753777321 15 21 2221The Lowest Common Denominator in this case is 21, so we just multiplythe fractions by each others denominator as a fraction over itselfExample:Example:67123647 5162 4372444728 353366 21285866 ,328but we can simplify that,862423 The Lowest Common Denominator in this case is the denominator ofone of the two fractions, so we just multiply one of the fractions bywhatever multiple gets us the desired resultExample:31013510 1235210 210 11016Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Adding and Subtracting Mixed FractionsIt is good form and will limit errors if you always CONVERT from Mixed to Improper Fractionsbefore doing the operations.Example:13342 1132 1 34Example:7 7 3 45768 5 257 5 2 68 7 4 7 3 3 4 4 335 23 6828 21 12 12 35 4 23 3 64 8 3712 140 69 2424 7124The Lowest Common Denominator in this case is 24, so multiply thefractions by whatever multiple gets us the desired resultExample:2413521 3 42411 3 4 352 5 19 9 3 5 250 114 135 30 30305 10 19 6 9 15 3 10 5 6 2 15293017Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Section 1.3 – Practice ProblemsSimplify the following fractions1.5.1236 14212. 6.24120 10503. 7.2344681827 4. 8.36481177 Add the following fractions, leave answers in simplified form9.11.13.15.17.152713342 5 810.12. 14.21255 642755 235 2153144 11124 7215316.3 418. 2 3358618Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Subtract the following fractions, leave answers in simplified form19.21.23.25.3578342 5 920.173 143122. 24.3 426. 2 3115642535 217 221733548Perform the combined operations, leave answers as an improper fraction in simplified form27.29.345263 413826 5 2 4510322531528.2 4 ( 1)30. 3 1 ( 3 )12543619Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Section 1.4 – Multiplying and Dividing FractionsMultiplication of Fractions It is simply TOPS with TOPS and BOTTOMS with BOTTOMSπ‘π‘’π‘šπ‘’π‘Ÿπ‘Žπ‘‘π‘œπ‘Ÿ οΏ½οΏ½π‘šπ‘–π‘›π‘Žπ‘‘π‘œπ‘Ÿ e:Example:Example:Example:2352 573 7 594 7211 5 149 4 10 35 16511 4 3 7 5 1 65 11 536 12 35 655 5361235 655Simple enough?Now, what we can do though is SIMPLIFY the question first by identifying the Common Factors,just like when we simplified individual fractions.Example:14492 7can be written as:27 1 277 7and since77is equal to 1 what we have left is:see how we cancelled out the common factors20Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Now Watch this 2Example:7We can do the same steps before we multiply5 82 5 7 825 7 2 42 5 2 4 72 5 2 4 755 4 7 28Let’s try some.5Example:12 5 3 12 20 2 9 3 1421 42 36 153Example: 6 2 12 353 3 4 4 529314 Example:Example:32036 61211 4 4 16( 1)2 3 3 3 2 7( 1)2 3 3 3 2 7( 1) 3 33 777421533 76 7 6 6 3 3 17 5 3 3 4 4 5Remember ( 2) ( 1) 2 2 3 3 3 2 7215 3 3 4 4 5 3 7 6 7 6 6 3 3 173 7 6 7 6 6 3 3 177 749 6 3 17 30623( 1) 2 3 ( 1) 2 2 2 33( 1) 2 3 ( 1) 2 2 2 3 3 ( 1) 2 3 ( 1) 22 2 3 31321Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Division of Fractions First I’ll show you the somewhat complicated but quite gorgeous method.You may have been told somewhere along the line that dividing fractions is just flipping thesecond fraction and changing the division sign to multiplication, how many of you heard thisbefore?Do you know why?Here’s why.Example:1 2 𝑀𝑒𝑙𝑙 π‘‘β„Žπ‘’ π‘“π‘Ÿπ‘Žπ‘π‘‘π‘–π‘œπ‘› π‘π‘Žπ‘Ÿ π‘’π‘ π‘ π‘’π‘›π‘‘π‘–π‘Žπ‘™π‘™π‘¦ π‘šπ‘’π‘Žπ‘›π‘  π‘‘π‘–π‘£π‘–π‘ π‘–π‘œπ‘› π‘ π‘œ 𝑀𝑒 π‘π‘Žπ‘› π‘Ÿπ‘’π‘€π‘Ÿπ‘–π‘‘π‘’ π‘‘β„Žπ‘–π‘  π‘Žπ‘  2 31223 𝑦𝑒𝑠 𝑖𝑑 𝑖𝑠 π‘œπ‘›π‘’ 𝑏𝑖𝑔 π‘“π‘Ÿπ‘Žπ‘π‘‘π‘–π‘œπ‘›, π‘šπ‘Žπ‘‘π‘’ 𝑒𝑝 π‘œπ‘“ π‘‘π‘€π‘œ π‘“π‘Ÿπ‘Žπ‘π‘‘π‘–π‘œπ‘›π‘ Now let’s make this into an equivalent fraction with a denominator of one. Remember thatin order for it to be equivalent we need to multiply the big fraction by 1.1 3 2 2 π‘‘β„Žπ‘–π‘  π‘ π‘’π‘π‘œπ‘›π‘‘ π‘π‘œπ‘Ÿπ‘‘π‘–π‘œπ‘› 𝑖𝑠 π‘’π‘žπ‘’π‘Žπ‘™ π‘‘π‘œ 12 33 2So what do we get 1 3 1 32 2 2 2 1 3612 26We ended up with,1 3 2 2So what has happened? The division symbol changed to multiplication and the fraction flipped.And the result is:1 3 2 2 3422Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Now here is another method, the logic here is awesome Consider our starting point 1 2 β„Žπ‘œπ‘€ π‘π‘Žπ‘› 𝐼 𝑑𝑖𝑣𝑖𝑑𝑒 𝑒𝑝 𝑝𝑖𝑒𝑐𝑒𝑠 𝑖𝑓 π‘‘β„Žπ‘’π‘¦ π‘Žπ‘Ÿπ‘’ π‘‘β„Žπ‘’ π‘ π‘Žπ‘šπ‘’ 𝑠𝑖𝑧𝑒?2 3If I get a COMMON DENOMINATOR:1 3 2 6π‘Žπ‘›π‘‘So my equation now looks like:2 4 3 63 4 6 6If you now divide the same sized pieces,3 4 3 4 3 46 61Example:Example:23 34BOOM!57Flip MethodDenominator Method2 5 2 7 14 3 7 3 5 152 5 14 15 14 15 14 15 14 3 7 21 21 21 211151213 611Flip MethodDenominator Method12 612 112 11 𝟐𝟐 13 11 13 613 1πŸπŸ‘12 6132 78132 78132 78 13 11 142 142 142 1421 132 66 𝟐𝟐 7839 πŸπŸ‘Simplified both of these to get our final answer.23Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Section 1.4 – Practice QuestionsMultiply the following, simplify before you multiply if desired, leave answer in simplified form1.3.5.13 1214514122.7 78 ( 2110) 1574.6.821916 825 354 72421 25 148Divide the following fractions, simplify when you can, leave answer in simplified form7.9.23 12589 438. 10.4 4158121524Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 911.13.34121 13171755 393412. 14.3827 3431255718 4925Answer the following, leave answer as a simplified fraction, improper if applicable11315.3 217. 5 319.3 1 12253148112316.3 218. 5 32520.3 2132132517416 11825Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Section 1.5 – Order of Operation – BEDMAS or PEDMAS There is a sequence of solving equations, an order to follow, just like a recipe.It goes like this:B – Brackets:Get inside any brackets then start the list again, are there more?Otherwise continue.E – Exponents:Solve any exponential statement and write as a resultD – Division:Do any multiplication and division statements at the same timefrom left to rightM – Multiplication:Do any multiplication and division statements at the same timefrom left to rightA – Addition:Do any remaining addition and subtraction at the same time,from left to rightS – Subtraction:Do any remaining addition and subtraction at the same time,from left to rightExample:2 3 5 56 5 56 17Example:42 2 6 316 2 6 332 6 338 33526Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Example:5(2 3 6) 4 25(5 6) 4 25( 1) 4 2( 5) 4 2 20 2 10Example:5 {62 2(5 2 3)}5 {62 2(3 3)}5 {62 2(6)}5 {36 2(6)}5 {18 6}5 {108}113Example:(15 4 5 5 2 3)2(15 4 1 2 3)2(15 4 1 6)2(11 1 6)2(12 6)2(6)23627Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Section 1.5 – Practice QuestionsCalculate the following using your Order of Operations1.6 2 32.2 3 2 43.4 6 5 34.16 8 4 25.12 3 16 86.25 18 6 107.7 3 10 28. 6 2 4 2Calculate the following using your Order of Operations9.6 (2 3)10.(6 2) 311. 8 (5 3)12.( 8 5) 313. (8 3) (3 7)14.100 (10 5)15.(128 32) 216.5 10 (7 3) 228Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Calculate the following using your Order of Operations17.3 2318.(3 2)319. 5 3220.( 5 3)221.23.24 22 25 2322.6 3 46 3 424.(24 22 ) (25 23 )(6 3)(4)(6 3)(4)Simplify the following using your Order of Operations25.27.12 2[(20 8) (1 32 )]20 4 {2 32 [3 (6 2)]}26.28.( 2)3 423 52 3 640 13 243(2 5) 229Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Answer KeySection 1.11.1 (See Diagram)2. 12 (See Diagram)3.8 (See Diagram)4.5 (See Diagram)5. 11 (See Diagram)6.117. 38. 119.310.1311.712.313.1114. 215. 916.1317. 2518.319. 320. 1721. 2422.323. 124.1025.1826. 2.2327. 9.34728.2.2329. 1.92630.9.00431. 9.00432. 2833.2834. 1835. 2836.7237. 7238. 60039. 24040.841. 2442. 5643. 4044.3545.2146. 4247.720Section 1.21.See Diagram2.See Diagram3.See 𝑠 π‘‰π‘Žπ‘Ÿπ‘¦7.128. 69.3610. 8011. 212.1813.15614.8115.816.2817.7218.2019.20. 21. 22. 23.CommonDenominator 24. 25. 26. 27. 28. 32. 36. 440. 329.33.37.23717624730. 1744334. 38. 3105631.33535.539.4233458113531030Adrian Herlaar, School District 61www.mrherlaar.weebly.com

Foundations of Math 9Section 1.31334231115111511611π‘œπ‘Ÿ 7 15151523 34472π‘œπ‘Ÿ 31515422π‘œπ‘Ÿ 8 551.4.7.10.13.16.19.22.25.28.2.155. 38.11.14.17.20.23.26.29.2172312541π‘œπ‘Ÿ 1848427934π‘œπ‘Ÿ 7 35351 141 12513 π‘œπ‘Ÿ 688151 π‘œπ‘Ÿ 7223.126. 59.3512. 215.18.21.24.27.30.11191235245887π‘œπ‘Ÿ 1 1211π‘œπ‘Ÿ 1 24221 21 π‘œπ‘Ÿ 1 2111129π‘œπ‘Ÿ4124Section 1.41.475.712. 6 or 1 6 28 or 1 286. 247.9.3510.511.13. 314. 5 or 1 517. 1818. 50 or 1 50451723.7781215.3119.34341011491or 8 66183or 3 554.28258. 512. 916.20.3or 1 252432321or 1 2or 112Section 1.51.122.143.94.125.26.127. 18. 189.010.711. 1012. 1613. 914.5015.216.5517.2418.21619. 1420.6421.1622.1623.124.125.1626. 227.1628.131Adrian Herlaar, School District 61www.mrherlaar.weebly.com

individual. In order to grow and be a life-long learner we need to develop the capacity to monitor, evaluate, and know what and where we need to focus on improvement. Read the following list of Core Competency Outcomes and reflect on your behaviour, attitude, effort, and actions throughout this unit. 4

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1. Rational Numbers: Students will understand that a rational number is an integer divided by an integer. Students will convert rational numbers to decimals, write decimals as fractions and order rational numbers. 2. Adding Rational Numbers: Students will add rational numbers. 3. Subtracting Rational Numbers: Students will subtract rational .

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