Add And Subtract Fractions - Nelson
Add and Subtract FractionsFractions have been a part of our lives for a long time. In ancient times,Sumerians, Babylonians, Romans, Egyptians, Greeks, Chinese, andArabians all used fractions.The Eye of Horus was used by ancient Egyptians to represent fractions.It was a powerful symbol that they believed protected against evil.According to an old myth, Horus’ eye was torn out, broken into pieces,and then put back together.What You Will Learnφto find a common denominator and use itto write equivalent fractionsφto add and subtract fractions with unlikedenominatorsφφto add and subtract mixed numbersKey Wordsmultiplecommon denominatorimproper fractionmixed numberto solve fraction problemsMATH LINKEach part of the Eye of Horus was afraction. When all the parts were puttogether, it was believed that the eyewas whole again. Ancient Egyptiansthought that the parts had a combinedvalue of 1. Were they correct? In thischapter, you will explore fractionsthrough history and around the b LinkTo learn more about the ancient Egyptian myth of the Eye of Horus,go to www.mathlinks7.ca and follow the links.228NEL Chapter 7
;DA967A:H /-ÌÕ ÞÊ/ Make the following Foldable to organizewhat you learn in Chapter 7.Step 1 Staple seven sheets of notebookpaper together along the top edge.Step 2 Make a line 9 cmup from thebottom of thetop page. Cutacross the entirepage at thismark.Step 3 Make a line 7.5 cm up from thebottom of the second page. Cutacross the entire page at this mark.Step 4 Cut across a line 6 cm up from thebottom of the third page.Step 5 Cut across a line 4.5 cm up fromthe bottom of the fourth page.Step 6 Cut across a line 3 cm up from thebottom of the fifth page.Step 7 Cut across a line 1.5 cm up fromthe bottom of the sixth page.Step 8 Label thetabs formedas shown.Chapter 7 Add and Subtract FractionsKey Words71727374What I Need to Work On.LiteracyLinkAs you work through Chapter 7, takenotes under the appropriate tab.Include information about the keywords, examples, and key ideas.Chapter 7 NEL229
Common DenominatorsFocus on After this lesson, youwill be able to.φ find a commonφdenominator for aset of fractionscompare andorder positivefractionsJasmin and Tyler collect trading cards. Jasmin has collected 31 of a set.of a set. They want to know who has more cards.Tyler has collected 14Jasmin and Tyler need to compare the fractions. It is easier to comparefractions when the denominators are the same. So, Jasmin and Tylerneed to find a common denominator.How can you determine a common denominator? coloured pencils230NEL Chapter 71.Fold a piece of paperinto 3 equal parts.of the paper red.Shade 132.Fold the same piece ofpaper into 4 equal partsthe other way.
How many equal parts is the paper divided into?b) Count how many parts you shaded red. Name an equivalent1 using your answer to part a) as the denominator.fraction for31 of the4. Fold a different piece of paper into 4 equal parts. Shade4paper blue.3. a)5.Fold the piece of paper into 3 equal parts the other way.6.Count how many parts you shaded blue. Name an equivalent1.fraction for4Reflect on Your FindingsWhat is the relationship between the denominators 3 and 4, andthe denominator 12?b) What is one method for determining a common denominator ?7. a)commondenominator a common multiple ofExample: Determine a Common Denominator.Determine a common denominator for 2 and 13221b) Determine equivalent fractions for and using the common32denominator from a).a)the denominators of aset of fractions a commondenominator for 14is 12 because aand 16common multiple of4 and 6 is 12SolutionMethod 1: Use Paper Folding or Diagramsa) Divide a rectangle into 3 equal parts. Either fold a pieceof paper, or draw a rectangle.Fold the paper or divide the rectangle into 2 equal partsthe other way.There are 6 parts in the rectangle.2 and 1is 6.A common denominator for32b)of the rectangle red.Shade 234 of the 6 parts are red.2 43 6Turn the paper over, or draw another rectangleand divide it as in step a).of this rectangle blue.Shade 121 33 of the 6 parts are blue.2 67.1 Common Denominators NEL231
multiple the product of a givennumber and a naturalnumber like 1, 2, 3,and so on for example, somemultiples of 3 are 3, 6,9, 12, and 15Method 2: Use Multiples1 is 2.a) The denominator of2Multiples of 2 are 2, 4, 6, 8, 10, 12, is 3.The denominator of 23Multiples of 3 are 3, 6, 9, 12, 15, Model ItRefer to page xvi.6 is divisible by both 2 and 3.So, multiples of both 2 and 3will be multiples of 6:6, 12, 18, The first multiple divisible by both 2 and 3 is 6.A common denominator is 6.b)StrategiesYou can use divisibilityrules to find multiples.You could use any multiple of 6 as thecommon denominator, but the firstmultiple is often better to use. Thedenominator will be a smaller number,which is easier to work with.Write equivalent fractions using 6 as the denominator. 3 21 32 62 4 3 23To determine equivalent fractions,multiply the numerator and denominatorby the same number. This process doesnot change the value of the fraction.6Check:Use pattern blocks.2 43 6 –12–36 –23–46Determine a common denominator for each pair of fractions. Thenuse the common denominator to write equivalent fractions. Showtwo different methods.51a) and 3b) and 13846232NEL Chapter 7
You can use paper folding, diagrams, or multiples to determinea common denominator.Paper Folding or Diagrams5 of the 10 parts are blue.6 of the 10 parts are red.6531 5 102 10Multiples1 is 2. Multiples of 2 are 2, 4, 6, 8, 10, The denominator of23 is 5. Multiples of 5 are 5, 10, 15, 20, The denominator of5A common denominator is 10. To write fractions with a commondenominator, determineequivalent fractions. 551 210 51. 23 6510 2Tina wanted to find a common denominator and equivalent3 and 2. This is what she did:fractions for53Was she correct? If not, what was her error?b) Draw diagrams to show what she should have done.c) Discuss your diagrams with a classmate.a)2.3.3 and 5is 12.” MekoIan says, “A common denominator for46says, “I think it is 10.” Do you agree with Ian or Meko? Why?How can you use multiples to find a common denominator for3?1,2, andthe fractions2 547.1 Common Denominators NEL233
7.Use a diagram to determine a commondenominator for each pair of fractions.Then write equivalent fractions using thecommon denominator.a) 3 and 1b) 5 and 3c) 1 and 15836428.Use multiples to determine a commondenominator for each set of fractions.Then write equivalent fractions using thecommon denominator.5,51, anda) 1 and 2b) 1 and 1c)52348 6129.Using multiples, determine a commondenominator for each set of fractions.Then use the common denominator towrite equivalent fractions.71,2, anda) 3 and 1b) 1 and 1c)5 3846410For help with #4 to #9, refer to the Example onpages 231–232.4.Use the folded papers shown to determinea common denominator and equivalentfractions for each pair of fractions.a)14231234b)5.Look at the diagrams to determine acommon denominator and equivalentfractions for each pair of fractions.a)1366.23414Draw a diagram to determine a commondenominator for each pair of fractions.Then use the common denominator towrite equivalent fractions.a) 1 and 1b) 2 and 1c) 1 and 2523356NEL Chapter 7Determine a common denominator foreach pair of fractions. Which is the largerfraction in each pair?3 135 36a) ,b) ,7 494 1611 312c) ,d) , 430 1027 911.Draw a Venn diagram like the one shownto list common denominators that are less1 and1.than 50 for4635b)510.Multiplesof 4Multiplesof 6
5 of a schoolyard is taken up by grass.127 is the track. The rest is pavement.18a) What common denominator could beused to compare these fractions?b) Does the grass or the track take upmore space?12.Fill in the blanks to make equivalentfractions. 1 a) 4812 16 20 24 285 7 14 112b) 3 5 24 12 6 3 48 9c) 56 10 5 15 d) 3048 96 3216.13.Fill in each blank with a numerator tomake the statement true. Provide as manyanswers as possible. Use diagrams to showhow you determined your answers.1 a) 34 2 41 b) 53 6 62 c) 45 10 517. a)14.Determine a common denominator forthe set of fractions. Use the commondenominator to write an equivalentfraction for each fraction. Then list thefractions in order from least to greatest.5,3, 111,2,,3 4 6 3 4 215.The ancient Greeks thought of numbersas being represented by rectangles. Theywould have made a rectangle like this torepresent 6:How could this rectangle be used to find1 and 1?a common denominator for23Explain.b) Use a rectangle to find a common3 and1.denominator for74Copy the shapes. For each shape,3.colour in8Which shapes were more difficult tocolour in? Which were easier? Explain.c) Imagine you are using paper folding todetermine a common denominator for32. Which of the shapes would itand58be possible for you to use? Show thework by drawing the fold lines on theshapes.d) Compare your drawings with aclassmate’s.b)18.Write as many different proper fractionsin lowest terms as you can that havedenominators from 2 to 9 and numeratorsthat are positive numbers.19.Which of the following fractions is closest3?to1091 B21ACD 25100404a)7.1 Common Denominators NEL235
You have three beakers that are the samesize. 2 of beaker 1 contains oil. 1 of34beaker 2 contains water. Beaker 3 isempty. When you pour the liquids intobeaker 3, the level of the combined liquidscorresponds exactly to one of themarkings on the side of beaker 3. Whichof the following beakers is beaker 3?20.AB21.The table shows the fraction of the totalnumber of students at Maple LeafElementary School that are in each grade.740320117253626180171801390KindergartenGrade 1Grade 2Grade 3Grade 4Grade 5CDGrade 6Which grade has the greatest numberof students?b) Which grade has the least numberof students?c) Which two grades have the samenumber of students?d) If there are 54 students in grade 1,what is the total number of studentsin the school?a)MATH LINK–18a) Determine a common denominator for the fractionsin the Eye of Horus. Show your work.b) Use this common denominator to determine an–12–141––16equivalent fraction for each part in the eye.1––64236NEL Chapter 71––32
Add and Subtract FractionsWith Unlike DenominatorsFocus on 1After this lesson, youwill be able to.φ add and subtractφφfractionswith unlikedenominatorssolve problemsinvolving theaddition andsubtraction offractionscheck that youranswers arereasonable usingestimation1–61–31–2How could you use pattern blocks to model addition and subtraction?How can you add and subtract fractions with unlikedenominators?1?What two pattern blocks would you use to represent 1 and231 1 is using these two patternb) Can you tell what the answer to2 3blocks? Explain.1. a). What fraction doesUse the green triangles to represent 1 and 123each green triangle represent?1 1is now? Explain.b) Can you tell what the answer to2 32. a)1?andWhat pattern blocks would you use to represent 1261 1is using these twob) Can you tell what the answer to2 6pattern blocks? Explain.3. a) pattern blocks coloured pencils1.Use the green triangles to represent21 1is now? Explain.b) Can you tell what the answer to2 6c) How many green triangles are left?4. a)Reflect on Your Findings5.How can you use pattern blocks to help you add and subtractfractions with unlike denominators?7.2 Add and Subtract Fractions With Unlike Denominators NEL237
Example 1: Add Fractions With Unlike DenominatorsAdd. Write the answer in lowest terms.11 3 6Is the sumclosest to,,01–2or?1SolutionMethod 1: Use Fraction Strips1 13 6 To add, you need to use parts that are the same size.1. Count the parts.Each part represents61 1 33 6 6Write the answer in lowest terms.3 16 2Method 2: Draw a Diagram1 13 6 To add, you need to use parts that are the same size.1 1 33 6 6StrategiesSolve a SimplerProblemRefer to page xvii. Write the answer in lowest terms.3 16 2238NEL Chapter 7
Method 3: Use a Common Denominator1 is 3.The denominator of3Multiples of 3 are 3, 6, 9, 12, is 6.The denominator of 16Multiples of 6 are 6, 12, 18, 24, The first multiple divisible by both 3 and 6 is 6.A common denominator is 6.Write equivalent fractions with 6 as the denominator.1 1 2 13 6 6 6 1 Add the numerators. 263 6Write the answer in lowest terms. 33 16 2 3Check:Use pattern blocks.Web LinkIscloser to–1 –13 6or–12?1. The answer is reasonable.It equals 12To learn more aboutadding fractions, go towww.mathlinks7.caand follow the links.LiteracyAdd. Write each answer in lowest terms.11 4 2a) 1b)c) 42 86 310 5LinkWhen the numeratorequals thedenominator, thefraction is equal to 1.163 1 11637.2 Add and Subtract Fractions With Unlike Denominators NEL239
Example 2: Subtract Fractions With Unlike DenominatorsSubtract.1 22 5Is thedifferencecloser to0or?1–2SolutionMethod 1: Use Fraction Strips1 22 5, you needTo subtract 25parts that are the same size.––Subtract.1 2 12 5 10Check:1?1 closer to 0 orIs102051 0 102 100 , or 0.1 is a little more than1010Method 2: Draw a Diagram12 2 5, you needTo subtract 25parts that are the same size.Subtract.1 2 12 5 10Method 3: Use a Common Denominator1 is 2.The denominator of2Multiples of 2 are 2, 4, 6, 8, 10, is 5.The denominator of 25Multiples of 5 are 5, 10, 15, 20, 240NEL Chapter 7Compare this to theestimate you madebefore yousubtracted.–
The first multiple divisible by both 2 and 5 is 10.A common denominator is 10.Write equivalent fractions with 10 as the denominator.5 12 4 2 5 10 105 4Subtract the numerators. 101 10Subtract. Write each answer in lowest terms.321 a) 3b) 1c) 13 44 84 2 When adding and subtracting fractions using models or diagrams,show each fraction using parts of the whole that are of equal size.Pattern BlocksDiagram – 1 3 21 2 11 4 2 3 6 63 6 6 6 To add or subtract fractions with unlike denominators, use acommon denominator. You can estimate when adding or subtracting fractions by, or 1.comparing fractions to 0, 121.alike? How are they different?How are 1 and 2361 1?How would you use diagrams to calculate4 2b) Compare your answer with a classmate’s.2. a)3.4?1 1 without changing 1toWhy is it difficult to calculate2 82 87.2 Add and Subtract Fractions With Unlike Denominators NEL241
8.For help with #4 to #7, refer to Example 1 onpages 238–239.4.5.a) Write each addition statementshown by the fraction strips.Estimate and then add.a) b) c) For each diagram, write an additionstatement. Then add.b) For help with #9 to #12, refer to Example 2 onpages 240–241.9.a) b) 10.c)7.242NEL Chapter 7a)–b)–c)–For each diagram, write a subtractionstatement. Then subtract.–b)Add. Write your answers in lowest terms.5 11a) 2 b)5 108 4151 c)d) 34 53 12311e)f) 1 2 58 6Determine the sum. Write your answersin lowest terms.31 1 5a)b)12 62 842 2c)d) 110 53 92 1 3e)f) 15 26 4Write each subtraction statementshown by the fraction strips.Estimate and then subtract.a) 6.Write each addition statement shown bythe pattern blocks. Then add.–c)–11.Subtract. Write your answers in lowestterms.3 35 1a)b)5 106 21 1 1c)d) 72 108 25 5 2e) 2f)3 58 12
12.13.Determine the difference. Write youranswers in lowest terms.3 111 5a)b)4 812 62 1 1c)d) 13 26 95 112 1e)f)5 46 1515.16.A friend shows you the following work foran addition problem.11 2 4 3 7a) Explain the error in your friend’s work.b) Use a diagram to show the correctanswer.17.An airplane was loading in Pond Inlet forits flight to Iqaluit, Nunavut. The planewas 1 full of passengers and 1 full of63cargo. How much space was left?18.You can use a number line to show9.21 3 12 12Write each subtraction statement shownby the pattern blocks. Then subtract.a)–b)–14.The students mademuffins in cookingclass. They get totake some muffinshome. There are12 muffins in amuffin tray.1 of a tray.”a) John says, “I’m taking4of a tray.”Katie says, “I’m taking 13What fraction of a tray are John andKatie taking altogether?b) Marjoe says, “I’m taking 1 of a tray.”61 of a tray.”Sandeep says, “I’m taking12What fraction of a tray are Marjoe andSandeep taking altogether?Zach was leading in a swimming race by 581of a length. He won the race by a length.2By how much did the second-placeswimmer catch up by the end of the race?2 8– ––3 121––128 9–– ––12 1201Draw number lines to add the fractions.13 3a) 1b) 1 1c)4 42 810 519.You can use a number line to show7.21 3 12 1228– ––3 1201––127 8–– ––12 121Draw number lines to subtract the fractions.1 11 1a)b)c) 5 12 84 126 47.2 Add and Subtract Fractions With Unlike Denominators NEL243
22.20.The ancient Egyptians thought the fractionsin the Eye of Horus added up to 1. Werethey correct? Show your work.The sum of each row, column, and diagonalin this magic square must equal 1. Copy thesquare and fill in the –32Water is pumped into a pool. Afterof the pool is filled.one hour, 15a) After 3 h, how full is the pool?b) How long does it take in total to fillthe pool? 57121413 12A tangram is a squarepuzzle that is dividedinto seven shapes.1.a) Suppose piece A is4What are the valuesof pieces B, C, D, E,F, and G?The Egyptians of 3000 B.C.E. used only unit fractions. These are fractions with a1, and1. They wrote all other fractions as sums of unit1,numerator of 1, such as423fractions. For example, 5 1 16 2 331 1 4 2 4These sums are called Egyptian fractions.a) Add the unit fractions. Use diagrams to show your work.11 11 4 83 9b) Which one of the two sums in a) is greater? By how much?512c) How would ancient Egyptians have written as the sum of two unit fractions?244NEL Chapter 7DEFBAWhat is the sum of A and B?c) Subtract the value of D from the whole.d) Which two tangram pieces add up tothe value of C?e) Make a problem of your own usingtangram pieces. Have a classmate solve it.b)MATH LINK CG
Add Mixed NumbersFocus on After this lesson,you will be able to.φ add mixedφφnumbers withlike and unlikedenominatorssolve problemsinvolving theaddition ofmixed numberscheck that youranswer isreasonable usingestimationAfter the class pizza party, there5 vegetarian pizzaswere 1 5 cheese pizzas and 166left over. How many pizzas were left over in total?To find out, you need to add mixed numbers .How do you add mixed numbers?mixed numbers a number made up ofa whole number and a1fraction, such as 23StrategiesExample 1: Add Mixed Numbers With Like DenominatorsAdd. Write the answer in lowest terms.5 15166SolutionMethod 1: Use Pattern BlocksModel ItRefer to page xvi. Add the whole yellow hexagons. Add the green triangles. 5 155 5 1 1 1666 67.3 Add Mixed Numbers NEL245
Move 1 green triangle to thehexagon with 5 green trianglesto make 1 whole hexagon.There are now 3 whole hexagons and 4 green triangles. 3 41 1 1 466Write the answer in lowest terms. 3 23463StrategiesSolve a SimplerProblemRefer to page xvii.improper fraction a fraction that has anumerator greaterthan the denominator,9such as8 Method 2: Use an Addition Statement5 1 1 55 Add the whole numbers. 1 15666 65 5 2 Add the fractions.610 2 6 4Write the improper fraction as a mixed number. 2 66 6 2 1 4You can use diagrams.64 36 Write the answer in lowest terms. 25 5 3 41 1 6 66 3 23463 2Check:5 2 2 115662 2 4is a little less than the estimate of 4. The answer is reasonable.323Add. Write each answer in lowest terms.1 211 252 2b) 3a) 1c) 333663 3246NEL Chapter 7
Example 2: Add Mixed Numbers With Unlike DenominatorsHow many pies are there in total?1 apple pies.12SolutionMethod 1: Use Pattern Blocks1 apple pies23Strategies Model ItRefer to page xvi. 2 11123Add the whole yellow hexagons. Add the red trapezoid and blue rhombus. 1 1 1 3 1 2 12 32 3and 1, you need to use pattern blocks that are the same size.To add 123 There are 5 green triangles altogether.1 1 3 53 2 365 365There are 3 pies.67.3 Add Mixed Numbers NEL247
StrategiesSolve a SimplerProblemRefer to page xvii.The Arabs were thefirst people to use afraction bar:1fraction bar5Method 2: Use an Addition Statement1 21 1 2 11 1232 32 Add the whole numbers. 1 2 36 6 2 3 36 63 2Add the numerators. 3 6 3 565 36pies altogether.There are 3 56Check:1 2 2 211232 2 4is a little less than the estimate of 4.356The answer is reasonable.Add. Write each answer in lowest terms.3 11 412 13a) 2b) 1c) 35 22634 When adding mixed numbers with like denominators, you can– add the whole numbers– add the fractions When adding mixed numbers with unlike denominators, you can– determine a common denominator for the fractions– add the whole numbers– add the fractions To check your answer, compare the answer to an estimate.248NEL Chapter 7Use multiples to determinea common denominator.Multiples of 2 are 2, 4, 6, 8, Multiples of 3 are 3, 6, 9, 12, Use 6 as a commondenominator.You can use diagrams. 1 2 3 3 2 56 6 6
1.2.3 egg salad sandwiches areham sandwiches and 2After dinner, 1 124left. Jeremy and his sister want to use 4 of the leftover sandwichesfor their lunches tomorrow.a) Are there enough sandwiches, not enough sandwiches, or morethan enough sandwiches left over?b) Describe the method you used to find your answer.c) Solve the problem using another method.Which method that you used in #1 did you prefer? Explain.How would you use estimation to check your answer in #1?b) Compare your estimate with a partner’s.3. a)6.Add. Write your answers in lowest terms.Check your answers using estimation.c) 3 1 1a) 1 1 1 1b) 3 1 5 533884478124 3d) 2e) 3 1f) 4 1 7551010997.Determine the sum. Write your answers inlowest terms.2 211 15b) 3c) 5 4 2a) 155889 93 47 6 111 23e) 2d) 2f) 45 5121244For help with #4 to #7, refer to Example 1 onpages 245–246.4.Write each addition statement shown.a) b) c)5. For help with #8 to #11, refer to Example 2 onpages 247–248.For each of the following, write theaddition statement.a)Write each addition statement shown.a) b)b) c)8. c) 7.3 Add Mixed Numbers NEL249
9.For each of the following, write anaddition statement.a)14. b) 15.c) 10.11.12.13.250Add. Write your answers in lowest terms.3 111 21a) 2b) 3510263531c) 2d) 5 462 10512 75e) 4 3f) 274312Determine the sum. Write your answers inlowest terms.1 211 32a) 4b) 353621141c) 1 5d) 4 55415103 591 e) 1f) 64 62 103 h and then walked forSusie ran for 14h. For how long did she travel?2143 pages of homeworkKathleen did 14before dinner. After dinner, she didof a page. In total, howanother 78many pages of homework didKathleen do?NEL Chapter 716.17.The camp cook uses 1 1 dozen eggs to2make pancakes. She uses another 3 1 dozen3for scrambled eggs. How many dozen eggsdoes she use altogether? Check youranswer using estimation.Chef Dimitri finished cutting 1 1 trays4of spinach pie before his break. After histrays. How manybreak he cut another 2 23trays of pie in total did he cut? Includediagrams with your answer.1 h for her mathJenny studied 13h for her science test. Fortest and 34how long did she study in total? Checkyour answer using estimation.Jonas and Amy collect comic books. Jonasboxes of Granite Guy comics andhas 211022 boxes of Quest of Koko comics. Amy3boxes of Alpha Woman comics andhas 2 5631 boxes of Quest of Koko comics.5a) Who has the larger collection?b) How many boxes of Quest of Kokocomics do Jonas and Amy ownaltogether?7c) Jonas trades10of a box ofcomics to Amyfor her GraniteGuy DVD. Howmany boxes ofcomics does shehave now?
18.19.At the school’s spring fair they sold3 pepperoni pizzas,1 vegetarian pizzas, 6534cheese pizzas.and 4 56a) Draw diagrams to show how much ofeach pizza was sold.b) Estimate, then calculate how muchpizza was sold altogether.20.The movie started 2 h 12 min ago.5 h.The movie will end in 16a) What is the total length of the movie inhours written as a fraction?b) If the movie started at 2:15 p.m., whendid the movie end? Write the time as afraction.Melissa is in training for a rowingcompetition. She keeps track of the hoursshe practises. At the end of the week, shetotals her hours.Hours PractisedSunMonTuesWedThursFriSat2342141 341121141 12This week she had a goal to practisefor a total of at least 10 h. Estimatewhether she met her goal.b) How many hours did she practise?c) Was your estimate reasonable? Explain.a)MATH LINKEgyptian fractions can be useful today. Suppose you have 13 sacksof rice to divide among 8 people. That means each person would5 sacks.get 18sacks of rice if you do not have aHow can you give each person 1 58calculator or scale?First, give each person 1 whole sack. Then, use Egyptian5 sack:fractions to determine how to give each person85 1 18 2 8sack, plus 1sack.The Egyptian fraction shows that you should give each person 1281 sack to each person, there will be 1 sack left.After you give21.You then divide this sack into 8 and give each person8The diagram shows that each person gets1 sack and 1sack.1 whole sack, plus28How would you divide the following?StrategiesSolve a SimplerProblemRefer to page xvii.a) 7 sacks of potatoes among 4 peopleb) 7 bags of flour among 5 peoplec) 9 loaves of bread among 5 people7.3 Add Mixed Numbers NEL251
Subtract Mixed NumbersFocus on After this lesson,you will be able to.φ subtract mixedφφnumbers withlike and unlikedenominatorssolve problemsinvolving thesubtraction ofmixed numberscheck that youranswers arereasonable usingestimationAfter Lucy worked on her art project, she had 2 43 jars of paint left.jars of paint to finish her painting. How much paintLater, she used 1 14is left now?How do you subtract mixed numbers?Example 1: Subtract Mixed Numbers With Like DenominatorsSubtract. Write the answer in lowest terms.3 11244SolutionMethod 1: Use Fraction Strips3 11244Subtract.252NEL Chapter 7–
2 fraction strips.There are now 14Write the answer in lowest terms. 1 11242Method 2: Use a Subtraction StatementSubtract the whole numbers.2 1 1Subtract the fractions.31 2 4 4 41 1 2 123444StrategiesSolve a SimplerProblemRefer to page xvii.You can use diagrams.2–1 1Write the answer in lowest terms. 2 1 112423124–4 4 2Check:3 11 3 12443 1 2is close to the estimate of 2.112The answer is reasonable.Subtract. Write each answer in lowest terms.73231a) 2 1b) 3 1c) 4 1384 4387.4 Subtract Mixed Numbers NEL253
Example 2: Subtract Mixed Numbers With Unlike DenominatorsSubtract.3 11382SolutionMethod 1: Use Fraction Strips–3 - 11382and 1, you need to use parts that are the same size.To subtract 382.You cannot subtract 4 from 3888.Take 1 whole strip from 3 3 and make it the equivalent fraction88Subtract.–7 strips left.There are 181 1 7 133828Method 2: Use a Subtraction Statement and RegroupUse multiples to determine a common denominator.Multiples of 2 are 2, 4, 6, 8, Multiples of 8 are 8, 16, Use 8 as a common denominator.3 1 41 3 13388283. You need to regroup.fromYou cannot subtract 488254NEL Chapter 7
3.Regroup 1 whole from 383 2 8 3388 8 2 1183411Subtract the whole3 1 2 148888numbers and subtract 1 7the fractions.8You can use diagrams.11 – 14 172888Method 3: Use a Subtraction Statement and Improper FractionsDetermine a common denominator.3 13 1 41 338288from 3.You cannot subtract 488You can use diagrams.You can change to improperfractions.3 14 27 123Subtract.888815 152712 –88 88 1 7 1788Check:1 31 1 1 13382221 2 13122is a little less than the estimate of 2. The answer is reasonable.178Subtract. Write each answer in lowest terms.31 321b) 4a) 3 1 1c) 4 7844 852Chinese fractions do not have a fraction bar. A symbol is used that represents the1 is written or spoken as “1 part of 2.”words “part of” or “parts of.”27.4 Subtract Mixed Numbers NEL255
When subtracting mixed numbers with like denominators, you can– subtract the whole numbers– subtract the fractions When subtracting mixed numbers with unlike denominators, you can– determine a common denominator for the fractions– subtract the whole numbers– subtract the fractions Sometimes, mixed numbers need to be regrouped or changed to improperfractions before subtracting.Regroup5 311 1 5 14388886 28 234Change to Improper Fractions3 15 35 134888822 8 2 68 2 34 To check your answer, compare to an estimate.1.bottles of pop were left. The next day, Jack’sAfter Jack’s party, 2 341family drank 2 bottles. How much pop is left now? Discuss with a4partner how you would solve this problem.5?1 1What do you need to do before you can calculate 26125.1 1b) Determine the answer to 2612c) Use estimation to check your answer. What method did you use?d) With a partner, compare how you calculated the answer to5 . Then compare the method you used to check your answer. 1216122. a)256NEL Chapter 7
For help with #7 to #10, refer to Example 2 onpages 254–255.For help with #3 to #6, refer to Example 1 onpages 252–253.3.7.For each set of fraction strips, write thesubtraction statement.Write a subtraction statement for eachset of fraction strips.a)–a)–b)b)c)––c)––4.Write a subtraction statement to representeach diagram.a)–8.b)–For each diagram, write a . Write your answers inlowest terms. Check your answersusing estimation.2 1 1 5 5a) 1b) 6 755881711c) 3 1d) 3 112441251 e) 2f) 4 1 176 6Determine the difference. Write youranswers in lowest terms.5 2 1a) 4 3 1b) 2 199333294c) 5 1d) 4 25105107 2 7e) 5 4f) 3 51288–9.Subtract. Write your answers inlowest terms. Check your answersusing estimation.71 1a) 6 3 2b) 4 102 5557 31c) 7d) 5 2 2915633642e) 1 1f) 2 14 7537.4 Subtract Mixed Numbers NEL257
10.11.12.Determine the difference. Write youranswers in lowest terms.32 11 11a) 3b) 1510345151c) 7 5d) 4 294612331 e) 3f) 2 1 4456 41hKaren goes t
8. Use multiples to determine a common denominator for each set of fractions. Then write equivalent fractions using the common denominator. a) 1_ 2 and 2_ 5 b) 1_ 3 and 1_ 4 c) 5_ 8 1_and 6 _5 12 9. Using multiples, determine a common denominator for each set of fractions. Then use the common denominator to write equivalent fractions. a .
1. Adding 2. Subtracting 3. Multiplying 4. Dividing 5. Order of Operations FRACTIONS 6. Mixed Numbers 7. Prime Factorization 8. Least Common Multiple 9. Simplifying Fractions 10. Add & Subtract Fractions 11. Add & Subtract Mixed Numbers 12. Multiply Fractions 13. Divide Fractions DECIMALS 14. Decimals to Fractions 15. Add & Subtract Decimals 16 .
Add and Subtract Fractions Practice to review I can add and subtract fractions that have the same denominators! Think about combining groups to add. Think about separating or comparing groups to subtract. 3!eighths 1!eighth _eighths 3!eighths 1!eighth _eighths Think about equivalent fractions to find the simplest form. 3 8 1 8 .
New Jersey Student Learning Standards for Mathematics 5 Number and Operations—Fractions 5.NF. A. Use equivalent fractions as a strategy to add and subtract fractions. 1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent .
Exercise Worksheets . Add & Subtract Fractions 11. Add & Subtract Mixed Numbers 12. Multiply Fractions 13. Divide Fractions DECIMALS 14. Decimals to Fractions 15. Add & Subtract Decimals 16. Multiply Decimals 17. Divide Decimals . Worksheet #3 Multiplying Whole Numbers 46 x 72 205 x 34 493 x 67 800 x 30 376 x 18 776 x 98 2309 x 278 79,248 x .
Adding & Subtracting fractions 28-30 Multiplying Fractions 31-33 Dividing Fractions 34-37 Converting fractions to decimals 38-40 Using your calculator to add, subtract, multiply, divide, reduce fractions and to change fractions to decimals 41-42 DECIMALS 43 Comparing Decimals to fractions 44-46 Reading & Writing Decimals 47-49
Adding and Subtracting Fractions Objective 1: Adding or subtracting fractions with common denominators When adding or subtracting fractions, all you need to do is add or subtract the numerators if the denominators are the same. Example: Add or subtract. Remember to leave all fractions in lowe
Grade 4 Lesson 17 Equivalent Fractions Lesson 20 Add and Subtract Fractions Lesson 21 Add and Subtract Mixed Numbers Grade 5 Lesson 12 Add Fractions with Unlike Denominators REINFORCE Math Center Activity Grade 5 Lesson 12 Fraction Addition: True or False! EXTEND Enrichment Activity Grade 5 Lesson 12 Addition Grids
Fractions Prerequisite Skill: 3, 4, 5 Prior Math-U-See levels Epsilon Adding Fractions (Lessons 5, 8) Subtracting Fractions (Lesson 5) Multiplying Fractions (Lesson 9) Dividing Fractions (Lesson 10) Simplifying Fractions (Lessons 12, 13) Recording Mixed Numbers as Improper Fractions (Lesson 15) Mixed Numbers (Lessons 17-25)
