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FractionsPacketContentsIntro to Fractions . page 2Reducing Fractions . page 13Ordering Fractions page 16Multiplication and Division of Fractions page 18Addition and Subtraction of Fractions . page 26Answer Keys . page 39Note to the Student: This packet is a supplement to your textbookFractions PacketCreated by MLC @ 2009 page 1 of 42
Intro to FractionsReading FractionsFractions are parts. We use them to write and work with amounts that are lessthan a whole number (one) but more than zero. The form of a fraction is onenumber over another, separated by a fraction (divide) line.i.e.1,23,4and59These are fractions. Each of the two numbers tells certain information aboutthe fraction (partial number). The bottom number (denominator) tells how manyparts the whole (one) was divided into. The top number (numerator) tells howmany of the parts to count.1says, “Count one of two equal ports.”23says, “Count three of four equal parts.”45says, “Count five of nine equal parts.”9Fractions can be used to stand for information about wholes and their parts:EX. A class of 20 students had 6 people absent one day. 6 absentees arepart of a whole class of 20 people.6represents the fraction of people20absent.EX. A “Goodbar” candy breaks up into 16 small sections. If someone ate 5of those sections, that person ate5of the “Goodbar”.16Fractions PacketCreated by MLC @ 2009 page 2 of 42
Exercise 1 Write fractions that tell the following information:(answers on page 39)1.Count two of five equal parts2.Count one of four equal parts3.Count eleven of twelve equal parts4.Count three of five equal parts5.Count twenty of fifty equal parts6.It’s 25 miles to Gramma’s. We have already driven 11 miles. Whatfraction of the way have we driven?7.A pizza was cut into twelve slices. Seven were eaten. What fraction ofthe pizza was eaten?8.There are 24 students in a class. 8 have passed the fractions test.What fraction of the students have passed fractions?The Fraction Form of OneBecause fractions show how many parts the whole has been divided into andhow many of the parts to count, the form also hints at the number of partsneeded to make up the whole thing. If the bottom number (denominator) isfive, we need 5 parts to make a whole:55need 18 parts to make a whole of 18 parts:1 . If the denominator is 18, we18181 . Any fraction whose topand bottom numbers are the same is equal to 1.Example:221,441,1001001,11111,661Fractions PacketCreated by MLC @ 2009 page 3 of 42
Complementary FractionsFractions tell us how many parts are in a whole and how many parts to count.The form also tells us how many parts have not been counted (the complement).The complement completes the whole and gives opposite information that canbe very useful.3says, “Count 3 of 4 equal parts.” That means 1 of the 4 was not counted and4is somehow different from the original 3.13143andmakeimplies another(its complement). Together,, the whole44444thing.5says, “Count 5 of 8 equal parts.” That means 3 of the 8 parts have not been83538counted, which implies another , the complement. Together, and make,8888which is equal to one.Complementary SituationsIt’s 8 miles to town, We have driven 5 miles. That’shave 3 miles to go to get there or3of the way.85 3 8 1 (1 is all the way to town).8 8 8A pizza was cut into 12 pieces. 7 were eatenleft or5of the way, but we still87. That means there are 5 slices1257512of the pizza. 1 (the whole pizza).1212 1212Mary had 10 dollars. She spent 5 dollars on gas, 1 dollar on parking, and 3dollars on lunch. In fraction form, how much money does she have left?513, parking , lunch 10101051391 ;is the complement (the leftover money)10 10 10101010Altogether it totalsor all of the money.10Gas Fractions PacketCreated by MLC @ 2009 page 4 of 42
Exercise 2(answers on page 39)Write the complements to answer the following questions:1.A cake had 16 slices. 5 were eaten. What fraction of the cake wasleft?2.There are 20 people in our class. 11 are women. What part of the classare men?3.It is 25 miles to grandma’s house. We have driven 11 miles already.What fraction of the way do we have left to go?4.There are 36 cookies in the jar. 10 are Oreos. What fraction of thecookies are not Oreos?Reducing FractionsIf I had 20 dollars and spent 10 dollars on a CD, it’s easy to see I’ve spent halfof my money. It must be that10201. Whenever the number of the part (top)2and the number of the whole (bottom) have the same relationship betweenthem that a pair of smaller numbers have, you should always give the smallerpair answer. 2 is half of 4. 5 is half of 10.210andand many other fractions.20415is the reduced form ofand210A fraction should be reduced any time both the top and bottom number can bedivided by the same smaller number. This way you can be sure the fraction is assimple as it can be.5both 5 and 10 can be divided by 51055 5 110 10 5 215describes the same number relationship that21015numbers.is the reduced form of.2106both 6 and 8 can be divided by 2.868did, but with smaller6 28 234Fractions PacketCreated by MLC @ 2009 page 5 of 42
36is the reduced form of.48When you divide both the top and bottom numbers of a fraction by the samenumber, you are dividing by a form of one so the value of the fraction doesn’tchange, only the size of the numbers used to express it.12161216226These numbers are smaller but they can go lower86 6 2 3because both 6 and 8 can be divided by 2 again.8 8 2 418 18 2 99 3 324 24 2 12 12 3 4276327 363 39219 321 337or276327 963 937Exercise 3 (answers on page 39)Try these. Keep dividing until you can’t divide anymore.1.6 82.12 153.14 184.8 105.6 126.16 24Good knowledge of times tables will help you see the dividers you need toreduce fractions.Here are some hints you can use that will help, too.Hint 1If the top and bottom numbers are both even, useHint 2If the sum of the digits is divisible by 3 then use2.23.3111looks impossible but note that 111 (1 1 1) adds up to three and 231 (2 3 1)231adds up to 6. Both 3 and 6 divide by 3 and so will both these numbers:111231111 3231 33777The new fraction doesn’t look too simple, but it is smaller than when we first started.Fractions PacketCreated by MLC @ 2009 page 6 of 42
Hint 3If the 2 numbers of the fraction end in 0 and/or 5, you can divide by457045 570 59145.5Hint 4If both numbers end in zeros, you can cancel the zeros in pairs, one from thetop and one from the bottom. This is the same as dividing them bycancelled pair.4000500004000500004504 250 210for each10225Hint 5If you have tried to cut the fraction by2 3 5, ,and gotten nowhere, you2 3 5should try to see if the top number divides into the bottom one evenly. For23, none of the other hints help here, but 69692323 23 23 1reduce by.69 69 23 32323 3. This means you canFor more help on reducing fractions, see page 13Exercise 4(answers on page 39)Directions: Reduce these fractions to lowest 58.63819.91210.11.175112.60855075Fractions PacketCreated by MLC @ 2009 page 7 of 42
Higher EquivalentsThere are good reasons for knowing how to build fractions up to a larger form.It is exactly the opposite of what we do in reducing. If reducing is done bydivision, it makes sense that building up should be done by multiplication.121 22 224353 35 3915898 69 64854A fraction can be built up to an equivalent form by multiplying by any form ofone, any number over itself.232 63 61218232 113 1123121881222332233232 43 4232 53 58121015226All are forms of ; all will reduce to933Comparing FractionsSometimes it is necessary to compare the size of fractions to see which islarger or smaller, or if the two are equal. Sometimes several fractions must beplaced in order of size. Unless fractions have the same bottom number(denominator) and thus parts of the same size, you can’t know for certain whichis larger or if they are equal.Which is larger25or? Who knows? A ruler might help, but rulers aren’t36usually graduated in thirds or sixths. Did you notice that if 3 were doubled, itwould be 6?Fractions PacketCreated by MLC @ 2009 page 8 of 42
So build up2 22by;2 332 23 2Then it’s easy to see that2445, so means3666Which is largerBuild up34by56465is larger because it counts more sixth parts than6315or?1644.4343 44 412.1615161215so161634Exercise 5 (answers on page 39)Use , , or to compare these ions PacketCreated by MLC @ 2009 page 9 of 42
Mixed NumbersA “mixed” number is one that is part whole number and part fraction.1523 , 4 , 11283are samples of mixed numbers. Mixed numbers have to bewritten as fractions only if you’re going to multiply or divide them or use themas multipliers or divisors in fraction problems. This change of form is easy to1. That’s 3 whole things and half another. Each of the 3222 2 21 ) . The number 3 is 1 1 1 or. That’swholes has 2 halves (22 2 2617and, with the original, there’s a total of. You don’t have to think of222do. Think about 3every one this way; just figure the whole number times the denominator581 3 2 1 7.2224 8 5 32 5 378885911 9 59(bottom) and add the numerator (top) 33123 2 12722232 3 236 234831199 59Exercise 6 (answers on page 39)Change these mixed numbers to “top heavy” fractions:1. 5785. 13122. 9233. 2126. 7347. 124. 1251049188. 959These “top heavy” forms are “work” forms, but they are not usually acceptableanswers. If the answer to a calculation comes out a top heavy fraction, it willhave to be changed to a mixed number. This can be done by reversing the timesand plus to divide and minus. 331212became72by2 3 12.72can go back toby dividing 7 and 2.Fractions PacketCreated by MLC @ 2009 page 10 of 42
3122 7The answer is the whole number 3. The remainder 1 is the top number of61the fraction and the divider 2 is the denominator (bottom fraction number).37848 3732554844 17161174144113 353323531123Exercise 7 (answers on page 39)Reduce these top heavy fractions to mixed numbers.2781.2.1353.9384.6675.252Top heavy fractions may contain common factors as well. They will need to bedivided out either before or after the top heavy fraction is changed to a mixednumber.26838 262432222butcan be divided by . Then 3888212 3422If you had noticed that both 26 and 8 are even, you could divide out2right2away and then go for the mixed number. Either way, the mixed number is thesame.26826 28 213434 13121314Exercise 8 (answers on page 39)1.65 102.40 63.22 44.22 85.30 9Fractions PacketCreated by MLC @ 2009 page 11 of 42
Estimating Fractions“One of the most important uses of estimation in mathematics is in the calculation ofproblems involving fractions. People find it easier to detect significant errors whenworking with whole numbers. However, the extra steps involved in the calculation withfractions and mixed numbers often distract our attention from an error that we shouldhave detected.” 1Students should ask the following questions as motivation for estimating:1)Would estimates “help” in the calculation?2)Is the answer I get reasonable?3)Does the answer seem realistic?Try to make every fraction you work with into a whole number. 0 and 1 should be your targets withfractions. Mixed numbers should be estimated to the nearest whole number (except Ex.8).Here are some examples of problems using estimation:Ex. 12312note: ⅔ is closer to 1 (than 0) and ½ should be considered 11 1 2This symbol means “approximately equal to”Ex. 2131211232Ex. 3 5note: ⅓ is closer to 0 (than 1)0 1 15-32note: 5⅓ is closer to 5 (than 6) and 2½ should be consideredcloser to 3 (than 2)21232Ex. 4 5Ex. 5Ex. 623 22132Ex. 7 5Ex. 8 5Exercise 91) 61723113132note: 5⅔ is closer to 6 (than 5)1 1 1see Ex. 1 above1 1 1see Ex. 1 above1226 3 3125 3 15 see Ex. 3 above6 32note: 5⅓ is made into a 6 because it is easier to divide by 3Estimate the answers to the following fractions operations (answers on page 39)12222322) 63) 64) 65) 3 66) 8 37373737373Basic College Mathematics ,4th Ed., Tobey & Slater, p. 176Fractions PacketCreated by MLC @ 2009 page 12 of 42
Reducing FractionsDivide by 2 if The top AND bottom numbers are EVEN numbersLike:214,,4263244Divide by 3 if The sum of the top numbers can be divided by 3 AND the sum of thebottom numbers can be divided by 3Like:5617625 6 1 127 6 2 1512 can be divided evenly by 315 can be divided evenly by 3Divide by 5 if The top AND bottom numbers end in 0 or 5Like:560,,1575255460Divide by 10 if The top AND bottom numbers end in 0.Like:20140,,40260320440Divide by 25 if The top AND bottom numbers end in 25 or 50 or 75 or 100Like:225150,,40027532754500Fractions PacketCreated by MLC @ 2009 page 13 of 42
Divisibility RULES!Dividing by 3Add up the digits: if the sum is divisible by three, then the numberdivides by three.Ex.2076032 0 76 0 39 39 332073thereforedivides by60333Dividing by 4Look at the last two digits. If they are divisible by four, then the numberdivides by four.Ex.124136243624364461244thereforedivides by13649Dividing by 6If the digits can be divided by two and three, then the number divides bysixEx. 6121806612 21806 2306903And6121806therefore612 31806 36126divides by18066204602Dividing by 7Take the last digit, double it, and then subtract it from the othernumbers. If the answer is divisible by seven, then the number divides byseven.Ex.28731528 - 1431 - 1014217722877thereforedivides by31573Dividing by 8If the last three digits are divisible by eight then the number divides byeight.Ex. 21043160104160881382104thereforedivides by8316020Fractions PacketCreated by MLC @ 2009 page 14 of 42
Dividing by 12If the number divides by both 3 and 4, then the number will divide by 12Ex. ore44306903121224divides by123612Dividing by 13Delete the last digit. Subtract nine times the deleted digit from theremaining number. If what is left is divisible by thirteen, then the numberdivides by thirteen.Ex.Forget it! This is too much work!Remember to try to reduce with any number that makes the reduction simpleand easy for you.Good Luck!Fractions PacketCreated by MLC @ 2009 page 15 of 42
ORDERINGFractionsBeing able to place numbers in order (smallest to largest or largest to smallest)is fundamental to the understanding of mathematics. In these exercises we willlearn how to order fractions.Ordering FractionsThere are several ways to order fractions. One way is to use common sense.This method can be simple but requires some general knowledge. If nothingelse, it can be used as a starting point to finding the necessary order.Take a look at the following examples:Ex. Place the following fractions from smallest to largest order1 1 1,,3 5 2The larger the number on the bottom of a fraction (assuming the numerator isthe same for all the fractions), the smaller the fraction is. In the above1is the smallest fraction because the 5 is the largest denominator.51Next in order would be thebecause the 3 is the next largest denominator.31This leaves the , which has the smallest denominator. Therefore, the order2example,for these fractions is:1,51,312Ex. Place the following fractions from smallest to largest3,5The larger bottom number here is the 6 in2,3565. But the student should ask, “Is this the6smallest fraction?” By inspection, it does not seem to be. But with fractions of this sort(different numerators), students run into the most problems when ordering.Fractions PacketCreated by MLC @ 2009 page 16 of 42
Another way to order fractions is to find common denominators for all thefractions; build up the fractions; then compare the top numbers (numerators)of all the fractions.Look at the following example:Ex.Order the following fractions from smallest to largest5 3 2,,6 5 3The fractions will be rewritten with common denominators. This process is calledbuilding. Once the denominators change, then the numerators will change by the sameamount.353 65 618,30232 103 1020,30565 56 52530By looking at the top numbers, the order of these fractions is:3,52,356Exercise A (answers on page 42)Order these fractions from SMALLEST to largest.1.3,43,72.13,,7 1423328Exercise B (answers on page 42)Order these fractions from LARGEST to smallest.1.8,112.7,83,41322355,64 16Fractions PacketCreated by MLC @ 2009 page 17 of 42
Multiplication and Division of Fractions WorksheetsWhen multiplying fractions, simply multiply the numerators (top number of thefractions) together and multiply the denominators (bottom number of thefractions) together. It is good practice to check to see if any of the numberscan cancel. Canceling is done when the numerator and denominator can bedivided evenly by the same number.Note: canceling can happen top-to-bottom and/or diagonally but never across.2this product can be canceled. Divide the numbers in the62 2 1fraction by 2 to get the canceled answer.6 2 3Ex. 1:1223The fractions in Ex. 1 can cancel before they are multiplied.Ex. 1:11221 13 3The 2’s cancel by dividing by 2. Cross them out and place 1’s close by. Nowmultiply the top numbers together, then the bottom numbers. The product isthe final answer.7Ex. 2:354010035can be rewritten as1000408110010007811078010Cancel by dividing by 5. Then cancel by dividing by 100. Multiply and get theproduct.1Ex. 3:313can be written like.31multiply to find the product.13111 Cancel by dividing by 3. Finally,1Fractions PacketCreated by MLC @ 2003 page 18 of 42
Exercise 1 (answers on page 40)Multiply these fractions. Cancel and simplify if . 1013.7816.16172324453.3 105 105010022113132030Fractions PacketCreated by MLC @ 2003 page 19 of 42
Multiplying Mixed NumbersChange mixed numbers into improper fractions then multiply as before.11 5 102323 12 3Ex. 1:5253813Change the mixed numbers to improper fractions by:1 2 2 1 4 1 522221 2 2 1 4 1 522 top2 and bottom.22Cancel1) multiplying the bottom number by the whole number2) add the top number2Ex.2:117464243) keep the bottom number.Multiply. Improper fractions simplify by dividing.6135122512Change the mixed number into an improperfraction. Change the whole number into an improper fraction. Cancel. Multiply.Simplify to get the quotient.Exercise 2 (answers on page 40)Multiply these fractions. Cancel and simplify if necessary.1. 1131242.2125353. 4171384.122185. 314786. 55714157.7 1388.24559.23911. 717810. 18519625612. 117913Fractions PacketCreated by MLC @ 2003 page 20 of 42
Dividing FractionsWhen dividing fractions, invert (turn over) the fraction to the right of the(“divide by”) symbol. Cancel (if possible) then multiply.Ex. 1:Ex. 2:12343551243355112233515325Exercise 3 (answers on page 40)Divide these fractions. Cancel if necessary and simplify1.234.9117.7810.151613. 2562.9105.25148.155811.7127223814. ons PacketCreated by MLC @ 2003 page 21 of 42
Dividing Mixed Number FractionsWhen dividing mixed numbers, change the mixed numbers to improperfractions, invert the fraction on the right of themultiply then simplify.11123Ex. 1:2Ex. 2:142524352341581symbol, cancel if possible,783692619216342Exercise 4 (answers on page 40)Divide the following mixed numbers. Cancel and simplify when possible.341.24.347.8 15637310. 7841211212. 16239101316Fractions PacketCreated by MLC @ 2003 page 22 of 42
Fraction Word Problems (Multiplication/Division)When solving word problems, make sure to UNDERSTAND THE QUESTION.Look for bits of information that will help get to the answer. Keep in mind thatsome sentences may not have key words or key words might even be misleading.USE COMMON SENSE when thinking about how to solve word problems. Thefirst thing you think of might be the best way to solve the problem.Here are some KEY WORDS to look for in word problems:Product, times: mean to multiplyQuotient, per, for each, average: mean to divideEx. 1:If 3 boxes of candy weigh 6½ pounds, find the weight per box.“per” means to divide6Ex. 2:123132311321313621pounds6If one “2 by 4” is actually 3½ inches wide, find the width of twelve“2 by 4”s.3112217 122 16twelve 2” by 4”’s here means 12 times as wide as one 2”by 4”42 inches2 inches3½ inchesFractions PacketCreated by MLC @ 2003 page 23 of 42
Exercise 5 (answers on page 40)Solve the following fraction word problems. Cancel and simplify your answers.1. A stack of boards is 21 inches high. Each board is 1¾ inches thick. Howmany boards are there?2. A satellite makes 4 revolutions of the earth in one day. How manyrevolutions would it make in 6½ days?3. A bolt has 16½ turns per inch. How many turns would be in 2½ inches ofthreads?4. If a bookshelf is 28hold?18inches long, how many 178inch thick books will it5. Deborah needs to make 16 costumes for the school play. Each costumerequires 2need?14yards of material. How many yards of material will sheFractions PacketCreated by MLC @ 2003 page 24 of 42
6. The Coffee Pub has cans of coffee that weigh 314pounds each. The Pubhas 8½ cans of coffee left. What is the total weight of 8½cans?7. Belinda baked 9 pies that weigh 20pie weigh?8. A piece of paper is4100014pounds total. How much does eachinches thick. How many sheets of paper will ittake to make a stack 1 inch high?9. Tanya has read34of a book, which is 390 pages. How many pages are inthe entire book?10. DJ Gabe is going to serve ⅓ of a whole pizza to each guest at hisparty. If he expects 24 guests, how many pizza’s will he need?Fractions PacketCreated by MLC @ 2003 page 25 of 42
To the student:The fractions chapter is split into two parts. The first part introduces what fractions are andshows how to multiply and divide them. The second part shows how to add and subtract.The methods for accomplishing these operations can be confusing if studied all at once.Before proceeding with this packet, please talk to your instructor about what you should donext. The Editors.Addition and Subtraction of FractionsFinding the LEAST COMMON DENOMINATOR (LCD)When adding and subtracting fractions, there must be a common denominatorso that the fractions can be added or subtracted. Common denominators arethe same number on the bottom of fractions.There are several methods for finding the common denominator. The following is one inwhich we will find the least common denominator or LCD. Each set of fractions has manycommon denominators; we will find the smallest number that one or both fractions willchange to.Ex. Suppose we are going to add these fractions:1 22 3Step 1: Start with the largest of the denominatorsEx: 3 is the largestStep 2: See if the other denominator can divide into the largest without getting aremainder. If there is no remainder, then you have found the LCD!Ex. 3 divided by 2 has a remainder of 1Step 3: If there is a remainder, multiply the largest denominator by the number 2 andrepeat step 2 above. If there is no remainder, then you have found the LCD! If there is aremainder, keep multiplying the denominator by successive numbers (3, 4, 5, etc.) until thereis no remainder. This process may take several steps but it will eventually get to the LCD.Ex. 3 x 2 6; 2 divides evenly into 6; therefore, 6 is the LCD.Ex. 1:1214Step 1: 4 is the largest denominatorStep 2: 4 divided by 2 has no remainder, therefore 4 is the LCD!Fractions PacketCreated by MLC @ 2003 page 26 of 42
Ex. 2:1 15 6Step 1: 6 is the largest denominatorStep 2: 6 divided by 5 has a remainder.Multiply 6 x 2 12.12 divided by 5 has a remainder6 x 3 18.18 divided by 5 has a remainder6 x 4 2424 divided by 5 has a remainder6 x 5 3030 divided by 5 has NO remainder, therefore 30 is the LCD!Note: You may have noticed that multiplying the denominators together also gets the LCD. Thismethod will always get a common denominator but it may not get a lowest common denominator.Exercise 1(answers on page 41)Using the previously shown method, write just the LCD for the following setsof fractions (Do Not Solve)1)1 1,2 32)2 2,5 33)5 1,8 24)1 1,4 35)1 2,7 56)4 1,9 37)3 1,4 28)7 3,8 59)3 2,10 310)13 4,15 511)1 2 5, ,2 3 612)3 5 7, ,4 8 1613)3 1 1, ,8 6 314)1 1 1, ,7 2 315)3 1 1, ,8 5 3Fractions PacketCreated by MLC @ 2003 page 27 of 42
Getting equivalent Fractions and Reducing FractionsOnce we have found the LCD for a set of fractions, the next step is to changeeach fraction to one of its equivalents so that we may add or subtract it.An equivalent fraction has the same value as the original fraction it looks alittle different!Here are some examples of equivalent fractions:121314152426282102426282103639312315 etc. etc.An equivalent fraction is obtained by multiplying both the numerator anddenominator of the fraction by the same number. This is called BUILDING.Here are some examples:5x3158x3247x21412x2241x17173x17515 and 8 were both multiplied by 37 and 12 were both multiplied by 21 and 3 were both multiplied by 17Note: the numbers used to multiply look like fraction versions of 1.An equivalent fraction can also obtained by dividing both the numerator anddenominator of the fraction by the same number. This is called REDUCING.Here are some more examples:10251226842124310 and 12 were both divided by 28 and 12 were both divided by 4200258225259200 and 225 were both divided by 25Fractions PacketCreated by MLC @ 2003 page 28 of 42
Exercise 2(answers on page 41)Find the number that belongs in the space by building or reducing 5320221110303Fractions PacketCreated by MLC @ 2003 page 29 of 42
Simplifying Improper FractionsAn improper fraction is one in which the numerator is larger than thedenominator. If the answer to an addition, subtraction, multiplication, ordivision fraction is improper, simplify it and reduce if possible.Ex. 1:4 is an improper fraction. Divide the denominator into3numerator.3Ex. 2:Ex. 3:143111310is an improper fraction. Divide to simplify. Reduce.8110 8 10 1 2 1 188482136is an improper fraction. Divide to simplify. Reduce.206136 20 136 6 16 6 42020512016Fractions PacketCreated by MLC @ 2003 page 30 of 42
Exercise 3 (answers on page 41)Simplify the following fractions. Reduce if possible.1)6 52)5 43)7 34)10 65)4 26)6 47)15 38)20 129)19 410)23 511)18 312)17 513)37 914)28 815)47 916)106 417)17 218)140 2019)162 1020)38 521)52 3Fractions PacketCreated by MLC @ 2003 page 31 of 42
Adding and Subtracting of FractionsWhen adding or subtracting, there must be a common denominator. If thedenominators are different:(a) Write the problem vertically (top to bottom)(b) Find the LCD(c) Change to equivalent fractions (by building)(d) Add or subtract the numerators (leave the denominators the same)(e) Simplify and reduce, if possibleEx. 1:314555The denominators are the same. Add the numerators, keepthe denominator. This fraction cannot be simplified or reduced.Ex. 2:Ex. 3:11245183?122411443The denominators are different numbers.4Therefore, change to515See page82418324equivalentfractions.25724Ex. 4:2334?2831239412171211 11Ex. 5:111153?1515153151512Simplifying and reducingcompletes addition andsubtraction problems.See page 25 & 2762155Fractions PacketCreated by MLC @ 2003 page 32 of 42
Exercise 4 (answers on page 41)Add or subtract the following fractions. Simplify and reduce when 2338Fractions PacketCreated by MLC @ 2003 page 33 of 42
Adding and subtracting mixed numbersA mixed number has a whole number followed by a fraction:1511 , 2 , 176 ,382and86are examples of mixed numbers7When adding or subtracting mixed numbers, use the procedure from page 7.Note: Don’t forget to add or subtract the whole numbers.11223131126122236Ex. 1: 13Ex. 3: 551335181685Ex. 2: 6?1118Ex. 4: When mixed numbers cannot be subtracted because the bottom fraction islarger than the top fraction, BORROW so that the fractions can be subtractedfrom each other.The 2 cannot beEx. 5: 8 - 2832447432415434Ex. 6: 5?The 34cannot besubtracted from nothing.One was borrowed from the8 and changed to 4 . 84was changed to a 7.Now themixed numbers can besubtracted from each other.15612316215622613?7462265266subtracted from the 1 .6One was borrowed fromthe 5, changed to 66and then added to the16to make 76. Thewhole number 5 waschanged to a 4. Now themixed numbers can besubtracted.Fractions PacketCreated by MLC @ 2003 page 34 of 42
Exercise 5 (answers on page 41)Add or subtract the following mixed numbers. Simplify and reduce when possible.2 3415 112) 1 8 1) 83) 16 3 75108 1211124) 3421165 53155) 17) 5112 638) 1410) 22313) 1616) 519)1 4512 635 10 6 1227 32 36) 411 8112 289) 7211 5 511) 12128 731914) 14 2 17) 6 420) 27 84 21 8 312) 4463 771515) 146 8 18) 1135 53821) 100 4 Fractions PacketCreated by MLC @ 2003 page 35 of 42
Fraction Word Problems (Addition/Subtraction)When solving word problems, make sure to UNDERSTAND THE QUESTION.Look for bits of information that will help get to the answer. Keep in mind thatsome sentences may not have key words or key words might even be misleading.USE COMMON SENSE when thinking about how to solve word problems. Thefirst thing you think of might be the best way to solve the problem.Here are some KEY WORDS to look for in word problems:Sum, total, more than: mean to addDifference, less than, how much more than: mean to subtractEx. 1: If brand X can of beans weighs 15 1 ounces and brand Y weighs212 3 ounces, how much larger is the brand X can?4121515243312124461443124234means to subtractBorrow from thewhole number andadd to the fractionEx. 2: Find the total snowfall for this year if it snowedNovember, 21inch in1013inches in December and 1 inches in January.34mean
Fractions Packet Created by MLC @ 2009 page 6 of 42 4 3 is the reduced form of 8 6. When you divide both the top and bottom numbers of a fraction by the same number, you are divid
