Fractions PDF - Lesson 7

Jesson 7 Fractions Afraction is apart (or parts) of a whole. Look at the shaded portion in each of the following figures 1 3 3...

Jesson 7 Fractions Afraction is apart (or parts) of a whole. Look at the shaded portion in each of the following figures 1 3 3 4 Here. 1 1 3 7 are all fractions. 3 48 A fraction is of the form numerator denominator (denominator z 0). Types of Fractions 1. Like and Unlike Fractions: (a) Look at the fractions : 4 3 6 1 2 777 7' 7 In all of these fractions, the denominators are same. Such fractions are (b) Look at the fractions : called like fo 2 11 1 4 3 7 13' 9' 5' 8 In all of these fractions, the denominators are different. Such fractions are alled unli 2. Unit Fractions : Look at the fractions : 1 1 1 1 1 7 9 11 3 5 In each of these fractions, the numerator is 1. Such fractions are called unit fraCtions 3. Proper and Improper Fractions : (a) Look at the fractions : 5 3 1 6 11 7' 11 9' 7' 15 MATHEMATICS MATHENA 64  ln cach of these fractions. the numerator is less than the denominator Such fractons are called proper fractions. (b) Look at the fractions : 1| 23 14 20 1| 9 12 1| 13 11 In cach of these fractions. the numerator IS greater than or equal to the denom1nator Stuch fractions are called improper fractions. Equivalent Fractions 4 16 Look at the fractions: 1 2 and 4 48 16 1 4 4 16 They are called equivalent fractions. We have already learnt to form equivalent fractions by multiplying the numerator and denominator by the same number. 1x2 2 Examples: (a) 6 ; and 6 are equivalent fractions. 3x2 3x7 21 and 21 (b) 5 5x7 35 35 are equivalent fractions. e have already learnt about fractions in class IV. Let us revise them. Activity-1 Do you remember 1. Fill in the blanks : (a) Fractions with the same denominator are called fractions. (b) Afraction whose value is less than l is called fraction. (c) If the numerator is greater than the denominator, then the fraction is a/an fraction. 5 is the (d) In fraction 95 and 9 is the 2. Write the fraction for the shaded parts. (a) (b) (c) ATHEMATICS In Real Life-5 65  Chassil thetolln 21 lionsinto mixed (b) improper trac Ifractions 106 followimg 46 (d) (c) 13 (e) 28 (onertthe 121 4 fracttonsinto inproper fractions : (a) mixed tollowing Comertthe (e) 73 4 S lse or < (b) 18 6 fractions equivalent of pairtsl (b) andl0 ldencify the 15 (c) 5 (a)and fractions of cach of the following 8 Find the first chree (b) cquivalent fractions (a) ascending order: the following in 5 5 Arrange 9 85 17 (b) 12 2 (a) 9 6 18 descending order the following in 10. Arrange 13 1! (b) 21 7 63 in the lowest terms write the answer 11 Add and + 210 7 l (b) 10 10 (c) 3+ (a) 24 terIRS: 24 answer in the lOwest 12 Subtract and write the 13_ 5 (a) - ! (b) 21 21 Equivalent Fractions denomina to form equivalent fractions by dividing the numerator and Let us now learn same number. fraction of Find an equivalent fractio Examples : 1 Find an equivalent 20 36 = 6 X 6;42 =6 X 7 15 =3 x 5 20 = 4 X 5 HCF of 36 and 42 = 6 HCF of 15 and 20 = 5 15+5 36 36+6 6 20 20 +5 42 42 +6 15 and are equivalent fractions. 36 42 and b are equivale 20 MATHEMAT 66  hnsteher a Activity-2 Chexhethe th ong ra are uvaien Reducina a Fraction to the Lowest Terms 35 = ATHEMATC Rta Li 67  tivdingr e uterdie 24 HCF sretuced t, the irse terms as duce tothe iowest Louest Terms tothe Reduang mgroper Fratuor 13 24 =2 2 2 HE = 2 rl=6 12 butis mprope fraction. 4arnd 3ae Corrime mers The lowest term of an improper fraction is usualy expressed as mixed frac We tantedute afraction to its lwest terms by ciding the numerator and the denominz Common factors al. 68 MATHEWATCS  in west tems 24 And e opne mbts hrotat he tersit ed uthet hs.edu 4 ed to eIowet terms as le Redue olowet tens (Drvidiny by 2 twre to get the lwest tetms And 4are coprifne Humbers. Thus, seduced tt, the lraest terms Activity-3 elre the followmg fhclios to the liwst terms by dradng with thest H 4 (a) 28 id) (e) 35 112 (hi 92 19 Pedi the following lractions lo the iywest tems by daciung them with the rn Tattiis 1) (b (a) 38 64 (c) (e) 38 12 (f) 28 () 122 64 236, 124 Comparison of Fractions us learn to compare like and unlike frations. 5 Compare 12 L and 12 Here, the denominators are same, s0 we compare the numerators. As 7> 5. so, >2 12 12 Iftwo fractions have the sane denominator the frattit witlh greater ume ratot s reater 2 Compare 2 and The numerators are same, s0, we compare the denominators. As9>3,so, If tuo fractiots have the samne nunierator the iraction with reater tlenorminaltc h. allee THEMATICS In Real Life-5 69  Activity-4 (h) (c) 0 15 (h) | t) 4 order 2 AuaHge in astCndmg 2 7 4 (a) (b) 5 0 15 20 Attae in deseending order 71 17 (a) I6 4 2 24 (b) 2. 14 Addition and Subtraction of Mixed Fractions addsubtact mixed Irations, we lst convet hem into improper frations. Then we convert e fractions into ike fractions (i1 neeSsary). inally we add/subtract the two frations. mple I: Add. 2 and 2 7 8 3 12 Ix8+3 8 +3 ition: 8 8 8 8 x3 +23+2 5 3 3 3 2 2x 12 +7 24 +7 31 12 12 12 12 ICM of 8, 3 and 12 = 2x 2 x 3× 2 = 24. 2 8, 3. 12 11 11x3 33 2 4, 3. 6 8 8x3 24 5 5x8 40 3 2, 3, 3 3 3 3x8 24 2., 1, 1 2 31 31× 2 62 12 12 12 x 2 24 7 33 40 62 33 +40 +62 135 45 + 5 8 3 12 24 24 24 24 24 8 EMATICS In Real Life-5 71  Sabtract 371 Erample2 Ss25. 1 22 22 4 Soution and 7 ot4 LCM 7 74 88-49 39 49 28 28 28 28 28 morningand 4! km in the ever the 5z kmin Roitwalk day? Erample3 walkina doeshe 5fkn- 4 km = Salution Totaldiszarce Vcw. 15. and5 is LOMof3 5 57 85-63 15 Rotitwaiks9 km in a day. Thus 3mo bouzht 3% mof ribbonand Preeti bought Example4 iani much? and by bow 37-3 15-2 7 Solustion 5 LM of5 and 7 is 35. 17/7-119 32 = 2 = 24/ 5/7 35 12 So. Preeti boUgt more ribbon. 22-34+ Thus. Preet bruznt =mmoreb:ar Pari 72  Properties of Addition and Subtraction of fractions naddhnon, ihe oder of hatios can be hanged but n subtraen its not possibie 3 3 Example but If we subtrat 0 tron athaion, the answer is the fation itself Ixample: If twe add '0' lo attaction, the answer is the fraction itse. FxampBe:2 + 0= : 0 + 7 7 9 Activity-5 Fil the blanks : la) 2 + 0= (b):+ - + 3 (c) 13 3 17 15 13 9 13 27 (a) 3 + 3 (b) 20 +3 (c) 20 15 30 23 (e) 3 (d) 4 + + 36 ++ () 3+ 1 2% 3 Subtract : la) 10 - 7 (b) 2 125 (c) 22- 36 l (d) 3 - (e) - () s -1 4 Maya has a red ribbon of length 5 5 mand a green ribbon of length 2 m. What is the total length of the two ribbons ? The weight oftwo books together is 3-4 kg. If the weight of one book is 1= kg. find the weight of the other book. 5 6 Nina bought 46 metres of cloth while Rajan bought 24 metres of cloth. (a) Find the total length of the cloth bought altogether. (b) Who bought more cloth and by how many metres? 1 3 Subtract the sum of 3-3 and 23 from the sum of 24 and 53 THEMATICS In Real Life-5 73