Fractions and Chapter 2 - NCERT

1 Fractions AND INTRODUCTIONYou have learnt Fractions and decimals in earlier classes. The study of Fractions includedproper, improper and mixed Fractions as well as their addition and subtraction. We alsostudied comparison of Fractions , equivalent Fractions , representation of Fractions on thenumber line and ordering of study of decimals included, their comparison, their representation on the numberline and their addition and shall now learn multiplication and division of Fractions as well as of HOW WELL HAVE YOU LEARNT ABOUT Fractions ?A proper fraction is a fraction that represents a part of a whole.

2 Is 74a proper fraction?Which is bigger, the numerator or the denominator?An improper fraction is a combination of whole and a proper fraction. Is 74 animproper fraction? Which is bigger here, the numerator or the denominator?The improper fraction 74can be written as 314. This is a mixed you write five examples each of proper, improper and mixed Fractions ?EXAMPLE 1 Write five equivalent Fractions of 35 .SOLUTIONOne of the equivalent Fractions of 35 is33 2655 210 == . Find the other 2 Fractions andDecimals2021 22 MATHEMATICS3030303030 EXAMPLE 2 Ramesh solved 27part of an exercise while Seema solved 45 of it.

3 Whosolved lesser part?SOLUTIONIn order to find who solved lesser part of the exercise, let us compare27 and them to like Fractions we have, 210735= , 428535=.Since10 < 28 , so 10283535<.Thus,24<75 .Ramesh solved lesser part than 3 Sameera purchased 132 kg apples and 344 kg oranges. What is thetotal weight of fruits purchased by her?SOLUTIONThe total weight of the fruits 1334kg24 =+ = 7 1914 19kgkg2444 +=+ = 331kg8 kg44=EXAMPLE 4 Suman studies for 253 hours daily. She devotes 425 hours of her timefor Science and Mathematics. How much time does she devote forother subjects?

4 SOLUTIONT otal time of Suman s study = 253 h = 173 hTime devoted by her for Science and Mathematics = 425 = 145 h2021 22 Fractions AND DECIMALS3131313131 Thus, time devoted by her for other subjects = 17 1435 h = 17 5 14 3 h1515 = 85 42h15 = 4315 h = 13215 hEXERCISE :(i)325 (ii)748+(iii)3257+(iv)9411 15 (v)7231052+ +(vi)212332+(vii)158328 the following in descending order:(i)2923821, ,(ii)1537710, ,. a magic square , the sum of the numbers in each row, in each column and alongthe diagonals is the same. Is this a magic square? rectangular sheet of paper is 1122cm long and 2103 cm its the perimeters of (i) ABE (ii) the rectangle BCDE in thisfigure.

5 Whose perimeter is greater? wants to put a picture in a frame. The picture is 735 cm fit in the frame the picture cannot be more than 7310 cm wide. How much shouldthe picture be trimmed?(Along the first row 4921511 11 1111++=).5cm232 cm433 cm57cm62021 ate 35 part of an apple and the remaining apple was eaten by her brother much part of the apple did Somu eat? Who had the larger share? By howmuch? finished colouring a picture in 712 hour . Vaibhav finished colouring the samepicture in 34 hour . Who worked longer? By what fraction was it longer? MULTIPLICATION OF FRACTIONSYou know how to find the area of a rectangle.

6 It is equal to length breadth. If the lengthand breadth of a rectangle are 7 cm and 4 cm respectively, then what will be its area? Itsarea would be 7 4 = 28 will be the area of the rectangle if its length and breadth are 712 cm and312 cm respectively? You will say it will be 712 312 = 152 72 cm2. The numbers 152and 72 are Fractions . To calculate the area of the given rectangle, we need to know how tomultiply Fractions . We shall learn that Multiplication of a Fraction by a Whole NumberObserve the pictures at the left (Fig ). Each shaded part is 14 part ofa circle. How much will the two shaded parts represent together?

7 Theywill represent 1144+ = 12 the two shaded parts, we get Fig . What part of a circle does theshaded part in Fig represent? It represents 24 part of a circle .Fig 22 Fractions AND DECIMALS3333333333 The shaded portions in Fig taken together are the same as the shaded portion inFig , , we get Fig 4 =24 .Can you now tell what this picture will represent? (Fig ) Fig this? (Fig )Fig us now find 13 have13 2 =11132222++=We also have 1111 +1 +13 13+ +===222222So13 2 =3 12 = 32 Similarly2 53 =2 53 = ?Can you tell23 7 =?

8 34 ?5=The Fractions that we considered till now, , 1 2 2 3, , ,2 3 7 5 and 35 were proper 22 MATHEMATICS3434343434 For improper Fractions also we have,52 3 =2 53 = 103 Try,83 7 =?74 5 = ?Thus, to multiply a whole number with a proper or an improper fraction, wemultiply the whole number with the numerator of the fraction, keeping thedenominator : (a) 2 37 (b) 967 (c) 13 8(d) 13 611 If the product is an improper fraction express it as a mixed pictorially : 24255 =To multiply a mixed fraction to a whole number, first convert themixed fraction to an improper fraction and then ,53 27 =1937 = 577 = ,22 45 =2225 = ?

9 Fraction as an operator of Observe these figures (Fig )The two squares are exactly shaded portion represents 12 of , both the shaded portions together will represent 12 of the 2 shaded 12 parts. It represents , we say 12 of 2 is 1. We can also get it as 12 2 = , 12 of 2 = 12 2 = 1 TRY THESETRY THESEFind: (i) 35 27 (ii) 41 69 Fig 22 Fractions AND DECIMALS3535353535 Also, look at these similar squares (Fig ).Each shaded portion represents 12 of , the three shaded portions represent 12 of the 3 shaded represents 112 , , 12 of 3 is 32. Also, 12 3 = , 12 of 3 = 12 3 = we see that of represents has 20 marbles.

10 Reshma has 1th5of the number of marbles whatFarida has. How many marbles Reshma has? As, of indicates multiplication,so, Reshma has 1 205 = 4 , we have 12of 16 is 1 162 = 162 = you tell, what is (i) 12of 10?, (ii) 14of 16?, (iii) 25 of 25?EXAMPLE 5In a class of 40 students 15 of the total number of studetns like to studyEnglish, 25 of the total number like to study Mathematics and the remainingstudents like to study Science.(i)How many students like to study English?(ii)How many students like to study Mathematics?(iii)What fraction of the total number of students like to study Science?