1=:1 Fractions (iv) TEXTBOOK QUESTIONS SOLVED. t?t?t?t?t? t?t?t?t?t? Learn and Remember EXERCISE 7.1

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$FRACTIONS 7 =: Fractions (iv) (v) Learn and Remember. Fraction means a part of a group or a region. is a fraction. is numerator and is denominator.$

1 FRACTIONS 7 =: Fractions (iv) (v) Learn and Remember. Fraction means a part of a group or a region. is a fraction. is numerator and is denominator.. Proper fraction is the fraction where numerator is less than denominator.. Improper fraction is the fraction where the numerator is more than denominator. 4. Mixed fraction is the fraction with an integer and proper fraction.. To find an equivalent fraction of a given fraction, you may multiply both the numerator and the denominator ofthe given fraction by the same number. 6. If we divide both numerator and denominator by same number, the fraction become same. 7. A fraction is said to be in the simplest form if its numerator and denominator have no common factor except l. 8. Fractions with same denominators are called like fractions. 9. Two fraction can be added or subtracted untill they have common denominator. TEXTBOOK QUESTIONS SOLVED EXERCISE 7. Q. Write the fraction representing the shaded portion. #""... -,t.. "'"'i;; ~.t~ "''I "'-~ clio ~ **** **** t?t?t?t?t? t?t?t?t?t? (vi) (I!ii) (viii) (ix) 8 4 Sol. (i) - (ii) 9" (iii) "8 (iv) '4 (v) (vi) (vii) 0 (viii) 9" (ix) "8 (x) ". Q. Colour the part according to the given fraction: V ~ (i) 6" (ii) '4 (x) (iii) 8888 (0 (ii) (iii) (iv) '4 4 (v) 9"

$For the fraction it is necessary that figure is to be divided in equal parts. What fraction of a day is 8 hours? In a day, there are 4 hours.$

2 7 MATHEMATICS-VI Sol. (i) (ii) (iii) (iv) (u) Q. Identify the error, if any? Sol. Q4. Sol. Q. Sol. Q6. This is / This is /4 This is /4 The main error is figures are not equally divided. For the fraction it is necessary that figure is to be divided in equal parts. What fraction of a day is 8 hours? In a day, there are 4 hours. Therefore the fraction of 8 hours is 8 = 4 or "' What fraction of an hour is 40 minutes? In an hour, there are 60 minutes. Therefore the required fraction is 40 -or-. 60 Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. Tbe other two boys forgot to bring their lunch.arya agreed to share his sandwiches so that each person will have en equal share of each sandwich. (a) How canarya divide his sandwiches so that each person has an equal share? (b) What part of a sandwich will each boy recei"~? FRACTIONS Sol. (a) Arya will divide each Sandwich into three equal parts, and give one part of each Sandwich to each one of them. (b)lx-=-. Q7. Kanchan dyes dresses. She had to dye 0 dresses. She has so far finished 0 dresses. What fraction of dresses has she finished? Sol. Total number of dresses = 0 Work already finished = Fraction = - = --- = Q8. Write the natural numbers from to. What fraction ofthem are prime numbers? Sol. Natural numbers:,, 4,, 6, 7, 8, 9, 0,, Prime numbers :,,, 7, F. raction :. Q9. Write the natural numbers from 0 to. What fraction of them are prime numbers? Sol. Natural numbers: 0, 0, 04, 0, 06, 07, 08, 09, 0,,, Prime numbers: 0, 07, 09, F. 4 raction =. QI0. What fraction of these circles have 'X's in them? Sol. 8' Q. Kristin received a CD player for her birthday. She bought CDs and received others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts? Sol. Total CDs = + = 8 No. of CDs purchased = Fraction of CDs purchased = ~ Fraction of receive as gifts = 8'

$(a) MATHEMATIcs-VI 4 7 84 (a) '"4' "4<i (b) 8' 8' 8' 8 (c) ' ' '" (b) (c) ~ /4 / /4 4/4 \ I I I I ~ 0 /8 /8 7/8 -t + I I II I I I - 0 8 4/ 8/ \ t I I I I I I I I \ I - 0 / ~.$

3 74 EXERCISE 7. Q. Draw number lines and locate the points on them. Sol. (a) MATHEMATIcs-VI (a) '"4' "4<i (b) 8' 8' 8' 8 (c) ' ' '" (b) (c) ~ /4 / /4 4/4 \ I I I I ~ 0 /8 /8 7/8 -t + I I II I I I / 8/ \ t I I I I I I I I \ I - 0 / ~. Express the following as mixed fractions: 0 (a) - (b) (d) - (e) Sol. (a) }0 8 0., =6, (c) 7)I7 4 7., 7" =7 (e) 6~ ( =6 (b) 7 (c) 7' (n 9 }li , - (d) ) , - (j) 9) " =9, FRACTIONS 7 Q. Express the following as improper fractions: 6 (a) 7"4 (b) 7 (c) 6 4 (d) 0 (e) 9 (j) (7x4) + Sol. (a) 7- = 4 4 =4" (b) ~ = (x7)+6 = 4 (x6)+ 7 (lox ) + (c) - = - (d) 0- = (9x7) (8x 9)+4 76 (e) 9- = - (j) 8- = EXERCISE 7. Q. Write the fractions. Are all these fractions equivalent: (alcd ~o ~ (b) I Sol. (a) ' "4' 6' "8 Yes, all of these are equal. 4 6 (b) ' 9' 6' ' No, they are not equal. Q. Write the fractions and pair up the equivalent fractions from each row. [!B... w-..'.' []J.e fm mejj" ".,. " ~"-'.w, ':;, - _ ':,;,0,.,':"i." It;'. ;.'.. t.'~.:...." ,.".. ~ ;.... w! _....:... _... ""'--.,.'~- : ',' e (a) (b) (c) (d) (e)

FRACTIONS 77 76 - ------------- ----------'--'---- ~mgllj~ (i) Sol. (a) " (ii) (b).! = x =

4 FRACTIONS '--'---- ~mgllj~ (i) Sol. (a) " (ii) (b).! = x = ~ 6 x x (c) - = - =- 9 x (d) ~ = x =.! 8.xx 4 (iii) (iv) (v) MATHEMATIcs-VI (i) ~ = x =.! 8 x x (ii).! = x =.! 8 xx 4 x (iii) - = -- = - 6 4x x (iv) - = -- =- 4x 4 4 (e) _ (u) - = -- = x4 4 Therefore, (a) --7 (ii), (b) --7 (iv), (c) --7 (i), (d) --7 (u), (e) --7 (iii). Q. Replace 0 in each of the following by the correct number: (a) - = - (b) - = - (c) - = (d) 60 = 0 x4 _ ~ Sol. (a);; = 7x4 - ~ 8 0 (e) 4 = "4 x _ 0 (b) "8 = 8x (d) 4 = 4+ = (e) 8 = 8+6 JID ~ Q4. Find the equivalent fraction of " having: (a) denominator 0 (b) (c) denominator 0 (d) Sol. (a) ~ = x4 = x4 0 (c) ~ = x 6 = 8 x6 0 (b) (c) ~ = x4 - ~ x4-0 numerator 9 numerator 7 ~=x=~ x (d) ~ = x 9 _ 7 x9-4 6 Q. Find the equivalent fraction of 48 with (a) numerator 9 (b) denominator 4 Sol. (a) 6 = 6+4 = ~ (b) 6 = 6+ = ~ Q6. Check whether the given fractions are equivalent: 0 7 (a) "9' 4 (b) 0' 0 (c) ' Sol () ~ = x 6 = 0 0. a 9 9x6 4' 4 0. "9' 4 are equiva ent. b ~ _ x _ ( ) 0-0x - 0 ' 0 Their denominator are equal but numerator are not therefore fractions are not equivalent. 7 7x 77 x 6 (c) = x = 4 ; = x = 4 Since 77 * 6 therefore fractions are not equivalent. Q7. Reduce the following fractions to simplest form: (a) 60 (b) 60 (c) 98 (d) (e) 8 Sol. (a) 48 = f. xf. xxx, =.! (b) 0 = x, x)<"= ~ 60 f. xf. x, x 60 x, x)<" c 84 _ 6x4 _ ~ d _ xj _ ~ () 98-7 x 4-7. ( ) - xj -. 7 jx (e) - = -- =-. 8 jx4 4 Q8. Ramesh had 0 pencils, Sheelu had 0 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 0 pencils, Sheelu used up pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils? Sol. Ramesh: Total pencils = 0 Pencils used = 0. 0 Fraction = - = - 0

$40 Fraction = - = - 80 Since all of them used half of their pencils, therefore each one used up equal fraction of pencils. Q9. Match the equivalent fractions and write two more for each. Sol.$

5 78 Sheelu : Total pencils = 0 Pencils used = Fraction = - = - 0 Jamaal : Total pencils = 80 Pencils used = 40 MATHEMATlcs-VI. 40 Fraction = - = - 80 Since all of them used half of their pencils, therefore each one used up equal fraction of pencils. Q9. Match the equivalent fractions and write two more for each. Sol. 0 (i) (ii) tiii) (iv) 60 0 (u) 0.~0 (r) ~' 8' 6' 4 (ii) (a) (b)... ~ 4 6 (m)~''6'9 ~ 46 (v)~, ' 0' (i) -7 d, (ii) -7 e, (iii) -7 a, (iu) -7 c, (u) -7 b. EXERCISE 7.4 (c) (d) (e) Q. Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign '<', '=', '>' between the fractions: (a).j.s FRACTIONS 79 Sol. (b) ff8 ±JlliJ ±J (c) Show "6' "6' "6 and "6 on the number line. Put appropriate signs between the fractions given "6 "6'"6 0'"6 "6'"6 "6 6 4 (a) 8' 8' 8' 8 Ascending 46 order = - < - < - < Descending 64 order = - > - > - > (b) 9' 9' 9' Ascending order = - < - < - < Descendmg order = - > - > - > (c) Number line o I I I I I I I I I o "6 "6 "6 "6 - G G- 6 - El G Q. Compare the fractions and put an appropriate sign. 0 (a) (c) - - Sol. (a) - El (c) - El - 0 (b) (d) ~O~ 7 Q (b) - t.j (d) - G -

$Look at the figures and write '<' or '>', '=' between the given pairs of fractions. I o o " I I I I o " " " " I I I I I o 4 4" 4" 4" 4" 4" I I I I I I.Q. I 4 " " " I I I I ==r=:j.q.$

6 80 MATHEMATlCS-VI FRACTIONS Q. Make five more such pairs and put appropriate signs. 9 6 Sol (a) - G - (b) - G - (c) - E (d) - E - (e) - G Q4. Look at the figures and write '<' or '>', '=' between the given pairs of fractions. I o o " I I I I o " " " " I I I I I o 4 4" 4" 4" 4" 4" I I I I I I.Q. I 4 " " " I I I I ==r=:j.q. 6 "6 6 0 (a) (d) - - (e) "6 "6 "6 "6 (b) 4" 6 0 (c) 4" Make five more such problems and solve them with your friends. C Sol. (a) 6" 6 (d) ~ g 6 0 (b) - G (e) - E - 6 (c) - G Five problems: (i) - D- (ii) - 6 D- a a (iv) - D- (v) - D (iii) 4" D"6 Sol. (i) - E - (ii) - 6 G - (iii) ~ G ~. a a (iv) - E - (u) - 6 E - 6 Q. How quickly can you do this? Fill appropriate sign. «, =.» 0 (a) - - (b) (d) -0 - (e) (g) 4" 8 (h) 0 i (j) 0" (k)"7 Sol (a) - G - (b) - E (d) - G - (e) - E C 4 (g) - E - (h) C 4 C (j) (k) - CJ Q6. The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form. (a) (b) 6 0 (d) 00 (e) 60 6 (g) - (h) (j) 7 (k) 8 0 (c) i (fj 709" 0 7 (i) 4" 8 (c) - E (f) - G (i) - E - 8 (c) 0 (f) 7 (i) 7 4 (I) 8

8 SoL (a) - -- - 6 6 4 (d) 00 = (g) - -- 60 - (j) 7 = "6 Igroup = = b,f,g MATHEMATlCS-VI 8 4 (b) - -- (c) 0 = - 0 (e) 60 = "6 (j) 7 = 6 4 (h) 96 = "6 (0 7 = 4 4 (k) - =- (l) = 8 6 IIgroup = "6 = a,

7 8 SoL (a) (d) 00 = (g) (j) 7 = "6 Igroup = = b,f,g MATHEMATlCS-VI 8 4 (b) - -- (c) 0 = - 0 (e) 60 = "6 (j) 7 = 6 4 (h) 96 = "6 (0 7 = 4 4 (k) - =- (l) = 8 6 IIgroup = "6 = a, e, h,j, k FRACTIONS 8 Let Or 9 6 = "9 then 9 x 9 = 6 x, 8 = 80 But we know that 80 ""8 So 9. 6 IS not equa to " (c) " x 0 = 00 ; 0 x = = 00 4 IIIgroup = = c, d, i, l. Q7. Find answers to the following. Write and indicate how you solved them. 4 (a) Is 9" equal to "? 4 6 (c) Is " equal to 0? 9 (b) Is 6 equalto 9"? 4 (d) Is equal to 0? So ~ = 6 0 Or 4 6 Let - =- 0 then 4 x 0 = 6 x 80 = So is equal to 0 SoL (a) -x- = _. -x- = ' So 4 "" 4 then "9 IS not equal to Let So Or ~V~ 9A = 6 but we know that ""6 4 So "9 "" (b) - x - =_. - x - = ' So 44 * 44 then 6 IS not equal to "9 4xl 4 (d) x " = 0 ; 0xl = "" 0 S. 4 o IS not equa to 0 Or Let 4 = 0 So x 0 = 4 x 0 = 60 but we know that 0 is not equal to So is not equal to 0 Q8. Ila read pages of a book containing 00 pages. Lalita read " of the same book. Who read less? SoL Ila read pages out of 00 pages

8 84 MATHEMATcs-VI So Ila read 00 i.e., ~ th book (b)~_ ' FRACTIONS 8 40 Lalita read " of book i.e., 00 pages So 4 < " Ila read less. Q9. Rafiq exercised for 6 of an hour, while Rohit exercised for 4" of an hour. Who exercised SoL Rafiq exercised 6' of an hour Rohit exercised 4 of an hour We know that 4 > 6 for a longer time? So Rohit exercised for a longer time. QI0. In a class A of students 0 passed in first class; in another class B of 0 students, 4 passed in first class. In which class was a greater fraction of students getting first class? 0 SoL In class A 0 passed out of i.e., 4 In class B 4 passed out of 0 i.e., = " = " So each class have same fraction, of student getting first class. EXERCISE 7. Ql. Write the fractions appropriately as additions or subtractions: (a) nm ;i.~~l'...".-;",i~ =.\!;'.,: -,:",- _y,"", t-,,-;,..--i." -=rrj:,;(\l',.-\.,'4._+'.' I I (c) I ~ = I I SoL (a) " + " = -- =" (b) " -" = " Q. Solve: (a) (6) - +- (d) ~ + (e) _ ~ ( ) 0 (g) - - =- (h) (c) "6 +"6 ="6 (c) 7.. _ 7 "7 (f) - + 8" 8 (i) - SoL (a) ~ + ~ = + = s. =! ~. _ 8 + _ l8 9 (b) (c) "7 - "7 = -7- = "7 (e) _!...- = -7 = ~ =!.({J - (g) - - = - =- (i) _ = - = ~. ~ _ + _ J!i = (d) J!i. ~ + ~ = ; =!=. (h)! +.Q _ =4 Q. Shubham painted iof the wall space in his room. His sister Madhavi helped and painted! of the wall space. How much did they paint iogether? Sol. Fraction of wall painted by Shubham = ~

$86 MATHEMATICS-VI Fraction of wall painted by Madhavi = i To I.. b h + j ta painting y t em = - + - = -- = " = p Therefore they painted complete wall. Q4. Fill in the missing fractions.$

9 86 MATHEMATICS-VI Fraction of wall painted by Madhavi = i To I.. b h + j ta painting y t em = = -- = " = p Therefore they painted complete wall. Q4. Fill in the missing fractions. 7 D (a) 0 - = 0 D (c) -"6" " SoL (a) 0 (b) (c) "6 (d) 7. (b) D- (d) D+ 7 7 Q. Javed was given of a basket of oranges. What fraction of oranges was left in the basket? Sol. 'lbtal = Oranges left = EXERCISE 7.6 Q. solve: 7- =-7-=7 7 (a) - +- (b) (e) (f) (c) - +- (d) (g) - -- (h) (i) (j) (k) -+- (l) (m) (n) Sol. (a) L.C.M. of and 7 = x7+x 4+ 7 :. "+ 7 = = = FRACTIONS 87 (b) L;C.M. of 0 and = 0 " 7 x+7x "9+4 :. 0 + = 0 = --so- = 0 (c) L.C.M. of9 and 7 = 6 4 4x7+x :. "9 + 7 = 6 = ~ = 6 (d) L.C.M. of 7 and = :. ~ +! = x+7xl = +7 = =-.!:.. 7 (e) L.C.M. of and 6 = 0 x 6 + x + 7 :. + "6 = 0 = --so- = 0 (j) L.C.M. of and = ± ~ _ 4x+x _ +0 _ -~ (g) L.C.M. of 4 and = x-4xl "= ---- = = (h) L.C.M. of6 and = 6 -xl = (i) L.C.M. of, 4 and =.. ~ + ~ +! = x4+x+x6 = = 4 (j) L.C.M. of, and 6 = 6 lx+x :. " + " + "6 = 6 = 6 = "6 = (k) L.C.M. of and = 4 4 x + x 4 + :. " + " = = -- = " = (l) L.C.M. of and 4 = = 4x 4 + x = = 9 = 7 4

88 MATHEMATICS-VI (m) L.C.M. of and = 6 7 6-7 9 4 :.- = -- = = (n) L.C.M. of and = 6 4 8-.. -"=-6-=6 Q. Sarita bought " metre of ribbon and Lalita "4 metre of ribbon.

10 88 MATHEMATICS-VI (m) L.C.M. of and = :.- = -- = = (n) L.C.M. of and = "=-6-=6 Q. Sarita bought " metre of ribbon and Lalita "4 metre of ribbon. What is the total length of the ribbon they bought? SoL Ribbon bought by Sarita = ~ m Ribbon bought by Lalita = 4 m Total length of ribbon Now L.C.M. of and 4 = 0 x4+x +4= 0 = (~+ ~) m 8+ = -- = - = - metre Therefore total length of ribbon is 0 m. Q. Naina was given piece of cake and Najma was given piece of cake. Find the total amount them. Sol. Cake taken by Naina = " piece Cake taken by Najma = piece Thtal consumption of cake = ~ + ~ 4 Now = of cake given to both of FRACTIONS L.C.M. and = =--=-= Therefore total consumption is 6 pieces. Q4. Fillintheboxes:(a)D- ~ = ~ + 7 Sol. (a) = -- = (c) = - = Q. Complete the addition - subtraction box. t ~ - ~ 4 " " " " IJ... (al " (bl " 4" t ~ 4 6 " " " SoL (a) " " " " " O 89 0 (b) - " = (c) - = " (b) = -- = t (bl t ~ " " "6 IJ " 6" 7 Q6. A piece of wire 8 metre long broke into two pieces. One piece was "4 metre Sol. Thtallength long. How long is the other piece? of wire = ~ metre Length of first part = 4 metre Re.. 7 maimng part = Now

90 MATHEMATlCS-VI FRACTIONS 9 L.C.M. of 8 and 4 = 8 7 7-8 - 4 = -8- = 8 Therefore the length of remaining part is ~ metre. 9 Q7. Nandini's house is 0 km from her school.

11 90 MATHEMATlCS-VI FRACTIONS 9 L.C.M. of 8 and 4 = = -8- = 8 Therefore the length of remaining part is ~ metre. 9 Q7. Nandini's house is 0 km from her school. She walked some distance far did she walk? and then took a bus for " km to reach the school. How Sol. 'Ibtal distance between school and house =":0 km Q9. Jaidev takes " minutes to walk across the echool ground. Rahul takes by what fraction? 7 "4 minutes to do the same. Who takes less time and Sol. Time taken by Jaidev = ~ minutes = minutes.' 7 Time taken by Rahul = 4 minutes 7 44-' 9. Diftierence = = --- = - minutes Distance covered by bus = ~ km Thus Rahul takes less time, which is :0 minutes. Re mal.hi' ng di istance = 0 9 km - " km LlLl " = 0 = 0 = " Therefore distance covered by walking is ~ km, Q8. Asha and Samuel have bookshelves of the same size partly filled with books. Asha's shelf is "6 th full and Samu~l's shelf is " th full. Whose bookshelf is more full? By what fraction?. Sol. For comparing "6 and " - x- = x- = > 0.. Asha's bookshelf is more covered than Samuel. Difference = 0-0 = 0'

NCERT solution for Fractions-2

NCERT solution for Fractions-2 1 Exercise 7.3 Question 1 Write the fractions. Are all these fractions equivalent? (a) (b) a) We can find fraction in each figure by the formula Dark part/ total parts ½,