Page 1 : MATHEMATICS IN EVERYDAY LIFE–6, Chapter 5 : Fractions, , ANSWER KEYS, , EXERCISE 5.1, , 4., , 1. Natural numbers from 2 to 12:, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, Prime numbers between them are:, 2, 3, 5, 7, 11, Therefore, the required fraction =, 2., , (i), , ( 1 hour = 60 minutes), =, 5., , 5, 11, , 3, 7, Draw a number line. We divide the length, between 0 to 1 into seven equal, , 0, , 1, , 3, 7, , 30, 60, , A fraction:, (i) whose numerator is 6 and denominator is 11., , 6, 11, (ii) whose denominator is 9 and numerator is 4., =, , 4, 9, (iii) whose numerator and denominator add upto 9., =, , 2, , 3, means 3 part out of 7 equal parts near, 7, the zero., , 4 1, , , etc., 5 8, (iv) whose denominator is 3 more than the, , parts., , (ii), , 30 minutes, 30 minutes, =, 1 hours, 60 minutes, , =, , 5, 8, , numerator =, , Draw a number line. We divide the length, 5, betwen 0 to 1 into eight equal parts., means 5, 8, parts out of 8 equal parts near to 1., , 6., , 2 5, , , etc., 5 8, , (i) One-eighth,  One out of eight =, , 1, 8, , (ii) Four-elevenths, , 0, (iii), , 5, 8, , 1, , 2, , 2, 5, , (iii) Three-tenth, , Draw a number line. We divide the length, between 0 to 1 into 5 equal parts., parts out of 5 equal parts near to 0., , 0, 3., , 2, 5, , 1, , 1 day = 24 hours, =, , 2, means 2, 5, ,  Three out of ten =, , 6 hours, 6, =, 24 hours, 24, , Mathematics In Everyday Life-6, , 3, 10, , (iv) Two-sevenths,  Two out of seven =, , 2, 7. Deepti get erasers =, , 6 hours, 1 day, , , 4, 11, ,  Four out of eleven =, , 2, 7, , 3, of 24, 4, , 3,  24, 4, = 3 × 6 = 18 erasers, Hence, Deepti get 18 erasers and (24 – 18) = 6 erasers, left with Yamini., =, , 1

Page 2 : 8., , (i), , 2, of a collection of 15 books, 3, , =, (ii), , 5, of a collection of 28 cassettes, 7, , =, (iii), , 2,  15 = 2 × 5 = 10 books, 3, , 5,  28 = 5 × 4 = 20 cassettes, 7, , 3, of a collection of 88 apples, 11, , 3,  88 = 3 × 8 = 24 apples, 11, (i) There are six equal parts and 2 parts have been, shaded i.e., two-sixth is the shaded portion., , =, , 9., , Thus, the required fractions is, , 2, ., 6, , EXERCISE 5.2, 1. Like fractions: Frac tions having the same, denominators are called like fractions., So, (i), (v), (vi), (vii) and (viii) are pairs of like fractions., Unlike fractions: Fractions having the differents, denominators are called unlike fractions., So, (ii), (iii), (iv) are pairs of unlike fractions., 2. A fraction whose numerator is less than the, denominator is called a proper fraction., , 2 19 36, ,, ,, are proper fractions., 5 21 101, 3. A fraction whose numerator is greater than the, denominator is called improper fractions., So,, , (ii) There are 4 equal parts and 1 part has been, shaded i.e., one-fourth is the shaded portion., , 9 21 , ,, ,, are improper fractions., 1 16 5, 13, (i),  13 divided by 5, 5, Quotient = 2, Remainder = 3, Denominator = 5, , So,, 4., , , Thus, the required fraction is, , 1, ., 4, , (ii), , (iii) There are 16 equal parts and 4 parts have been, shaded i.e., four-sixteenth is the shaded portion., , 13, 3, = 2 ., 5, 5, 92,  92 divided by 13, 13, Quotient = 7, Remainder = 1, , Denominator = 13, , (iii), , 92, 1, = 7, ., 13, 13, 71,  71 divided by 9, 9, Quotient = 7, Remainder = 8, , Denominator = 9, Thus, the required fraction is, , 4, ., 16, , (iv) There are 18 equal parts and 7 parts have been, shaded i.e., seven-eighteenth is the shaded, portion., Thus, the required fraction is, , 2, , 7, ., 18, , , (iv), , , , 71, 8, = 7 ., 9, 9, 63,  63 divided by 8, 8, Quotient = 7, Remainder = 7, Denominator = 8, 63, 7, = 7 ., 8, 8, , 2, 5 13, –10, 3, , 7, 13 92, –91, 1, , 7, 9 71, –63, 8, , 7, 8 63, –56, 7, , Answer Keys

Page 3 : (v), , 103, 15, , Quotient = 6, Remainder = 13, Denominator = 15, 103, 13, = 6, ., 15, 15, , , (vi), , 88, 17, , 88, 3, = 5, ., 17, 17, , , 53, 7, , 53, 4, = 7 ., 7, 7, , , 135, 14, , (iii), , 3, with denominator 40., 8, 3  5 15, 3, , =, 8,  5 40, 8, , 5, 17 88, –85, 3, , (iv), , 5, with numerator 15., 9, 5, 5  3 15, , =, 9, 9  3 27, , 7, 7 53, –49, 4, , 7., , (i) The four equivalent fractions of, , 135, 9, , = 9, ., 14, 14, (3  7)  5 21  5 26, 5, , , 5. (i) 3 =, 7, 7, 7, 7, , 5, are :, 7, , 5  3 15, 5  2 10 5, 5, , , =, ,, =, 7  3 21, 7, 7  2 14 7, 5  5 25, 5, 5  4 20 5, , , =, ,, =, 7  5 35, 7, 7  4 28 7, ,  135 divided by 14, , Quotient = 9, Remainder = 9, Denominator = 14, , 9, 14 135, –126, 9, , Hence, four equivalent fractions of, , 5, 10, are, ,, 7, 14, , 15 20, 25, ,, and, ., 21 28, 35, (ii) Four equivalent fractions of, , 8, are, 11, , (ii) 8, , (8  5)  3 40  3 43, 3, , , =, 5, 5, 5, 5, , 8  3 24, 8  2 16 8, 8, , , =, ,, =, 11  3 33, 11, 11  2 22 11, , (iii) 4, , (4  9)  7 36  7 43, 7, , , =, 9, 9, 9, 9, , 8  5 40, 8  4 32 8, 8, , , =, ,, =, 11  5 55, 11, 11  4 44 11, , (iv) 5, , (5  11)  3 55  3 58, 3, , , =, 11, 11, 11, 11, , (v) 13, , (13  10)  7 130  7 137, 7, , , =, 10, 10, 10, 10, , (6  6)  5 36  5 41, 5, , , (vi) 6 =, 6, 6, 6, 6, , (vii) 11, , (11  8)  3 88  3 91, 3, , , =, 8, 8, 8, 8, , (13  5)  1 65  1 66, 1, , , (viii) 13 =, 5, 5, 5, 5, , 6., , 6  3 18, 6, =, , 7  3 21, 7, ,  53 divided by 7, , Quotient = 7, Remainder = 4, Denominator = 7, , (viii), , 6, 15 103, –90, 13, , 6, with numerator 18., 7, ,  88 divided by 17, , Quotient = 5, Remainder = 3, Denominator = 17, , (vii), , (ii), ,  103 divided by 15, , 3, (i), with denominator 20., 5, 3×4, 3, 12, =, =, 5×4, 20, 5, , Mathematics In Everyday Life-6, , Thus, four equivalent fractions are, and, , 16 24 32, ,, ,, 22 33 44, , 40, ., 55, 4, are, 9, 4  3 12, 42 8 4, 4, , , =, ,, =, 9  3 27, 9  2 18 9, 9, , (iii) Four equivalent fractions of, , 4  5 20, 4  4 16 4, 4, , , =, ,, =, 9  5 45, 9  4 36 9, 9, Hence, four equivalent fractions of, , 4, 8, are, ,, 9, 18, , 12 16, 20, ,, and, ., 27 36, 45, , 3

Page 4 : 3, are, 8, 3 3 9, 3, 3 2 6 3, , , =, ,, =, 8, 8  3 24, 8  2 16 8, , (iv) Four equivalent fractions of, , (iv), , 18   3, 18, , =, 30   5, 30, , 3  5 15, 3, 3  4 12 3, , , =, ,, =, 8,  5 40, 8, 8, 8  4 32, Hence, four equivalent fractions of, , 3 18, ,, 5 30, , Thus, 3 , 18 are equivalent fractions., 5 30, , 3, 6, are, ,, 8, 16, , (v), , 9 12, 15, ,, and, ., 24 32, 40, , 5 20, ,, 9 36, , 20   5, 20, , =, 36   9, 36, , 12, 8. Five equivalent fractions of, ., 36, 12   6, 12, , =, 36   18, 36, , 12   4, 12, , =, 36   12, 36, , (vi), , 3 9, ,, 10 60, , 3, 9, 3, , =, 10   30, 10, , 12   3, 12, , =, 36, 36   9, , Thus, 3 , 9 are not equivalent fractions., 10 60, , 12   2, 12, , =, 36   6, 36, 12   1, 12, , =, 36, 36   3, 12, Hence, five equivalent fractions for, are, 36, , 5 20, are equivalent fractions., ,, 9 36, , Thus,, , 10., , Hence, (i), (iv) and (v) are the pair of equivalent, fractions., (i) One part shaded out of four equal parts i.e. onefourth portion is shaded. Thus,, , 6, 4 3 2, 1, ,, , , , and ., 18 12 9 6, 3, , 9., , (i), , 3 15, ,, 7 35, , , , 15   3, 15, , =, 35   7, 35, , Hence, 3 , 15 are equivalent fractions., 7 35, (ii), , 1, 4, , Two parts is shaded out of eight equal parts i.e.,, two-eighth portion is shaded. Thus,, , 4 12, ,, 7 14, , 2, 8, , 4 8, 4, , =, 7   14, 7, Thus, 4 , 12 are not equivalent fractions., 7 14, (iii), , 7 21, ,, 5 10, , 7   14, 7, , =, 5   10, 5, Thus,, 4, , 7 21, are not equivalent fractions., ,, 5 10, , , , 1 2 2, 1, =, , 4, 42 8, , 1, 2, and, are equivalent fractions., 8, 4, Hence, they are equivalent., , , Answer Keys

Page 5 : (ii) Two parts is shaded out of six equal parts i.e.,, two-sixth is shaded portion. Thus,, , (iv) Two parts is shaded out of three equal parts i.e.,, , 2, 6, , 2, ., 3, , Four parts is shaded out of nine equal parts i.e.,, four-ninth is shaded portion. Thus,, , Four parts is shaded out of six equal parts i.e.,, 4, ., 6, , 4, 9, , , , 4, 2, and, are not equivalent fractions., 9, 6, Hence, they are not equivalent., , , (iii) One part is shaded out of two equal parts i.e.,, , 42 2, 4, , =, 6, 62 3, , 2, 4, and, are equivalent fractions., 3, 6, Hence, they are equivalent., , , 1, 2, , EXERCISE 5.3, 1., , (i) To reduce the given fraction into their lowest, terms, divide the numerator and denominator, by their H.C.F., H.C.F. of 18 and 27, 18 27 1, –18, 9 18 2, –18, 0, H.C.F. of 18 and 27 is 9., , Two parts is shaded out of four equal parts i.e.,, 2, 4, , , , 18  9 2, 18, , =, 27  9 3, 27, 35, ., 40, We find the H.C.F. of 35 and 40., , (ii) The given fraction is, , , , , , 1 2 2, 1, =, , 2, 22 4, , 1, 2, and, are equivalent fractions., 2, 4, , Hence, they are equivalent., Mathematics In Everyday Life-6, , 35 40 1, –35, 5 35 7, –35, 0, , H.C.F. of 35 and 40 is 5., 35  5 7, 35, , , =, 40  5 8, 40, 5

Page 6 : 24, ., 108, We find the H.C.F. of 24 and 108., , (iii) The given fraction is, , (vii) The given fraction is, , We find the H.C.F. of 60 and 68., , 24 108 4, –96, 12 24 2, –24, 0, H.C.F. of 24 and 108 is 12., , 60 68 1, –60, 8 60 7, –56, 4 8 2, –8, 0, , 24  12 2, 24, , =, 108  12 9, 108, 56, (iv) The given fraction is, ., 72, We find the H.C.F. of 56 and 72., , , H.C.F. of 60 and 68 is 4., , 60  4 15, 60, , =, 68  4 17, 68, , , , (viii) The given fraction is, , 56 72 1, –56, 16 56 3, –48, 8 16 2, –16, 0, , 36 63 1, –36, 27 36 1, –27, 9 27 3, –27, 0, , 56  8 7, 56, , =, 72  8 9, 72, , H.C.F. of 63 and 36 is 9., , 36, ., 48, We find the H.C.F. of 36 and 48., , (v) The given fraction is, , 36 48 1, –36, 12 36 3, –36, 0, , 72, ., 20, We find the H.C.F. of 72 and 20., 20 72 3, –60, 12 20 1, –12, 8 12 1, –8, 4 8 2, –8, 0, , H.C.F. of 72 and 20 is 4., , 6, , 72  4 18, 72, , =, 20  4 5, 20, , 63  9 7, 63,  ., =, 36  9 4, 36, , , 2., , (i), , 3, 18, =, 5, , 3 6, 18, 3, =, =, 30, 5 6, 5, , , , H.C.F. of 36 and 48 is 12., 36  12 3, 36, , , =, 48  12 4, 48, (vi) The given fraction is, , 63, ., 36, , We find the H.C.F. of 63 and 36., , H.C.F. of 56 and 72 is 8., , , 60, ., 68, , Hence,, , (ii), , 4, , =, , 3, 18, =, 5, 30, , 20, 16, 20  4, 5, 20, =, =, 4, 16  4, 16, , , , Hence,, (iii), , 7, , , , =, , 20, 5, =, 16, 4, , 42, 30, 7, 42  6, 42, =, =, 5, 30  6, 30, , Hence,, , 7, 5, , =, , 42, 30, Answer Keys

Page 7 : (iv), , 5, , 51, 15, , =, , 51  3, 17, 51, =, =, 15  3, 5, 15, , , , Hence,, (v), , (ii), , 5  4 20, 5, , =, 7  4 28, 7, 20, 5, Hence,, =, 28, 7, 5 7, (iii), ,, 9 12, L.C.M. of 9, 12 is 36., , 51, 17, =, 15, 5, , 44, =, 5, 20, , 44  4, 11, 44, =, =, 20  4, 5, 20, , , , 5 20, ,, 7 28, L.C.M. of 7 and 28 is 28., , 5, 5  4 20, , =, 9, 9  4 36, , 11, 44, Hence,, =, 5, 20, , (vi), , 56, , 7  3 21, 7, , =, 12  3 36, 12, , 7, 4, , =, , (iv), , 45  9, 5, 45, =, =, 36  9, 4, 36, , 3., , (i), , (v), , 15  4, 60, 15, =, =, 17, , 4, 68, 17, , 15, 60, =, 17, 68, , (vi), , L.C.M. of 14 and 21 is 42., , 13  3 39, 13, , =, 14  3 42, 14, 7 14, 21, 2, 3, , (vii), , 16, 39, >, (If denominator are same, then, 42, 42, with greater numerator is greater), 8, 13, >, 14, 12, , Mathematics In Everyday Life-6, , 1 1, ,, 3 4, 1, 3, , 1, 4, 4>3, 1, 1, >, 4, 3, , 7 1, ,, 8 2, 7, 8, , 1, 2, 14 > 8, 7, 1, >, 8, 2, , , , Since,, , , , 13, 8, >, 14, 29, , , , 13 8, ,, 14 21, , 8  2 16, 8, , =, 21  2 42, 12, , 13 8, ,, 14 29, 13, 8, 14, 29, 377 > 112, , , , 5, 45, Hence,, =, 4, 36, 15, 60, (viii), =, 17, , Hence,, , 7, 5, <, 12, 9, , , , 45, (vii), =, 4, 36, , , , 3, 4, , 20 21, <, (If denominator are same, then with, 36 36, greater numerator is greater), , 7, 56, Hence,, =, 4, 32, , , , 9, 12, , Since,, , 78, 56, 7, =, =, 48, 32, 4, , , , 3, , , , 5 3, ,, 12 7, 5, 12, , 3, 7, 35 < 36, , 5, 3, <, 12, 7, 7

Page 8 : (viii), , 4, 5, , (ix), , L.C.M of 3, 9, 18 and 27 is 54., , 4 3, ,, 5 10, 3, 10, 40 > 15, , 4, 4  6 24, , =, 9, 9  6 54, , 4, 3, >, 5, 10, , 7  3 21, 7, , =, 18  3 54, 18, , 1 2, ,, 8 3, , , , 11, 5, , 1, 2, <, 8, 3, , , , 1 10 7 4, ,, ,, ,, are in ascending order.., 3 27 18 9, , (iii), , , , (iv), , L.C.M. of 4, 8, 7, 14 is 56., , 3  14 42, 3, , =, 4  14 56, 4, 5, 5  7 35, =, , 8, 8  7 56, , 5, 6, 24 < 25, , 6  8 48, 6, , =, 7  8 56, 7, , 4, 5, <, 5, 6, , 9  4 36, 9, , =, 14  4 56, 14, , 2 4 6 5, , , ,, 7 7 7 7, , , , 2 4 5 6,   , 7 7 7 7, , 2 4 5 6, , , , are in ascending order.., 7 7 7 7, , 1 4 7 10, (ii), , , ,, 3 9 18 27, , 42, 36, 48, 35, <, <, <, 56, 56, 56, 56, , Since,, ,  All the fractions have same denominator, so, with greater numerator is greater., , 8, , 3 5 6 9, , , ,, 4 8 7 14, , 4 5, ,, 5 6, , Since,, , 8 8 8, 8, 8, ,, ,, ,, ,, are in ascending, 15 13 11 9 5, , order., , 5, 13, <, 6, 15, , , (i), , 8, 8, 8, 8, 8, <, <, <, <, 13, 5, 15, 9, 11, , Hence,, , 13, 15, 75 < 78, , 4, 5, , 4., , 8 8 8 8 8, , , , ,, 9 13 5 11 15, , Since, if numerator are same then with smaller, denominator is greater., , 5 13, (xi), ,, 6 15, , (xii), , 1, 1, 2, 3, , 18, 20, 21, 24, <, <, <, 54, 54, 54, 54, , 11, 20, <, 5, 3, , , , 1, 3, 6, 9, , , , 20, 3, 33 < 100, , 5, 6, , 3, , 2, 3, 3 < 16, , 11 20, ,, 5, 3, , , , 3 3, 9, 18, 27, , 10  2 20, 10, , =, 27  2 54, 27, , 1, 8, , (x), , 1  18 18, 1, , =, 3  18 54, 3, , Hence,, (v), , 5 9 3 6, ,, , ,, are in ascending order.., 8 14 4 7, , 2 2 4 1, , , ,, 5 3 12 5, , L.C.M. of 5, 3, 12 and 5 is 60., , 2  12 24, 2, , =, 5  12 60, 5, Answer Keys

Page 9 : 2  20 40, 2, , =, 3, 3  20 60, , , , 4  5 20, 4, , =, 12  5 60, 12, , Hence,, , 1  12 12, 1, , =, 5  12 60, 5, , , , , (vi), , (viii), , 24, 12, 20, 40, <, <, <, 60, 60, 60, 60, , L.C.M. of 3, 12, 15 and 8 is 120., , 2  40 80, 2, , =, 3  40 120, 3, 5  10, 5, 50, , =, 12, 12  10 120, , 1 4 2 2, ,, , ,, are in ascending order.., 5 12 5 3, , 48, 32, 4, , =, 15  8 120, 15, , 7 3 5 11, , , ,, 12 4 8 6, , 1  15 15, 1, , =, 8  15 120, 8, , L.C.M. of 12, 4, 8 and 6 is 24., , 7  2 14, 7, , =, 12  2 24, 12, , , , 50, 15, 32, 80, <, <, <, 120, 120, 120, 120, , 3, 3  6 18, , =, 4, 4  6 24, , , , 1, 5, 4, 2, <, <, <, 8, 12, 15, 3, , 5  3 15, 5, , =, 8  3 24, 8, , Hence,, , 11  4 44, 11, , =, 6  4 24, 6, , , , , 5., , (i), , 18, 14, 15, 44, <, <, <, 24, 24, 24, 24, , L.C.M. of 5, 10, 3, 15 is 30., , 3  6 18, 3, , =, 5  6 30, 5, 7  3 21, 7, , =, 10, 10  3 30, , 7 5 3 11, , , ,, are in ascending order.., 12 8 4 6, , 2  10 20, 2, , =, 3  10 30, 3, , 15 3 5 7, , ,, ,, 21 14 42 2, , 7  2 14, 7, , =, 15  2 30, 15, , L.C.M. of 21, 14, 42 and 2 is 42., , 15  2 30, 15, , =, 21  2 42, 21, , , , 18, 21, 20, 14, >, >, >, 30, 30, 30, 30, , 3 3, 3, 9, , =, 14, 14  3 42, , , , 7, 7, 2, 3, >, >, >, 10, 15, 3, 5, , 51, 5, 5, , =, 42  1 42, 42, , Hence,, , 7  21 147, 7, , =, 2  21 42, 2, , , 1 4, 5 2, ,, ,, ,, are in ascending order.., 8 15 12 3, , 3 7 2 7, , , ,, 5 10 3 15, , 3, 11, 7, 5, <, <, <, 4, 6, 12, 8, , Hence,, (vii), , 3 15 7, 5, ,, ,, ,, are in ascending order.., 42 14 21 2, , 2 5 4 1, , , ,, 3 12 15 8, , 1, 2, 4, 2, <, <, <, 5, 3, 12, 5, , Hence,, , 3, 7, 5, 15, <, <, <, 14, 2, 42, 21, , 30, 5, 9, 147, <, <, <, 42, 42, 42, 42, , Mathematics In Everyday Life-6, , (ii), , 7 2 3 7, , , ,, are in descending order.., 10 3 5 15, , 5 7 13 17, , , ,, 9 12 36 18, , L.C.M. of 9, 12, 36 and 18 is 36., 9

Page 10 : 5  4 20, 5, , =, 9  4 36, 9, , 2  12 24, 2, , =, 3  12 36, 3, , 7  3 21, 7, , =, 12, 12  3 36, , , , 24, 32, 30, 15, >, >, >, 36, 36, 36, 36, , 13  1 13, 13, , =, 36  1 36, 36, , , , 2, 5, 8, 5, >, >, >, 3, 12, 9, 6, , 17  2 34, 17, , =, 18  2 36, 18, , Hence,, , , , 20, 34, 21, 13, >, >, >, 36, 36, 36, 36, , , , 17, 7, 5, 13, >, >, >, 18, 12, 9, 36, , Hence,, , (iii), , (v), , 1 2 2 5, , , ,, 3 5 3 6, , L.C.M. of 3, 5, 3 and 6 is 30., , 1  10 10, 1, , =, 3  10 30, 3, , 17 7 5 13, ,, , ,, are in descending order.., 18 12 9 36, , 2  6 12, 2, , =, 5, 5  6 30, , 1 5 2 7 4, , , , ,, 6 9 3 12 9, , 2  10 20, 2, , =, 3  10 30, 3, , L.C.M. of 6, 9, 3, 12 and 9 is 36., , 1 6 6, 1, , =, 6,  6 36, 6, , 5  5 25, 5, , =, 6  5 30, 6, , 5  4 20, 5, , =, 9, 9  4 36, , , , 2  12 24, 2, , =, 3  12 36, 3, , , , 7  3 21, 7, , =, 12  3 36, 12, 4  4 16, 4, , =, 9  4 36, 9, , , 24, 16, 6, 21, 20, >, >, >, >, 36, 36, 36, 36, 36, , Hence,, (iv), , 12, 25, 20, 10, >, >, >, 30, 30, 30, 30, 5, 2, 2, 1, >, >, >, 6, 5, 3, 3, , Hence,, (vi), , 13  2 26, 13, , =, 18  2 36, 18, 73, 7, 21, , =, 12, 12  3 36, , 2 7 5 4 1, ,, , , , are in descending order.., 3 12 9 9 6, , 2  12 24, 2, , =, 3  12 36, 3, , 8 5 5 2, , , ,, 9 12 6 3, , 5  4 20, 5, , =, 9  4 36, 9, , L.C.M. of 9, 12, 6 and 3 is 36., , 8  4 32, 8, , =, 9  4 36, 9, , , , 21, 26, 24, 20, >, >, >, 36, 36, 36, 36, , 5  3 15, 5, , =, 12, 12  3 36, , , , 7, 5, 13, 2, >, >, >, 12, 9, 18, 3, , 5  6 30, 5, , =, 6,  6 36, 6, 10, , 5 2 2 1, , , ,, are in descending order.., 6 3 5 3, , 13 7 2 5, , , ,, 18 12 3 9, L.C.M. of 18, 12, 3 and 9 is 36., , 7, 5, 4, 2, 1, >, >, >, >, 12, 9, 9, 3, 6, , , , 8 5 2 5, , , ,, are in descending order.., 9 6 3 12, , Hence,, , 13 2 7 5, , ,, ,, are in descending order.., 18 3 12 9, Answer Keys

Page 11 : 2, of a book, 3, 1, Second day, boy reads, of a book. Therefore,, 5, 2, 1, 3, 5, 10 > 3, , 6. First day, boy reads, , 9. L.C.M. of 5, 4, 7 and 2 is 140., , 3  28 84, 3, , =, 5, 5  28 140, 3  35 105, 3, , =, 4  35 140, 4, 2  20 40, 2, , =, 7  20 140, 7, , 2, 1, >, 3, 5, Hence, on first day he did read major part of the, book., , , , 7. On a particular day, A walked = 2, , 1  70 70, 1, , =, 2  70 140, 2, , 2, 8, km =, km, 3, 3, , , , 1, 15, B walked = 2 km =, km, 7, 7, , C walked = 1, , 3, 8, km =, km, 5, 5, , L.C.M. of 3, 7 and 5 is 105., , 70, 84, 40, 105, >, >, >, 140, 140, 140, 140, 3, 3, 1, 2, >, >, >, 5, 4, 2, 7, , , , Hence,, 10., , 8 × 35, 8, 280, =, =, 3, 3 × 35, 105, , 4, , 3, is the greatest of all fractions., 4, , 2, 1, 3, 1, 14 13 11 16, , 3 , 2 , 5 or, ,, ,, ,, 3, 4, 4, 3, 3, 4, 4, 3, , L.C.M. of 3, 4, 4 and 3 is 12., 14, 14  4 56, , =, 3, 3  4 12, , 15 × 15, 15, 225, =, =, 7, 7 × 15, 105, , 13  3 39, 13, , =, 4, 4  3 12, , 8 × 21, 8, 168, =, =, 5, 5 × 21, 105, , 11  3 33, 11, , =, 4, 4  3 12, ,  Denominators are same., , , , 280, 225, 168, >, >, 105, 105, 105, , , , 8, 15, 8, >, >, 3, 7, 5, , , , 2, 1, 3, > 2 >1, 3, 7, 5, , 56, 39, 64, 33, <, <, <, 12, 12, 12, 12, , , , 16, 13, 14, 11, <, <, <, 3, 3, 4, 4, , or, , 2, , 16  4 64, 16, , =, 3  4 12, 3, , 2, 1, 3, km, 2 km, 1 covered by, 3, 7, 5, them in descending order., , Hence, the distence 2, , 3, of total toffees, 8, 1, Suresh got =, of total toffees, 2, 1, Prakesh got =, of total toffees, 8, 3 1 4, 4 1, ,, = ,, 8 24, 8 8, , or, , 4, 1, 3, >, >, 8, 8, 8, 1, 3, 1, , >, >, 2, 8, 8, Hence, Suresh got the maximum number of toffees., Mathematics In Everyday Life-6, , 3, 1, 2, 1, < 3 < 4 < 5, 4, 4, 3, 3, , Hence, 2 3 is the smallest of all fractions., 4, , 8. Ramesh got =, , , , 2, , EXERCISE 5.4, 1., , (i), , 7, 3, and, are like fractions. Therefore,, 11, 11, 73, 10, 7, 3, , =, =, 11, 11, 11 11, , (ii), , 9, 2, and, are like fractions. Therefore,, 5, 5, , 92, 11, 1, 9 2,  =, =, = 2, 5, 5, 5 5, 5, 11

Page 12 : (iii), , 7, 4, and, are like fractions. Therefore,, 8, 8, , 11 3, 11  3, 8, 1, 1,  =, (ix) 5  1 =, =, =4, 2 2, 2, 2, 2, 2, , 74, 11, 3, 7 4,  =, =, = 1, 8, 8, 8 8, 8, (iv), , (v), , (x) 1, , 7, 3, 17  13, 17 13, 4, 2, 1, , =, =, =, =, 10, 10, 10, 10, 5, 10 10, , 7, 3, and, 12, 12, , (xi), , 97, 1, 9, 7, 2, , =, =, =, 10 10, 10, 5, 10, , 7, 3, 73, 10, 5, , =, =, =, 12 12, 12, 12, 6, , (xii), , 52, 3, 5 2,  =, =, 5, 5, 5 5, , 8 3, 1, ,, and, 9 9, 9, , 3., , 11 5 1, 1, 1 1,  , (i) 5  2  =, 2 2 2, 2, 2 2, , 8 3, 1, ,, and, are like fractions. Therefore,, 9 9, 9, , 831, 4, 8 3 1, 12,  , =, =, =, 9 9 9, 9, 3, 9, 1, 1, (vi) 2 1 , 3 and, 3, 3, 3, , (ii), , 2, 1, and 2, 3, 3, , 2., , (i), , (iii), , 74, 11, =, =1, 11, 11, , 7  9  1  11, 7, 9, 1 11, , , , =, 24, 24 24 24 24, , 1, 1, and 1, 7, 7, , 16  1  11, 24, , =, , 15  8, 15 8, 23, 2, , =, =, = 3, 7 7, 7, 7, 7, , 26, 15  11, =, 24, 24, , =, , 1, 13, = 1, 12, 12, , (iv), , 13  7, 2, 6, 13 7, , =, =, =, 15, 5, 15, 15 15, 84, 2, 1, 8 4, 4, 1, 1 =  =, =, =1, 3, 3, 3 3, 3, 3, 3, , 781, 7, 8, 1, , , =, 15, 15 15 15, , =, , 15  1, 14, =, 15, 15, , (v), , 317, 27, 3 1 7, 1, 9,   =, =, =, = 2, 4 4 4, 4, 4, 4, 4, , (iii), , 12  3, 9, 4, 12 3,  =, =, =1, 5, 5, 5, 5 5, , (vi), , (iv), , 11  9, 1, 2, 11 9, , =, =, =, 5, 10, 10, 10 10, , 942, 11, 9, 4, 2, 1, , , =, =, = 1, 10, 10, 10 10 10, 10, , (vii), , 751, 21, 7 5 1, 3,   =, =, =, 8, 8 8 8, 8, 8, , (viii), , 231, 33, , 2 3 1,   =, =, =, =0, 5, 5, 5, 5 5 5, , 97, 9 7, 2, 1, 1, (v) 4  3 =  =, =, =1, 2 2, 2, 2, 2, 2, , (vi), , 51, 4, 5 1,  =, =, 7, 7, 7 7, , 15 9, 3, 1, 15  9, 6, 3, 1,  =, (vii) 3  2 =, =, =, = 1, 4 4, 4, 2, 2, 4, 4, 4, (viii), 12, , 15, 1, = 7, 2, 2, , =, , 13, 7, and, are like fractions. Therefore,, 15, 15, , (ii) 2, , =, , =, , 17 7, 17  7, 24,  =, =, =8, 3 3, 3, 3, (viii) 2, , 16  1, 11  5  1, =, 2, 2, , 12  5  4, 12 5, 4, , , =, 11, 11 11 11, , 7 10 1, 7  10  1, 18, ,  =, =, =6, 3 3 3, 3, 3, (vii) 5, , =, , 41, 3, 4 1,  =, =, 7, 7, 7 7, , 4. Sum of 2, , 3, 2, 3, 2, and 1 = 2  1, 5, 5, 5, 5, , =, , 13 7, , 5 5, , =, , 13  7, 20, =, 5, 5, Answer Keys

Page 13 : Now, subtract, , 3 20, 20, 3, from 7 = 7 , 5 5, 5, 5, , =, , 38 20, , 5, 5, , 38  20, 18, 3, =, = 3, 5, 5, 5, 3, Hence, the required difference is 3 ., 5, , 5. Difference of 7, , 61 27, 5, 3, , and 3 =, 8, 8, 8, 8, , 61  27, 34, =, 8, 8, 3 34, 3, 34, Now, addition of 2 and, = 2 , 8 8, 8, 8, =, , 19 34, , =, 8, 8, 19  34, =, 8, 53, 5, =, = 6, 8, 8, 5, Hence, required sum is 6 ., 8, 6. Total weight of dry fruits purchased by Jayant, 4, =, kg, 5, 2, Jayant ate dry fruits =, kg, 5, 4 2, Quantity of dry fruits left =    kg, 5 5, , 2, 4  2, = , kg,  kg =,  5 , 5, , 2, Hence, the length of other piece of ribben is 1 m ., 3, 2, 9. The cost of a pen = ` 9, 5, 1, The cost of a pencil = ` 3, 5, 2, 1, Difference of cost of both things = `  9  3 ,  5, 5, 47 16 , = ` ,  ,  5, 5 , 47  16 , = ` , ,  5 , , = `, , 31, 1, = `6, 5, 5, , Hence, ` 6 1 is more cost of pen from pencil., 5, 1, 10. Total weight of milk purchased by Mrs. Sood = 5 litres, 2, 1, Total weight of consumed milk = 3 litres, 2, 5 1  3 1, Quantity of left milk = ,  litres,  2, 2,  11 7 , =    litres,  2 2,  11  7 , = ,  litres,  2 , , =, , 4, = 2 litres, 2, , Hence, 2 litres of milk is left., , 2, kg of dry fruits were left., 5, 3, 7. On Saturday, Sunil done, of his homework and on, 7, 2, Sunday,, of his homework. Therefore,, 7, 3 2, Total homework done by Sunil = , 7 7, 32, 5, =, =, 7, 7, 5, Hence,, of his homework did he done over the, 7, weekend., , Hence,, , 2,  1, 8. The length of other pieces of ribben =  4  2  m,  3, 3,  13 8 , =   m,  3 3, Mathematics In Everyday Life-6, , 2, 5,  13  8 , = , m = m = 1 m,  3 , 3, 3, , 5,  4, 11. The length of the other piece =  8  3  m,  9, 9,  76  32  m, = , ,  9, 9 ,  76  32 , = , m,  9 , , =, , 44, 8, m= 4 m, 9, 9, , 8, Hence, the length of the other piece of wire = 4 m ., 9, 2, 12. Weight of sugar purchased by Naresh = 2 kg, 3, 1, Weight of sugar purchased by Ramesh = 3 kg, 3, 4, Weight of sugar purchased by Sunil = kg, 3, Total weight of sugar purchased by them, 13

Page 14 : (v) L.C.M. of 7 and 3 is 21., , 1 4,  2, =  2  3   kg,  3, 3 3, , 5 1, 5  3 1 7, 15 7,  =, , , =, 7 3, 73 37, 21 21, , 8 10 4 , =  ,   kg, 3 3 3, , =, ,  8  10  4 , = ,  kg, , 3, , , =, , 1, 22, = 1, 21, 21, (vi) L.C.M. of 7 and 9 is 63., , =, , 22, 1, kg = 7 kg, 3, 3, , Hence, total weight of sugar is 7, , 1, kg., 3, , EXERCISE 5.5, 1., , (i) L.C.M. of 5 and 15 is 15., 3 7, 3 3 7, , , =, 5 15, 5  3 15, , =, , 97, 9, 7, , =, 15, 15 15, , 16, 1, = 1, 15, 15, (ii) L.C.M. of 5 and 6 is 30., , =, , 2, 5, 22 23, 4 3 =, , 5, 6, 5, 6, 22  6 23  5, , =, 5 6, 65, 132 115, , 30, 30, 132  115, =, 30, , =, , 247, 7, = 8, 30, 30, (iii) L.C.M. of 3 and 5 is 15., , =, , 17 16, 2, 1, , 5 3 =, 3, 5, 3, 5, =, , 17  5 16  3, , 35, 5 3, , =, , 85 48, , 15 15, , 85  48, 133, 13, =, = 8, 15, 15, 15, (iv) L.C.M. of 10 and 15 is 30., , =, , 73, 82, 21 16, 7, 8, , , , =, =, 10  3 15  2, 30 30, 10 15, 21  16, 37, 7, =, =, = 1, 30, 30, 30, , 14, , 15  7, 21, , 3  9 1 7, 27 7, 3 1, , ,  =, =, 79 97, 63 63, 7 9, 34, 27  7, =, 63, 63, (vii) L.C.M. of 5 and 7 is 35., , =, , 47 35, 28 15, 4 3, , ,  =, =, 35 35, 5, , 7, 7, , 5, 5 7, =, , 28  15, 35, , 8, 43, = 1, 35, 35, (viii) L.C.M. of 4 and 3 is 12., , =, , 1, 1, 13 13, 3 4 =, , 4, 3, 4, 3, 13  3 13  4, , =, 43, 3 4, 39  52, 39 52, , =, 12 12, 12, 91, 7, =, = 7, 12, 12, (ix) L.C.M. of 5, 2 and 10 is 10., =, , 3  2 1 5 7, 3 1 7, , ,  , =, 5  2 2  5 10, 5 2 10, 6, 5, 7, , , 10 10 10, 657, =, 10, , =, , 9, 4, 18, =, = 1, 5, 5, 10, (x) L.C.M. of 9, 5 and 5 is 45., , =, , 1 2, 2, 73 2 17, 8  3 =,  , 9 5, 5, 9 5 5, 73  5 2  9 17  9, , , =, 9 5 59 59, 365 18 153, , , 45 45 45, 365  18  153, 41, 536, =, =, = 11, 45, 45, 45, =, , Answer Keys

Page 15 : (xi) L.C.M. of 10, 6 and 15 is 30., 1, , 3, 1 4, 13 13 4, 2 , , , =, 10, 6 15, 10 6 15, , =, , 13  3 13  5 4  2, , , 10  3 6  5 15  2, , 39 65 8, , , 30 30 30, 39  65  8, 112, =, =, 30, 30, 56, 11, =, = 3, 15, 15, , =, , 7 17 2, 1, 5 2, , (xii) 2  2  = , 3 6 9, 3, 6 9, , L.C.M. of 3, 6 and 9 is 18., , 7  6 17  3 2  2, , , =, 36 63 92, , 42 51 4, , , 18 18 18, 42  51  4, =, 18, 97, 7, =, = 5, 18, 18, (i) L.C.M. of 7 and 4 is 28., =, , 2., , 5 1, 5  4 1 7,  =, , 7 4, 74 47, 20 7, , 28 28, 20  7, 13, =, =, 28, 28, (ii) L.C.M. of 12 and 15 is 60., , =, , 3, , 37 31, 1, 1, , 2, =, 12 15, 12, 15, , =, , 37  5 31  4, , 12  5 15  4, , 185  124, 185 124, , =, 60, 60, 60, 1, 61, =, = 1, 60, 60, (iii) L.C.M. of 4 and 10 is 20., =, , 35 72, 3 7, , , =, 4  5 10  2, 4 10, 15 14, , 20 20, 15  14, 1, =, =, 20, 20, , =, , Mathematics In Everyday Life-6, , (iv) L.C.M. of 2 and 3 is 6., , 7 10, 1, 1, 3 3 = , 2 3, 2, 3, 7  3 10  2, 21 20, , , =, =, 2 3 3 2, 6, 6, 21  20, 1, =, 6, 6, (v) L.C.M. of 6 and 3 is 6., , =, , 5, 1, 29 7, 4 2 =, , 6, 3, 6 3, 29 7  2, , =, 6 32, 29 14, , 6, 6, , =, , 29  14, 15, =, 6, 6, 5, 1, =, = 2, 2, 2, (vi) L.C.M. of 9 and 6 is 18., , =, , 28 17, 1, 5, , 3 2 =, 9, 6, 9, 6, 28  2 17  3, , =, 92, 63, 56 51, , 18 18, 56  51, 5, =, =, 18, 18, (vii) L.C.M. of 10 and 15 is 30., , =, , 2, , 27 17, 7, 2, , 1, =, 10 15, 10, 15, 27  3 17  2, , =, 10  3 15  2, , 81 34, , 30 30, 81  34, =, 30, 47, 17, =, = 1, 30, 30, (viii) L.C.M. of 6 and 15 is 30., , =, , 19  5 31  2, 19 31, 1, 1, , , 3 2, =, =, 6  5 15  2, 6 15, 6, 15, 95 62, , 30 30, 95  62, =, 30, 11, 1, 33, =, =, = 1, 30, 10, 10, , =, , 15

Page 16 : (ix) 2, , 19 9, 1, 3, , 1 =, 9 6, 9, 6, =, , (iii) 2, , 19  2 9  3, , 92 63, , 5 31 13, 1, 1, 1, , 5 3 = , 2 6, 4, 2, 6, 4, ( L.C.M. of 2, 6, 4 is 12), , =, , 38  27, 38 27, , =, 18, 18 18, 11, =, 18, , =, , (x) 5  3, , (xi) 1 , , 10  7, 3, 1, =, = 1, 2, 2, 2, , 19 4 3, 4 4 3, =,  ,  , 15 5 10, 15 5 10, ( L.C.M. of 15, 5 and 10 is 30), , 95, 4, =, 9, 9, , 37 37, 7, 7, , =, 2, 10 15, 10, 15, , =, , 37  3 37  2, , 10  3 15  2, , 111 74, , 30 30, 111  74, 7, 37, =, =, = 1, 30, 30, 30, =, , 3., , (iv) 1, , 5, 1 9 5, 9 5,  = , =, 9, 1 9 9, 9 9, =, , (xii) 3, , 30 62 39, , , 12 12 12, 30  62  39, =, 12, 53, 92  39, 5, =, =, = 4, 12, 12, 12, , =, , 1, 5 2 7, 10 7,  =, , =, 2, 1 2 2, 2 2, , =, , 23  10 8  14 17  7, , , 7  10 5  14 10  7, , 230 112 119, , , =, 70, 70, 70, , =, , 230  112  119 118  119, =, 70, 70, , 38 24 9, , , 30 30 30, , =, , 38  24  9, 30, , =, , 14  9 5 1, , , 30, 30 6, , =, , 17 × 2 5 × 8 9, , , 8 × 2 2 × 8 16, , =, , 34 40 9, , , 16 16 16, , =, , 34  40  9, 16, , 9, 1 7,  , 12 12 12, 9 1 7, =, 12, 3 1, =, , 12 4, , =, , ( L.C.M. of 5, 10 and 5 is 10), , 16, , =, , 74  9 65, 1, , 4, 16, 16, 16, 3 1 7, 3×3 1 7,  , (vi), =, , , 4 12 12, 4 × 3 12 12, , 72 1 42, 7 1 4, ,  =, , , 5 10 5, 5  2 10 5  2, , 14 1, 8, , , =, 10 10 10, 14  1  8, =, 10, 1, 21, =, = 2, 10, 10, , 19  2 4  6 3  3, , , 15  2 5  6 10  3, , =, , 237, 27, =, = 3, 70, 70, (ii), , =, , 1, 1 9, 17 5 9, (v) 2  2 , =,  , 8, 2 16, 8 2 16, , 23 8 17, 2, 3, 7,  , (i) 3  1  1, =, 7 5 10, 7, 5, 10, ( L.C.M. of 7, 5 and 10 is 70), , =, , 5  6 31  2 13  3, , , 26 62, 43, , (vii), , 5 × 2 1× 3 1× 6, 5 1 1, , ,   =, 6×2 4×3 2×6, 6 4 2, , =, , 10  3  6, 10 3, 6,  , =, 12, 12 12 12, , =, , 13  6 7, , 12, 12, Answer Keys

Page 17 : 1 13 2 5 9 13 2, (viii) 5  2      , 4 6 3 1 4 6 3, ( L.C.M. of 1, 4, 6 and 3 is 12), , , , 5  12 9  3 13  2 2  4, , , , 1  12 4  3 6  2 3  4, , 60 27 26 8, , , , 12 12 12 12, 60  27  26  8, , 12, , , 33  26  8 59  8 51, , , 12, 12, 12, 17, 1, , 4, 4, 4, 17 29 2, 5, 5, , , (ix) 2  3  2 , 6, 8 1, 6, 8, , , , , 17  4 29  3 2  24, , , 64, 8  3 1  24, ( L.C.M. of 6, 8 and 1 is 24), , (x) 5, , , , 68 87 48, , , 24 24 24, , , , 68  87  48, 24, , , , 116  87 29, 5, , 1, 24, 24, 24, , 57 17 61, 7, 2, 1, ,  , 3 4, 10, 5, 15 10 5 15, , , , 57  3 17  6 61  2, , , 10  3 5  6 15  2, , , , 171 102 122, , , 30, 30, 30, , , , 171  102  122, 30, , , , 69  122 191, 11, , 6, 30, 30, 30, , 4. The cost of a notebook = ` 13, The cost of an eraser = ` 1, The cost of a pen = ` 11, , 2, 5, , 3, 4, , 2, 3, , 3, 2,  2, Total amount = `  13  1  11 , 4, 3,  5,  67 7 35 , = `   ,  5 4 3 , ( L.C.M. of 5, 4 and 3 is 60), Mathematics In Everyday Life-6, ,  67  12 7  15 35  20 , = `, , , ,  5  12 4  15 3  20 , 804 105 700 , = ` , , , , 60 60 ,  60,  804  105  700 , = `, , 60, , , 1609, 49, =`, = ` 26, 60, 60, 49, Hence, Vibha paid ` 26, ., 60, 2, 5. A labourer earned money = `152, 3, 1, Spended money = `82, 3, 2, 1, , Left of money = `  152  82 , 3, 3, ,  458  247 , , = `, 3 ,  3,  458  247 , = `, , 3, , , 211, 1, = `, = ` 70, 3, 3, 1, Hence, ` 70 is left with him., 3, 2, 3, 6. The required fractions = 9  7, 7, 11, 65 80, , =, 7 11, 65  11 80  7, , =, 7  11 11  7, 715 560, , =, 77 77, 715  560, =, 77, 155, 1, 2, =, 77, 77, 2, 3, 1, Hence, 2, should be added to 7, to get 9 ., 7, 11, 77, 1, 2, 7. The required fraction = 23  19, 2, 3, 47 59, , =, 2, 3, 47  3 59  2, , =, 23, 32, 141  118, 141 118, , =, 6, 6, 6, 5, 23, =, = 3, 6, 6, 2, 5, 1, Hence, 3 should be added to 19 to get 23 ., 3, 6, 2, , =, , 17

Page 18 : 8. Sum of 4, , 2, 2 14 11, 2, 2, , and 1 = 4  1 , 3, 9 3 9, 3, 9, , And, sum of 2, , Now,, ,  52 61 , =    minutes, 5,  3, , =, , 14  3 11 42 11,  , , 33 9, 9, 9, ,  52  5 61  3 , , = ,  minutes, 53 ,  35, , =, , 42  11 53, , 9, 9, , 260 183 , = , ,  minutes,  15 15 , , 5, 2 19 11, , and 3 , 7, 3 7, 3, ,  260  183  minutes, = , , 15, , , , =, , 19  3 11  7, , 7 3 37, , =, , 57 77, , 21 21, , =, , 57  77 134, , 21, 21, , 134 53 134  3 53  7, , , , 21 9, 21  3, 97, , =, Hence, Sunils 5, , 77, 2, minutes = 5, minutes, 15, 15, , 2, minutes lesser than Anil., 15, , MULTIPLE CHOICE QUESTIONS, 1. Fraction of 1 metre is 60 cm =, , ( 1 m = 100 cm), , ( L.C.M. of 21 and 9 is 63), =, , 402 371, , 63, 63, , =, , 402  371 31, , 63, 63, , 1,  1, 9. The length of other piece of pipe =  5  3  m, 7,  3,  16 22 , =   m,  3 7 ,  16  7 22  3 , , m, = , 73 ,  37, , 60 cm, 60 3, , , 100 cm 100 5, Hence, option (b) is correct., , =, , 2. Difference between, =, , =, , 46, 4, m2 m, 21, 21, , 51 51  17 3, , , 85 85  17 5, Hence, option (c) is correct., , , , 4., , 7 4 9 8, , , ,, 20 15 5 5, L.C.M. of 20, 15, 5 and 5 is 60., , 7, 7 3, 21, , , 20 20  3 60, 4   16, 4, , , 15    60, , 10. To run one round the school ground,, 1, minutes, 3, , 9 9   108, , , 5    60, , 1, minutes,, 5, Difference in time taken by both of them, , To run one round, Sunil takes = 12, , 1, 1, =  17  12  minutes, 5,  3, 18, , 5 2 5 22, ,  , 6 12 6 12  2, , 51 4 2, 5 1,  ,  =, 6, 6 3, 6 6, Hence, option (d) is correct., 3. H.C.F. of 51 and 85 is 17., , 4, Hence, the length of other piece of pipe is 2 m ., 21, , Anil takes = 17, , 2, 5, and, 12, 6, , =, ,  112  66  m, , = ,  21 21 ,  112  66  m, , = ,  21 , , 60 cm, 1 metre, , 8 8   96, , , 5    60, , , 16 21 96 108, , , , 60 60 60 60, Answer Keys

Page 19 : 4, 7 8 9, ,   ., 15 20 5 5, , , , 4, is the smallest fraction., 15, Hence, option (b) is correct., , 13., , Hence, option (b) is correct., , Thus,, , 5., , 14., , 2 4 5 3, , , ,, 6 6 6 6, , , , 5 4 3 2,   , 6 6 6 6, , x, 21, =, 39, 39, , x = 21, Hence, option (d) is correct., , 15., , Hence, option (d) is correct., 7. Option (a) is correct., “A proper fraction is always less than 1”., 8. Option (b) is correct., 2, is fraction with denominator 5 and which, 5, is less than 1., , 1 1,  3, 3 x, , , , 1, 1,  3, x, 3, , , , 1 9 1, ,  , x 3 3, , 11., , 83 5, , 12, 12, Hence, option (a) is correct., , =, , 12., , 60 4, , 75 x, , 16., , , 20 20  5 4, , , 25 25  5 5, , 8, 3, 2 × 4 1× 3, 2 1, , , =,  =, 12 12, 3×4 4×3, 3 4, , 17., , 4 4, , 5 x, , , , 60  15 4, , 75  15 x, ,  x=5, , 3 2 1 4 5, , , , ,, 5 7 7 5 7, L.C.M. of 5 and 7 is 35., , 3 3   21, , , 5    35, 2 2   10 1 1  5 5, ,  ; , , 7    35 7 7  5 35, , a 5 1 5,   , 6 3 3 6, , 4 4   28 5 5  5 25, , , ; , , 5    35 7 7  5 35, , a 5 ×  1× 2 5, , , , 6 × 3×2 6, , , , 1 91, , x, , , Hence, option (b) is correct., , 1 5 a 5,   , 3 6 6 3, , , , 1 3 1, , , x  3, , , , 9. The required fraction =, , , , , , 1 8, 3, ,  x, x 3, , Hence, option (b) is correct., , Since,, , 5 3, 53, 2,  =, =, =1, 2 2, 2, 2, Hence, option (c) is correct., 10. Option (c) is correct., , 7×, x, =, 39,  × , , , , 5, is the greatest fraction., 6, Hence, option (c) is correct., , 15 15  5 3 3   9, ,  , , ., 35 35  5 7    21, , 7, x, , 13 39, , , , Thus,, , 6., , 1 1 1 1 1 1 3,   , , 2 2 2, 2, 2, , a 10 2 5, ,  , 6 6 6 6, , , , 5 10 21 25 28, , , , , 35 35 35 35 35, , a 10  2  5, , 6, 6, , , , 1 2 3 5 4,    , 7 7 5 7 5, , a 3, , 6 6, , Thus,, ,  a=3, , Hence, option (d) is correct., Mathematics In Everyday Life-6, , 1, is smallest fraction., 7, Hence, option (a) is correct., 19

Page 20 : 18. The required number =, =, , 1 1, , 2 6, , 1 1, ,  6, , 3 1 3 1 2 1,  , =, = , 6 6, 6, 6 3, Hence, option (c) is correct., , 19., , 11. A fraction equivalent to, equal to, , , 3 x, , 4 32, , , , REVIEW EXERCISE, 1., , (i)  H.C.F. of 27 and 72 is 9., , , MENTAL MATHS CORNER, , 160 160  40 4, , , 360 360  40 9, (iii) H.C.F. of 105 and 168 is 21., , a, , b is called denominator and a is called, b, numerator., 2. A fraction is a number representing a part of whole., , , , 1. In, , 1, 4. The fraction 3 can be written as 10 ., 3, 3, 1 (3     9  1 10, , , , 3, , 3, 3, , 5. A fraction having 1 as its numerator is called unit, fraction., 6. The fraction, , , 17, 2, can be written as 3 ., 5, 5, , 17, 2, 3 ., 5, 5, , 10. The fraction, , , 20, , 2., , (i), , 7 11, ,, 5 30, , , , 7   11, ,,    30, , 2, 28, in its simplest form is ., 3, 42, , 28 28  14 2, , , 42 42  14 3, , , , 42 11, ,, 30 30, , 7 9, ,, 6 16, L.C.M. of 6 and 16 is 48., , (ii), , , , 7 9, ,,      , , Hence,, , 7. A fraction is said to be in its simplest form when the, H.C.F. of denominator and numerator is 1., 8. The fractions having the same denominator are, called like fraction., 9. When numerator of a fraction is greater than, denominator, then fraction is called as improper, fraction., , 105 105  21 5, , , 168 168  21 8, , , , 3. The fractions with different denominators are, known as unlike fractions., , 3, , 27 27  9 3, , , 72 72  9 8, , (ii)  H.C.F. of 160 and 360 is 40., , Fill in the blanks:, , , , 1, is an improper form is equivalent, 7, , to, , 3 x, ,    32, , 24 x, , ,  x = 24, 32 32, Hence, option (b) is correct., , 24 24  6 4, , , 30 30  6 5, , 36, ., 7, 1 (5     35  1 36,  5 , , , 7, , 7, 7, , 5, , 20., , 4, ., 5, , 12. The fraction 5, , 3 (5   20  3 23, , , , 4, , 4, 4, Hence, option (d) is correct., , 24, with numerator 4 is, 30, , (iii), , , , 56 27, ,, 48 48, , 56 27, ,, are the equivalent like fraction., 48 48, , 5 19, ,, 12 72, , 30 19, 5   19, ,, ,, , 72 72,    , 3. L.C.M. of 9, 18, 27 and 2 is 54., , , 4 4   24, , , 9    54, 7   21, 7, , , 18    54, 5   10, 5, , , 27    54, Answer Keys

Page 21 : 1 1   27, , , 2    54, , , 10 21 24 27, , , , 54 54 54 54, , , , 5, 7 4 1, ,  , 27 18 9 2, , 6., , (i), , 3 5, ,, 7 12, 3, 7, , 36 > 35, 3 5, ., , 7 12, 9 4, ,, (ii), 13 17, , Hence,, , 5 7 4 1, Hence,, , , , are in ascending order.., 27 18 9 2, 4. L.C.M. of 5, 15, 12 and 3 is 60., , 2 2   24, , , 5    60, , 9, 13, , 4   16, 4, , , 15    60, , (iii), , 2 2   40, , , 3    60, , , , 5., , (i), , 2 5 2 4, ,, , ,, are in descending order.., 3 12 5 15, , 72,  72 divided by 13., 13, Quotient = 5,, , Remainder = 7,, Denominator = 13., , (ii), , Remainder = 5,, Denominator = 8., , (iii), , 13, 14, 154 < 195, , Hence, 11  13 ., 15 14, 7., , (i), , 5 5 5 53, , , , 9 12    12  3, ( L.C.M. of 9 and 12 is 36), , 13 72 5, – 65, 7, , , , (ii), , 72, 7, 5 ., 13, 13, , 101,  101 divided by 8., 8, Quotient = 12,, , 9, 4, , ., 13 17, , 11 13, ,, 15 14, 11, 15, , 40 25 24 16, , , , 60 60 60 60, 2 5, 2, 4, , , , 3 12 15 15, , Hence,, , 4, 17, 153 > 68, , Hence,, , 5   25, 5, , , 12    60, , , , 5, 12, , 5 3 5   3  8 25 24,  , , , , 8 5 8  5 5  8 40 40, ( L.C.M. of 8 and 5 is 40), , , 8 101 12, – 96, 5, , (iii), , 16 91 5, – 80, 11, , 8., , (i), , 91, 11, 5 ., 16, 16, , Mathematics In Everyday Life-6, , , , 6, 4, 3,  , 12 12 12, , , , 6  4  3 13, 1, , 1, 12, 12, 12, , 3 1 3 1 4,  , , 4 3  34, , Denominator = 16., , , 25  24 49, 9, , 1, 40, 40, 40, , 1 1 1 1  1 4 1 3,   , , , 2 3 4  34 43, , 101, 5,  12, 8, 8, , 91,  91 divided by 16., 16, Quotient = 5,, Remainder = 11,, , 20 15 20  15 35, ., , , , 36 36, 36, 36, , ( L.C.M. of 4 and 3 is 12), , , , 9, 4 94 5, , , , 12 12, 12, 12, , 21

Page 22 : (ii), , 4 1 4  1 3,  , , 3 2  23, , , (iii), , 11 16 11  5 16  3, , , , 3 5, 35 53, , , (iv), , 8 3 83 5,  , , 6 6, 6, 6, , 1, 4 33 14, 8 2 , , 4, 5 4, 5, , 33  5 14  4 165 56, , , , 45, 54, 20 20, , , , 165  56 109, 9, , 5, 20, 20, 20, , 1, 1, 9. Total amount of cake = 1  1, 3, 2, , (iii) 2 , , 4 3 42 33, =  , , 3 2 32 23, , 8 9 8  9 17, 5, =  , , 2, 6 6, 6, 6, 6, , Hence, total amount of cake is 2, , 5, ., 6, , 3, 10. Length of ribben purchased by Rajni = m., 5, , Length of ribben purchased by Sunidhi =, , 3, m., 4, , Total length of ribben purchased by both of them, , (i), , 25  30  12, 15, , , , 37  30 7, , 15, 15, , 12., , , , 13  3 15  3 1  4, , , 43 43 34, , , , 39 45 4, , , 12 12 12, , , , 39  45  4, 12, , , , 80 20, 2, , 6, 12 3, 3, , 2  15 2  3 1  5 4  3, 2 1 4,   =, , , , 1  15 5  3 3  5 5  3, 5 3 5, , =, , 30 6, 5 12,   , 15 15 15 15, , =, , 30  6  5  12 7, , 15, 15, , 12 3 10 1, 5 3, 3 1,   , (i) 1   1  =, 7 14 7 7, 7 14, 7 7,  12 10 1  3, =    ,  7, 7 7  14,  12  10  1  3, = ,   14, , 7, , =, , 23 3, , 7 14, , 3  4 3  5, , , m, 5  4 4  5, , =, , 23 × 2 3 46 3, , , , 7 × 2 14 14 14, , 12 15,     m,  20 20 , , =, , 46  3 43, 1, , 3, 14, 14, 14, , 5, 4 5 2 4, 21   , 3, 5 3 1 5, , , , 22, , , , 3 3,     m, 5 4, , 27, 7, , m 1 m, 20, 20, Hence, total length of ribben purchased by both of, 7, them is 1 m., 20, , 11., , 25 30 12,  , 15 15 15, , 1, 3 1 13 15 1, (ii) 3  3  ,  , 4, 4 3 4, 4 3, , 55 48 55  48 7, , , , 15 15, 15, 15, , , , , , 5  5 2  15 4  3, , , 3  5 1  15 5  3, , 8 31 13, 3, 1, 3, (ii) 1  2  1, =  , 5 15 10, 5, 15, 10, , =, , 8  6 31  2 13  3, , , 5  6 15  2 10  3, , =, , 48 62 39, , , 30 30 30, , =, , 48  62  39, 30, , =, , 110  39 71, 11, , 2, 30, 30, 30, Answer Keys

Page 23 : HOTS QUESTIONS, 1., , x, 3, 5, 8  3  12, 6, 8, 24, , , , 8, , x, 5, 3,  12  3, 6, 24, 8, , , , 8, , x 293 27, , , 6 24, 8, , , , 8, , x 293 27  3, , , 6 24, 83, , , , 8, , x 293 81, , , 6 24 24, , , , 8, , x 293  81, , 6, 24, , , , 8, , x 212 53, , , 6 24, 6, , , , 8, , x, 5, 8, 6, 6, ,  1  1  1  1   1  1  1  1    1  1 , , , , ,  , ,  2  3   4  5   10 , , 1 , 1 , 1 , 1 , 1 , 1,  1  1  1  1  1  1 , , 2 , 3 , 4 , 5 , 6 , 7, , 1 , 1 , 1,  1  8   1  9   1  10 , , 1 2 3 4 5 6 7 8 9, × × × × × × × ×, 2 3 4 5 6 7 8 9 10, 1, 1× 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9, , , 10, 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10, , , VALUE BASED QUESTION, SUMMATIVE ASSESSMENT, 1 1 1 1, , , , ,, 2 4 8 16, , Hence, x  5, 2. Mohit had bananas =, bananas, , 3, 1, 2, of, of, of a dozen, 4, 2, 3, , =, , 3 1 2 12,   , 4 2 3 1, , =, , 3  1  2  12, 3, 4  2 31, , Hence, Mohit have 3 bananas., , ( 1 dozen = 12), , 1, 4, 1, 2, 1, 8, , 1, 16, 1, 1 64, 32, , 1, 256 1, 128, 1, 512, , “We are one country ......, we may be divided by states,, castes, religions etc., but we are still a part of whole.”, , Mathematics In Everyday Life-6, , 23