CSS Primary Standard “Mathematics” 51 3423 3 1141 3 7 163 So, prime factors are 3, 7, 163 vi. 84368 Ans: 84368 2 42184 2 21092 2 10546 2 2 2 2 5273 So, prime factors are 2, 2, 2, 2, 5273 vii. 7345 Ans: 7345 5 1469 5 13 113 Q.2 Find the prime factorization of the given numbers by repeated division method. i. 230400 Ans: 2 230400 2 115200 2 57600 2 28800 2 14400 2 7200 2 3600
CSS Primary Standard “Mathematics” 52 2 1800 2 900 2 450 5 225 5 45 3 9 3 3 1 So, 230400 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 3 × 3 ii. 64878 Ans: 2 6878 3 32439 11 1083 983 983 1 So, 64878 = 2 × 3 × 11 × 983 iii. 31515 Ans: 5 31515 3 6303 11 2101 191 191 1 So, 31515 = 2 × 3 × 11 × 191 iv. 36005 Ans: 5 36005 19 1701 379 379 1 So, 36005 = 5 × 19 × 379 v. 705642 Ans: 2 705642 3 352821
CSS Primary Standard “Mathematics” 53 7 117607 53 16801 317 317 1 So, 705642 = 2 × 3 × 7 × 53 × 317 vi. 136004 Ans: 2 136004 2 68002 11 34001 11 3091 281 281 1 So, 705642 = 2 × 2 × 11 × 11 × 281 vii. 756 Ans: 2 756 2 378 3 189 3 63 3 21 7 7 1 So, 756 = 2 × 2 × 3 × 3 × 3 × 7 viii. 333 Ans: 3 333 37 111 3 3 1 So, 333 = 3 × 3 × 37 ix. 42894 Ans: 2 42894 3 21447
CSS Primary Standard “Mathematics” 54 3 7149 2383 2383 1 So, 42894 = 2 × 3 × 3 × 2383 x. 3000 Ans: 2 3000 2 1500 2 750 5 375 5 75 5 15 3 3 1 So, 3000 = 2 × 2 × 2 × 3 × 5 × 5 × 5 xi. 1935 Ans: 5 1935 43 387 3 9 3 3 1 So, 1935 = 3 × 3 × 5 × 43 Q 3: Write in index notation. i. 2 × 2 × 3 × 3 × 3 × 5 Ans: 2 2 x 33 x 51 ii. 2 × 5 × 5 × 5 × 8 × 8 Ans: 2 1 x 53 x 82 iii. 3 × 4 × 4 × 4 × 4 × 5 × 5 × 5 × 7 × 7 Ans: 3 1 x 44 x 53 x 72 Q.4 Factorize the given numbers and express their factors in the index notation. i. 756 Ans: 2 756 2 378 3 189
CSS Primary Standard “Mathematics” 55 3 63 3 21 7 7 1 So, 230400 = 2 × 2 × 3 × 3 × 3 × 7 2 2 × 33 × 71 ii. 630 Ans: 2 630 3 315 3 105 5 35 7 7 1 So, 230400 = 2 × 3 × 3 × 5 × 7 2 1 × 32 × 51 × 71 iii. 665 Ans: 5 665 7 133 19 19 1 So, 230400 = 5 × 7 × 19 5 1 × 71 × 191 iv. 840 Ans: 2 840 2 420 2 210 5 105 5 35 7 7 1 So, 840 = 2 × 2 × 2 × 5 × 5 × 7 = 23 × 52 × 71 v. 1159
CSS Primary Standard “Mathematics” 56 Ans: 19 1159 61 61 1 So, 840 = 19 × 61 = 191 × 611 vi. 1225 Ans: 5 1225 5 245 7 49 7 7 1 So, 840 = 5 × 5 × 7 × 7 = 52 × 72 vii. 1482 Ans: 2 1482 3 741 13 247 19 19 1 So, 840 = 2 × 3 × 13 × 19 = 21 × 31 × 131 × 191 viii. 3996 Ans: 2 3996 2 1996 3 999 3 333 3 111 37 So, 3996 = 2 × 2 × 3 × 3 × 3 × 37 = 22 × 33 × 371 ix. 9090
CSS Primary Standard “Mathematics” 57 Ans: 2 9090 3 4545 3 1515 5 505 101 101 1 So, 9090 = 2 × 3 × 3 × 5 × 101 = 21 × 32 × 51 × 1011 x. 8700 Ans: 2 8700 2 4350 3 2175 5 725 5 145 29 29 1 So, 8700 = 2 × 2 × 3 × 5 × 5 × 29 = 22 × 31 × 52 × 291 Week 8 Highest Common Factor Lesson # 4 Classroom Activity: ☻ Put the chart of prime numbers between 1 and 1000 in class. Use the explanation as given on pages # 49, 50, 51, and 52 to calculate the H.C.F of two or more than two, 2-digits number. ☻ Explain the Prime Factorization method to find the H.C.F of given numbers as explained on page # 50, 51. ☻ Explain the Long Division method to find the H.C.F of given numbers as explained on page # 51 & 52.
CSS Primary Standard “Mathematics” 58 Exercise 3d Q.1 Find H.C.F by Prime factorization method. i. 54, 99 Ans: Prime factors of 54 = 2 × 33 Prime factors 99 = 32 × 11 Common factors of 54 and 99 = 3 × 3 = 9 Hence the highest common factor (HCF) = 9 ii. 25, 100 Ans: Prime factors of 25 = 5 × 5 Prime factors 99 = 2 × 2 × 5 × 5 Common factors of 54 and 99 = 5 × 5 = 25 HCF of 25 and 100 = 25 iii. 44, 88, 176 Ans: Prime factors of 44 = 2 × 2 × 11 Prime factors 88 = 2 × 2 × 2 × 11 Prime factors of 176 = 2 × 2 × 2 × 2 × 11 2 54 2 27 3 9 3 3 1 2 99 2 33 3 11 3 1 5 25 5 5 1 2 100 2 50 5 25 5 5 1 2 44 2 22 11 11 1 2 88 2 44 2 22 5 5 11 11 1 2 176 2 88 2 44 2 22 11 11 1
CSS Primary Standard “Mathematics” 59 Common factors of 44, 88 and 176 = 2 × 2 × 11 = 44 HCF of 44, 88 and 176 = 44 iv. 184, 230, 276 Ans: Prime factors of 184 = 2 × 2 × 2 × 23 Prime factors of 230 = 2 × 5 × 23 Prime factors of 276 = 2 × 2 × 3 × 23 Common factors of 184, 230 and 276 = 2 × 23 = 46 HCF of 44, 88 and 176 = 46 v. 184, 230, 276, 99 Ans: Prime factors of 22 = 2 × 11 Prime factors of 77 = 7 × 11 Prime factors of 55 = 5 × 11 Prime factors of 99 = 3 × 3 × 11 Common factors of 22, 77, 55 and 99 = 11 HCF of 22, 77, 55 and 99 = 11 Q.2 Find the H.C.F of the following numbers by long division method. i. 180, 270 Ans: 1 180 270 180 2 90 180 180 0 Therefore HFC of 180 and 270 is 90. 2 184 2 92 2 46 23 23 1 2 230 5 115 23 23 1 2 276 2 138 2 69 23 23 1 2 22 11 11 1 7 77 11 11 1 5 55 11 11 1 3 99 3 33 11 11 1
CSS Primary Standard “Mathematics” 60 ii. 852, 1065 Ans: 1 852 1065 852 4 213 852 852 0 Therefore HCF of 852 and 1065 is 213. iii. 300, 396 Ans: 1 300 396 300 3 96 300 288 8 12 96 96 0 Therefore HCF of 300 and 396 is 12. iv. 735, 840, 1050 Ans: 1 3 840 1050 210 735 840 4 630 14 210 840 15 210 840 210 0 0 Therefore HCF of 735, 840 and 1050 is 15. v. 11, 77, 300 Ans: 3 11 77 300 1 11 231 1 11 69 77 0 69 8 8 69
CSS Primary Standard “Mathematics” 61 64 1 5 8 5 1 3 5 3 1 2 3 2 2 1 2 2 0 Therefore HCF of 11, 77 and 300 is 1 vi. 399, 665 and 1463 Ans: 2 3 665 1463 133 399 1330 5 399 133 665 0 665 0 Therefore HCF of 399, 665 and 1463 is 133. vii. 44, 132 and 66 Ans: 2 1 66 132 44 66 132 44 2 0 22 44 44 0 Therefore HCF of 44, 132 and 66 is 22. viii. 36, 180 and 200 Ans: 2 1 66 200 20 36 180 9 20 1 20 180 16 20 180 16 4
CSS Primary Standard “Mathematics” 62 0 4 16 16 0 Therefore HCF of 36, 180 and 200 is 4. ix. 100, 1000, 4850, 245 Ans: 19 10 245 4850 100 1000 4655 1 1000 195 245 0 195 3 50 195 150 1 45 50 459 5 45 45 0 HCF of 245 and 8450 is 5. HCF of 100 and 1000 is 100. Now HCF of 5 and 100 is 5 because: 20 5 100 100 0 Therefore HCF of 245, 4850, 100 and 1000 is 5. x. 145, 540, 675, 765 Ans: 1 4 540 765 145 675 540 2 580 1 225 540 95 145 450 2 95 1 90 225 50 95 180 2 50 1 45 90 45 50 90 45 9
CSS Primary Standard “Mathematics” 63 0 5 45 45 0 HCF of 545, 765 is 45. HCF of 145, 675 is 5. Now of HCF of 45 and 5 is 5, because: 9 5 45 45 0 Therefore HCF of 145, 540, 675 and 765 is 5. Q.3 Find the highest number which exactly divides these numbers. i. 24, 240, 304 Ans: Prime factors of 24 = 2 × 2 × 2 × 3 Prime factors of 240 = 2 × 2 × 2 × 2 × 3 × 5 Prime factors of 304 = 2 × 2 × 2 × 2 × 17 HCF of 24, 240 and 304 is 23 = 8 ii. 196, 490, 1190 Ans: Prime factors of 196 = 2 × 2 × 7 × 7 Prime factors of 490 = 2 × 5 × 7 × 7 2 24 2 12 2 6 3 3 1 2 240 2 120 2 60 2 30 3 15 5 5 1 2 304 2 152 2 76 2 34 17 17 1 2 196 2 98 7 49 7 7 1 2 490 5 245 7 49 7 7 1 2 1190 5 595 7 119 17 17 1
CSS Primary Standard “Mathematics” 64 Prime factors of 1190 = 2 × 5 × 7 × 17 HCF of 196, 490 and 1190 = 2 × 7 = 14 iii. 147, 217, 3514 Ans: Prime factors of 147 = 3 × 7 × 7 Prime factors of 217 = 7 × 31 Prime factors of 3514 = 2 × 7 × 251 HCF of 147, 217 and 3514 = 7 iv. 225, 525, 675 Ans: Prime factors of 225 = 3 × 3 × 5 × 5 Prime factors of 525 = 3 × 5 × 5 × 7 Prime factors of 675 = 3 × 3 × 3 × 5 × 5 HCF of 225, 525 and 675 = 3 × 5 × 5 = 15 × 5 = 75 Week 9 Least Common Multiple Lesson # 5 Classroom Activity: ☻ Use the explanation as given on page # 53 to calculate the L.C.M of two or more 2 147 2 21 7 7 7 1 2 217 31 31 1 7 3514 2 502 251 251 1 2 225 2 45 7 9 7 3 1 5 525 5 105 3 21 7 7 1 5 675 5 135 3 27 3 9 3 3 1
CSS Primary Standard “Mathematics” 65 than two, 2-digits number. ☻ Explain the Prime Factorization method to find the L.C.M of given numbers as explained on page # 53 & 54. ☻ Explain the Division method to find the L.C.M of given numbers as explained on page # 54 & 55. Exercise 3e Q.1 Find the L.C.M of the following numbers by Prime factorization method. i. 100, 400 Ans: 100 = 2 × 2 × 5 × 5 = 22 × 52 400 = 2 × 2 × 2 × 2 × 5 × 5 = 24 × 52 L.C.M = 24 × 52 = 400 ii. 70, 98, 175 Ans: 70 = 2 × 5 × 7 98 = 2 × 7 × 7 = 2 × 72 175 = 5 × 5 × 7 = 52 × 7 L.C.M = 2 × 52 × 72 = 2450 iii. 8, 12, 18 Ans: 2 100 2 50 5 25 5 5 1 2 400 2 200 2 100 2 50 3 25 2 70 5 35 7 7 1 2 98 7 49 7 7 1 5 175 5 35 7 7 1 2 8 2 4 2 2 1 2 12 2 6 3 3 1 2 18 3 9 3 3 1 5 5 1
CSS Primary Standard “Mathematics” 66 8 = 2 × 2 × 2 = 23 12 = 2 × 2 × 3 = 22 × 3 18 = 2 × 3 × 3 = 2 × 32 L.C.M = 23 × 32 = 8 × 9 = 72 iv. 77, 33, 55 Ans: 77 = 7 × 11 33 = 3 × 11 55 = 5 × 11 L.C.M = 3 × 5 × 7 × 11 = 1155 v. 49, 70, 149 Ans: 49 = 7 × 7 70 = 2 × 5 × 7 149 = 149 L.C.M = 2 × 5 × 72 × 149 = 73010 vi. 32, 36, 48 Ans: 32 = 2 × 2 × 2 × 2 × 2 = 25 36 = 2 × 2 × 3 × 3 = 22 × 32 48 = 2 × 2 × 2 × 2 × 3 = 24 × 3 7 77 11 11 1 3 33 11 11 1 5 55 11 11 1 7 49 7 7 1 2 70 5 35 7 7 1 149 149 1 2 32 2 16 2 8 2 4 2 2 1 2 36 2 18 3 9 3 3 1 2 48 2 24 2 12 2 6 3 3 1
CSS Primary Standard “Mathematics” 67 L.C.M = 25 × 32 = 288 vii. 320, 480, 720 Ans: 320 = 2 × 2 × 2 × 2 × 2 × 5 = 25 × 5 480 = 2 × 2 × 2 × 2 × 2 × 3 × 5 = 25 × 3 × 5 720 = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 24 × 32 × 5 L.C.M = 25 × 32 × 5 = 2880 viii. 21, 28, 35, 77 Ans: 21 = 3 × 7 28 = 2 × 2 × 7 = 22 × 7 35 = 5 × 7 77 = 7 × 11 L.C.M = 22 × 3 × 5 × 7 × 11 = 4620 Q.2 Find the L.C.M of the following numbers by division Method. i. 20, 24, 45 Ans: 2 320 2 160 2 80 2 40 2 20 2 10 5 5 1 2 480 2 240 2 120 2 60 2 30 3 15 5 5 1 2 720 2 360 2 180 2 90 3 45 3 15 5 5 1 3 21 7 7 1 2 28 2 14 2 7 1 2 35 2 5 2 1 7 77 11 11 1
CSS Primary Standard “Mathematics” 68 2 × 2 × 2 × 3 × 3 × 5 = 360 Therefore, LCM = 360 ii. 12, 15, 18, 21 Ans: LCM = 2 × 2 × 3 × 3 × 5 × 7 = 1260 iii. 72, 240, 196 Ans: LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 × 7 = 35, 280 2 20, 24, 45 2 10, 12, 45 2 5, 6, 45 3 5, 3, 45 3 5, 1, 15 5 5, 1, 5 1, 1, 1 2 12, 15, 18, 21 2 6, 15, 9, 21 3 3, 15, 9, 21 3 1, 5, 3, 7 5 1, 5, 1, 7 7 1, 1, 1, 7 1, 1, 1, 1 2 72, 240, 196 2 36, 120, 98 2 18, 60, 49 2 9, 30, 49 3 9, 15, 49 3 3, 5, 49 5 1, 5, 49 7 1, 1, 49 7 1, 1, 7 1, 1, 1
CSS Primary Standard “Mathematics” 69 iv. 60, 75, 80 Ans: LCM = 2 × 2 × 2 × 2 × 3 × 5 × 5 × 5 = 6000 v. 16, 24, 30, 36 Ans: LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720 vi. 72, 96, 144, 168 Ans: 2 60, 75, 80 2 30, 75, 40 2 15, 75, 20 2 15, 75, 10 3 15, 75, 5 3 5, 25, 5 5 1, 25, 1 7 1, 5, 1 7 1, 1, 1 2 72, 96, 144, 168 2 36, 48, 72, 84 2 18, 24, 36, 42 2 9, 12, 18, 21 3 9, 6, 9, 21 3 9, 3, 9, 21 5 3, 1, 3, 7 7 1, 1, 1, 7 1, 1, 1, 1 2 16, 24, 30, 36 2 8, 12, 15, 18 2 4, 6, 15, 9 2 2, 3, 15, 9 3 1, 3, 15, 9 3 1, 1, 5, 3 5 1, 1, 5, 1 7 1, 1, 1, 1
CSS Primary Standard “Mathematics” 70 LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 = 2016 vii. 75, 125, 175, 225 Ans: LCM = 3 × 3 × 3 × 5 × 5 × 5 × 7 = 23625 Week 9 Applications of HCF and LCM Lesson # 6 HCF is important to find the largest size of tiles that may fit into rooms, while constructing a building. Any such activity is not merely useful in its mathematical field, but increases the power of reasoning and thinking. Why do we need to find LCM of numbers? Subtraction / Addition of fractions cannot be done accurately without finding the LCM of denominators. LCM is important in everyday life for time and speed, and time and work problems, different people running around circular race tracks, timing of bells and flashing lights, such as from a lighthouse. Exercise 3f 3 75, 125, 175, 225 3 15, 125, 175, 75 3 5, 125, 175, 15 5 5, 125, 175, 5 5 1, 25, 35, 1 5 1, 5, 7, 1 7 1, 1, 7, 1 1, 1, 1, 1 1, 1, 1, 1
CSS Primary Standard “Mathematics” 71 Q1. Find the greatest number that can completely divide the number 252, 441, 504 and 315. Ans: Prime factors of 252 = 2 × 2 × 3 × 3 × 7 Prime factors of 441 = 3 × 3 × 7 × 7 Prime factors of 504 = 2 × 2 × 2 × 3 × 3 × 7 HCF = 3 × 3 × 7 = 63 Q2. Find the greatest capacity of a measuring cylinder that can exactly measure the liquids of 165l, 175l and 200l. Ans: Amounts of liquids 165 ltr, 175 ltr, 200 ltr. LCM = Highest Capacity = 2 × 2 × 2 × 3 × 5 × 5 × 7 × 11 = 46, 200 liters. Q3. Find the least length of a rope which can be cut into whole number of pieces of lengths 45cm, 75cm and 81cm. Ans: Lengths of pieces = 45 cm, 75 cm, 81 cm Least length = LCM 2 252 2 126 3 63 3 21 7 7 1 3 441 7 147 3 21 7 7 1 2 504 2 252 2 126 3 63 3 21 7 7 1 5 165, 175, 200 2 33, 35, 40 2 33, 35, 20 2 33, 35, 10 3 33, 35, 5 5 11, 35, 5 7 11, 7, 1 11 11, 1, 1 1, 1, 1
CSS Primary Standard “Mathematics” 72 Least length = 3 × 3 × 3 × 3 × 5 × 5 = 2025 Q4. Ibrahim art class held 4 days in a month, and Quran class held 5 days in a month. What is the next day his both classes will be held if the last common class was held on 20th of April. Ans: To find the next common class, we find LCM of 4 and 5. LCM = 2 × 2 × 5 = 20 So, next common class will be on 20th April + 20 = 10th may Q5. Find the smallest number that is exactly divisble by 84,78,144,174. Ans: Least length = 3 × 3 × 3 × 3 × 5 × 5 = 2025 3 45, 75, 81 3 15, 25, 27 3 5, 25, 9 3 5, 25, 3 5 5, 25, 1 5 1, 5, 1 1, 1, 1 2 4, 5 2 2, 5 5 1, 5 1, 1 2 84, 78, 144, 174 2 42, 39, 72, 87 2 21, 39, 36, 87 2 21, 39, 18, 87 3 21, 39, 9, 87 3 7, 13, 3, 29 7 7, 13, 1, 29 13 1, 13, 1, 29 29 1, 1, 1, 29 1, 1, 1, 1
CSS Primary Standard “Mathematics” 73 Q6. The length of four ropes are, 115m, 125m, 145m, 175m. Find the length of the road which covers the four ropes completely. Ans: Length of four ropes = 115m, 125m, 145m, 175m. Length of rope that covers completely = LCM Length of rope that covers completely = 583, 625 Q7. Find the least number of students exactly in groups of 45, 40 and 60 to participate in the exhibition. Ans: Least number of students = LCM LCM = 2 × 2 × 2 × 3 × 3 × 5 = 360 Review Exercise 3 Q 1: Choose the correct answer and fill the circle: i. A number which divides the _______completely having no remainder is called a ______: dividend, factor dividend, addition dividend, multiples dividend,subtraction ii. The number which are not the multiple of 2 is called a __________: composite number even number 5 115, 125, 145, 175 5 23, 25, 29, 35 5 23, 5, 29, 7 7 23, 1, 29, 7 23 23, 1, 29, 1 29 1, 1, 29, 1 1, 1, 1, 1 2 45, 40, 60 2 45, 20, 30 2 45, 10, 15 3 45, 5, 15 3 15, 5, 5 5 5, 5, 5 1, 1, 1
CSS Primary Standard “Mathematics” 74 odd number prime number iii. The only even prime number is: 4 0 2 10 iv. 13 is a ____________ because it is divisible by it self and _____________: odd number,1 prime number ,1 even number, 0 none v. Highest number which is a common _________of two or more number is HCF: factor greatest multiple all vi. The smallest number which is a common _______of two or more _______ is called LCM: multiple, factor multiple, number factor, number factor, dividend vii. 317 is a _________number: even composite negative prime viii. 191 is a/an _______number, but also a _________number: even, prime even, composite odd, prime none Q 2: i. Without dividing, find the numbers written on the books which are exactly divisible by 3 and 6. Ans: 960, 2460, 3030, 6480, 1740, 8100, 9510, 4290, 6690. ii. Explain how you found the numbers. Ans: We find these numbers by using divisibility test of 3 and 6. iii. How can you tell, without dividing, that a number is exactly divisible by 6? Ans: If the last digit of a number is 0, 2, 4, 6, 8 and sum of the digits is divisible by 3, than that number is exactly divisible by 6. Q 3: Without dividing List the numbers from 430 to 440 which are; i. Exactly divisible by 8 Ans: 432, 440 ii. Not exactly divisible by 6 Ans: 432, 438
CSS Primary Standard “Mathematics” 75 Q 4: Table number card: 32 50 85 70 95 56 62 48 80 37 65 92 (a) List the table of numbers which are (i) Multiples of 4 (ii) Multiples of 5 (b) List the first ten (i) Multiple of ..7.. (ii) Multiple of ..9.. (c) Which multiples of 7 in part (b) are exactly divisible by 3? (d) Which multiples of 9 in part (b) are exactly divisible by 4? Ans: (a) (i) 32, 56, 12, 80, 92 (ii) 50, 85, 70, 95, 80, 65 (b) (i) 7, 14, 21, 8, 35, 42, 49, 56, 63, 70 (ii) 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 (c) 21, 42, 63 (d) 36, 72 Q 5: List the first 20 multiples of 2 & 5. Which is the smallest numbers that is a common multiple of 2 and 5? Ans: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100 Q 6: List the Smallest number that is a common multiple of 22, 48, 88. Ans: 528 Q 7. Find all the factors of i. 180 Ans: 180 = 2 × 2 × 2 × 3 × 5 ii. 240 Ans: 2 180 2 90 2 45 3 15 5 5 1 2 240 2 120 2 60 2 30 3 15 5 5 1
CSS Primary Standard “Mathematics” 76 240 = 2 × 2 × 2 × 2 × 3 × 5 iii. 200 Ans: 200 = 2 × 2 × 2 × 5 × 5 iv. 550 Ans: 200 = 2 × 2 × 2 × 5 × 5 v. 770 Ans: 770 = 7 × 11 × 2 × 5 vi. 1175 Ans: 2 200 2 100 2 50 5 25 5 5 1 2 550 5 275 5 55 11 11 1 7 770 11 110 2 10 5 5 1
CSS Primary Standard “Mathematics” 77 1175 = 5 × 5 × 47 vii. 10000 Ans: 10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5 viii. 10005 Ans: 10005 = 5 × 3 × 23 × 29 Q 8. Find the H.C.F by Prime factorization. i. 48, 56, 72 Ans: Prime factors of 48 = 2 × 2 × 2 × 2 × 3 5 1175 5 235 47 47 1 2 1000 2 5000 2 2500 2 1250 5 625 5 125 5 25 5 5 1 5 10005 3 2001 23 667 29 29 1 2 48 2 24 2 12 2 6 3 3 1 2 56 2 28 2 14 7 7 1 2 72 2 36 2 18 3 9 3 3 1
CSS Primary Standard “Mathematics” 78 Prime factors of 56 = 2 × 2 × 2 × 7 Prime factors of 72 = 2 × 2 × 2 × 3 × 3 HCF = 2 × 2 × 2 = 8 ii. 102, 68, 136 Ans: Prime factors of 102 = 2 × 3 × 17 Prime factors of 68 = 2 × 2 × 17 Prime factors of 136 = 2 × 2 × 2 × 17 HCF = 2 × 17 = 34 iii. 405, 783, 513 Ans: Prime factors of 405 = 5 × 3 × 3 × 3 × 3 Prime factors of 783 = 3 × 3 × 3 × 29 Prime factors of 513 = 3 × 3 × 3 × 19 HCF = 3 × 3 × 3 = 27 iv. 198, 360 Ans: Prime factors of 198 = 2 × 3 × 3 × 11 Prime factors of 360 = 2 × 2 × 2 × 3 × 3 × 5 HCF = 2 × 3 × 3 = 18 2 102 3 51 17 17 1 2 68 2 34 17 17 1 2 136 2 68 2 34 17 17 1 5 405 3 81 3 27 3 9 3 3 1 3 783 3 261 3 87 29 29 1 3 513 3 171 3 57 19 19 1 2 198 3 99 3 33 11 11 1 2 360 2 180 2 90 3 45 3 15 5 5 1
CSS Primary Standard “Mathematics” 79 v. 1024, 576 Ans: Prime factors of 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 Prime factors of 576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 HCF = 2 × 2 × 2 × 2 × 2 × 2 = 64 Q9. Find the H.C.F by long division method. i. 84, 144 Ans: 1 245 144 84 1 60 84 60 2 24 60 48 2 12 24 24 0 HCF = 12 ii. 120, 168 Ans: 1 120 168 120 2 2 1024 2 512 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 2 1 2 576 2 288 2 144 2 72 2 36 2 18 3 9 3 3 1
CSS Primary Standard “Mathematics” 80 48 120 96 2 24 48 48 0 HCF = 24 iii. 430, 516, 817 Ans: 3 10 516 817 43 430 516 1 430 301 516 0 301 1 215 301 215 2 86 215 172 2 43 86 86 0 HCF = 43 iv. 632, 790, 869 Ans: 1 8 790 869 79 632 790 10 632 79 790 0 790 0 HCF = 79 Q 10. Find the L.C.M by division method. i. 16, 24, 40
CSS Primary Standard “Mathematics” 81 Ans: LCM = 2 × 2 × 2 × 2 × 3 × 5 ii. 40, 56, 60 Ans: LCM = 2 × 2 × 2 × 5 × 3 × 7 = 840 iii. 207, 318 Ans: LCM = 2 × 3 × 3 × 23 = 414 iv. 72, 96, 120 Ans: 2 16, 24, 40 2 8, 12, 20 2 4, 6, 10 2 2, 3, 5 3 1, 3, 5 5 1, 1, 5 1, 1, 1 2 40, 56, 60 2 20, 28, 30 2 10, 14, 15 5 5, 7, 15 3 1, 7, 3 7 1, 7, 1 1, 1, 1 3 207, 138 3 69, 46 23 23, 46 2 1, 2 1, 1 12 72, 96, 120 2 6, 8, 10 2 3, 4, 5 2 3, 2, 5 3 3, 1, 5 5 1, 1, 5 1, 1, 1
CSS Primary Standard “Mathematics” 82 LCM = 12 × 2 × 2 × 2 × 3 × 5 = 1440 v. 120, 150, 135 Ans: LCM = 5 × 3 × 2 × 2 × 2 × 5 × 3 × 3 = 5400 vi. 102, 170, 136 Ans: LCM = 2 × 2 × 2 × 3 × 5 × 17 = 2040 Q 11. Find the smallest number which on adding to 19 it is exactly divisible by 28, 36, and 45. Ans: Given that LCM of 28, 36 and 45 = x + 19 x = LCM – 19 LCM: 5 120, 150, 135 3 24, 30, 27 2 8, 10, 9 2 4, 5, 9 2 2, 5, 9 5 1, 5, 9 3 1, 1, 9 3 1, 1, 3 1, 1, 1 2 102, 170, 136 2 51, 85, 68 2 51, 85, 34 3 51, 85, 17 5 17, 85, 17 17 17, 17, 17 1, 1, 1 2 28, 36, 45 2 14, 18, 45 3 7, 9, 45 3 7, 3, 15 5 7, 1, 5 7 7, 1, 1 1, 1, 1
CSS Primary Standard “Mathematics” 83 LCM = 2 × 2 × 3 × 3 × 5 × 7 = 1260 x = 1260 – 19 = 1241 Q 12. Find the number which divides 167 and 95 leaving 5 as remainder? 9 5 18 167 18 95 162 90 5 5 0 0 Q 13. Solve and prove whether each number is a prime number or composite number. i. 33 Ans: 33 is composite because it is divisible by 3 and 11. 11 3 3 33 11 33 33 33 0 0 ii. 111 Ans: 111 is composite because it is divisible by 3 also. 37 3 111 111 0 iii. 55 Ans: 55 is composite because it is divisible by 5 and 11. 11 11 5 55 5 55 55 55 0 0 iv. 70 Ans: 70 is a composite number because it is divisible by 2, 5, 7, 10 also. For example 10 7 70
CSS Primary Standard “Mathematics” 84 70 0 v. 317 Ans: 317 is a prime number because it is divisible by 1 and 317 For example 1 317 317 317 0 vi. 18 Ans: 18 is a composite number because it is divisible by 2, 3, 6, 9 also. For example 3 6 18 18 0 vii. 83 Ans: 83 is a is prime number because it is divisible by 1 and 83 For example 1 83 83 83 0 viii. 300 Ans: 300 is a composite number because it is divisible by 2, 3, 5, 10, 25, 30 etc. For example: 10 30 300 300 0 ix. 120 Ans:
CSS Primary Standard “Mathematics” 85 120 is composite number because it is divisible by 2, 3, 4, 6, 8, 10, 12, 20, 24, 30, 40, 60, 120. x. 88 Ans: 88 is a composite number because it is divisible by 2, 4, 8, 11, 22, 44, 88. xi. 100 Ans: 100 is composite number because it is divisible by 2, 4, 5, 10, 20, 25, 50, 100 xii. 1000 Ans: 1000 is composite number because it is divisible by 2, 4, 5, 8, 10, 20, 25, 50, 100, 200, 250, 500, 1000. xiii. 167 Ans: 167 is prime numbers because it is divisible by 1 and 167. First Term Model Paper Model Paper No. 1 Section – A: Multiple Choice Questions Marks: 40 Time: 50 Minutes Roll No. __________ Choose the correct option. 40 1. {0,1,2,3,4…..} is the set of __________ numbers. Natural Odd Whole Even 2. If A = {1,2,3} and B = {1,2,3,4,5} then A is __________ subset of B. Proper Improper Super None of these 3. A set having no element is called __________ set. Super Improper Singleter Null 4. Two sets A and B are said to be __________ if they have equal number of elements. Equal Subsets Equivalent None of these 6. If two sets are equal, then they are also: Subset Equivalent Superset None of these 7. If A = {1,2,3,5,7}, then there are __________ possible subsets of A. 16 5 32 8 8. __________ is not Notation of a set.
CSS Primary Standard “Mathematics” 86 ∪ ∩ < 9. {a} is __________ set: Empty Infinite set singleton None of these 10. The __________ brackets are sometimes called set brackets. Round Square Curly None of these 11. If 30 ÷ 5, then quotient is: 0 30 5 6 12. Name the property 5+7 = 7+5 Commutative property w.r.t addition Commutative property w.r.t multiplication Associalive property w.r.t multiplication Associative property w.r.t addition 13. Any number divided by 1 is equal to: 1 0 number itself 7 14. Any number added by zero is equal to: 0 1 number itself 5 15. Whole number starts with: –1 1 0 2 16. 6 × (5–2) = (____ × ____) – 6 × 2 6,5 6,2 6,–2 5,–2 17. 1 0 ------------- 100 100 1 0 50 18. 20 × 50 = __________ 500 100 1000 250 19. 650 130 : 3 2 5 10 20. 37 × 12 = 460 444 424 464 21. 372 + (210 + 100) = 662 672 682 692 22. 35 × (13 + 20) = 3125 1525 1155 1375 23. 137 × (25 – 16) 1233 1163 1353 1237 24. For any z, z + 0 = 0, then __________ is called __________ identity. 0, multiplicative 1, additive 1, multiplicative 0, additive 25. Two numbers are called __________ if their only common factor is 1: Prime Coprime Compsite None of these
CSS Primary Standard “Mathematics” 87 26. The numbers which are multiple of 2 are called __________ number: Even Odd Prime Composite 27. The natural number which has only two divsor 1 and number itself is called _________ number: Prime Composite Even Odd 28. A number exactly divisible by 8 if last __________ digits are either zero or divisible by 8: 1 2 3 4 29. A __________ number can be written as the product of all of its prime factors. Prime Composite Even Odd 30. The HCF of two or more numbers is the __________ of common factors. sum difference product division 31. LCM of 352 and 216 is: 5984 9504 3015 9506 32. 83 is __________ number: negative even prime composite 33. 167 is a/an __________ number, but also a __________ number: even, composite composite, prime odd, composite odd, prime 34. The smallest number which is common __________ of two or more __________ is called LCM. facter, number factor, dividend multiple, factor multiple, number 35. The only even prime number is: 1 2 4 0 36. Which of the following number is divisible by 5: 3156 21352 1623 1535 37. The index notation of 2×2×3×3×3×5 is: 2 2 ×33 ×52 2 3 ×32 ×51 2 2 ×32 ×51 2 2 ×33 ×5 38. HCF of 45,75,180 is: 25 15 35 45 39. LCM of 60, 75: 150 200 250 300 40. 254 is a number: Composite Prime Negative Coprime Section – B: Constructed Response Questions Marks: 60 Time: 2 hours 10 minutes Attempt all questions. Each question carries equal marks. Q.1: Find proper and improper subsets of {1,2,3,5,8}? Q.2: Prove the distributive law of multiplication over addition for the following 890,345,100 .
CSS Primary Standard “Mathematics” 88 Q.3: Multiply the following: 3574 × 4592 × 320 Q.4: Solve the following: 5867316 ÷ 9 Q.5: An art gallery has 83542 painting. 32516 painting were damaged due to weather disaster and 1300 were shifted to other branch of gallery. How many painting left in gallery. Q.6: Find the prime factor of 512 by factor tree? Q.7: Factorize the given numbers and express their factors in index notation. Q.8: Find HCF by long division method: 48, 132, 352 Q.9: Find LCM by prime factorization: 340, 720, 480 Q.10: Find LCM by division method: 300, 175, 525, 25 Q.11: Find least number of students exactly in groups of 348, 64 and 84 to participate in a seminar. Model Paper No. 2 Section – A: Multiple Choice Questions Marks: 40 Time: 50 Minutes Roll No. __________ Choose the correct option. 40 1. {1, 2, 3, 4…..} is the set of __________ numbers. Whole Natural Even Odd 2. If S = {a, b, c, d} and T = {a, b, c} then S is __________ of T. Proper subset Improper subset Superset None of these 3. __________ is notation of Empty set. {1} ∪ < 4. If two sets A and B have same and equal number of elements, then they are called __________ sets. Equivalent Equal Subsets Supersets 6. If X = {a, b, c, d}, then there and __________ possible proper subsets of X. 4 8 16 15 7. Two sets A and B are improper subsets of each other if A __________ B. = ≠ 8. Any set has at most __________ improper sets.
CSS Primary Standard “Mathematics” 89 3 2 0 1 9. Set is a collection of __________ and objects. Well defined, distinct well defined, similar singleton None of these 10. A set contain __________ number of element is called finite set. indefinite uncountable definite both and b 11. Name the property a × (b × c) = (a × b) × c associative property w.r.t multiplication distributive property of multiplication over addition associative property w.r.t addition distributive property of multiplication over subtraction 12. Any number divided by itself is equal to __________. 1 number itself 1 2 13. a + (–a) = –a + a = 1 2a 0 a 14. If 20 ÷ 10, then quotient is: 0 10 20 2 15. 131 × 25 = __________ 3255 2375 3275 3165 16. 1 70 35 70 35 2 4 17. (a + b) + c = a + (_____ + _____) b, a a, c a, b b, c 18. 360 40 6 12 9 24 19. (25 + 12) × 3 = __________ 121 311 111 141 20. For any z, z × 1 = 1 × z = z then: 0, multiplicative 1, multiplicative 1, additive 0, additive 21. The numbers which is not multiple of 2 called __________ number. prime odd even composite 22. A natural number which has more than 2 factors is called __________ number: prime odd composite even 23. (63 – 40) × 10 = 260 630 400 230 24. 36 × (20 × 10) = 3600 7200 6200 5200
CSS Primary Standard “Mathematics” 90 25. A number is exactly divisible by 3 if the __________ of digits is divisible by __________. product, 6 differences, 3 product, 3 sum, 3 26. Which of following number is divisible by 8. 9004 1114 5300 20712 27. Factor tree continue till we have a __________ of prime number. column product row none of these 28. L.C.M is number which is completely __________ by the given number. add subtract multiple divisible 29. __________ numbers are those numbers whose common factor is only 1. prime odd even co-prime 30. The index notation of 2 × 3 × 3 × 4 × 4 × 4 is: 2 2 × 32 ×42 2 2 × 33 × 44 2 × 32 × 43 2 3 × 31 × 42 31. LCM of 70, 98, 175 is: 2350 2050 2130 2450 32. 7 and 9 are __________ numbers: prime composite even co-prime 33. H.C.F of 300, 75, 45 is: 25 15 30 35 34. 5 and 7n are __________ number: even competitive negative twin prime 35. The factor par of 15 are: 3 and 3 3 and 4 3 and 5 5 and 5 36. __________ is the number which is neither positive nor negative: 1 2 – 1 0 37. HCF can find by __________ methods: 3 4 5 2 38. 13 is a __________ because it is divisible by itself and __________. odd number, 0 prime number, 1 even number, 1 none 39. 143252 _____ 143123: > < = none 40. In the number line, numbers always increase on __________ side: left upper lower right Section – B: Constructed Response Questions Marks: 60 Time: 2 hours 10 minutes Attempt all questions. Each question carries equal marks. Q.1: Verify the associative law w.r.t multiplication for following whole number 120, 170, 250. Q.2: Find the proper subsets of {a, b, c, d, e, f}.
CSS Primary Standard “Mathematics” 91 Q.3: Solve the following: 653892 ÷ 12 Q.4: Multiply the following 324 × 512 × 132 Q.5: Which of following number are divisible by 15 and why? 352140, 8775, 843692, 732150, 43123, 654321 Q.6: Find the prime factorization of given numbers by repeated division method 7262, 36005, 4836? Q.7: Find the highest number which exactly divides these numbers? 575, 225, 600 Q.8: Find H.C.F by long division method? 145, 540, 675, 765 Q.9: Define the following: Proper subsets Equal sets Singleton sets Q.10: Find the increase in the number of people die during 2001 and 2010. The number of people die in 2001 was 132352279 and in 2010 was 207774550? Model Paper No. 3 Section – A: Multiple Choice Questions Marks: 40 Time: 50 Minutes Roll No. __________ Choose the correct option. 40 1. All the odd number in whole numbers are: empty set finite set infinite set singleton set 2. The set of prime numbers divisible by 2 is __________. empty set singleton set infinite set none of these 3. X is a set multiple of 2, Y is multiple of 4, and Z is a set multiple of 6, which on is true. X Y Y Z Z X 4. A = {a, b, c}, how many proper subset does A haves? 3 2 8 7 5. If A= {1, 2, 3, 4, 6, 8, 9} which one is superset of A: {1, 3, 4, 6, 8, 9} {1, 2, 3, 6, 8, 9, 10} {1, 2, 4, 6, 8, 9, 12} {1, 2, 3, 4, 6, 8, 9, 11} 6. A is a set of factor of 15, which one of following is not a number of A.
CSS Primary Standard “Mathematics” 92 3 1 5 2 7. {a, b, c} __________ {1, 2, 3}. = 8. __________ is subset of every set: empty set singleton set empty set None of these 9. __________ is notation for membership. ^ 10. { } has __________ subsets. 2 0 1 3 11. Name the property a × (b + c) = a × b + a × c: associative property w.r.t addition associative property w.r.t multiplication distributive property of multiplication over addition distributive property of multiplication over subtraction 12. __________ is the number which is neither negative nor positive. 1 0 2 None of these 13. Any number multiply by 1 is equal to: 1 0 number itself 5 14. 1 1 a a a a 0 1 a –a 15. 131 ÷ 5 = __________ 25 35 37 27 16. If 120 ÷ 6, the quotient is: 6 120 20 10 17. 540 45 10 5 15 12 19. 0 4 40 1 3 40 1 10 0 20. 4 + 5 = _____ + _____ 4, 3 5, 4 3, 5 5, 3 21. 3 × (4 + 5) + _____ × 4 + 3 × _____ 3, 4 3, 5 4, 5 5, 3 22. a × (b × c) = (a × _____) × c b c a none of these 23. 35 × (4 + 8) = _____ 400 380 420 320
CSS Primary Standard “Mathematics” 93 24. (850 + 300) + 250 = _____ 1200 4000 1400 1600 25. Which of following is divisible by 9: 35216 13724 45328 53721 26. If the common factor between any two number is only 1 they are called: composite Even prime co-prime 27. Sum of greatest three digit number and smallest digit number is: 199 1009 1091 1090 30. The factor 39 are __________ 1, 3, 9, 39 3, 13, 39 1, 3, 6, 9, 39 1, 3, 13, 39 31. Which of following is divisible by: 3040 15008 1836 25252 32. HCF of 5450 and 1000 is _____ 5 10 25 50 33. LCM of 120, 144 is __________ 1440 540 720 620 34. The index notation of 5 × 7 × 7 is 5 × 7 5 2 × 7 5 × 72 5 2 × 72 35. LCM of two or more numbers is the __________ of all their common __________: largest, divisor smallest, factor largest, multiple smallest, multiple 36. 0 is __________ number: whole number natural number negative number positive number 37. 125 × _____ = 125: 1 2 3 5 38. Multiplicative Identity is __________ 0 1 2 none of these 39. If zero is multiplied by any number is equal to __________: number itself 1 0 none of these 40. The concept of sets was given by __________. George James Canter Mil Canter Jone George Canter Section – B: Constructed Response Questions Marks: 60 Time: 2 hours 10 minutes Attempt all questions. Each question carries equal marks. Q.1: Differentiate between Equal and Equivalent set with example? Q.2: Find all possible subsets of following set? X = {g, h, k, l, m, n} Q.3: Verify the distributive property of multiplication over subtraction for following numbers? 384, 560, 480 Q.4: If a = 340, b = 120, C = 50, then prove the associative law of multiplication.
CSS Primary Standard “Mathematics” 94 Q.5: Solve 6853896 ÷ 14 Q.6: Using divisibility test, find out which of the following is divisibly by 6, 8, 9, 10? And why 573282, 325460, 7146000 Q.7: Find the prime factorization of given number with factor three. 705642 Q.8: Find HCF of following numbers by long division method. 150, 315, 435, 675 Q.9: Find LCM of 120, 144, 160, 180 by prime factorization method? Q.10: The length of five strings are 105m, 125m, 145m, 175m, 225m. Find the distance which covers the five strong completely. Week 7 Unit:4 Integers Lesson 1 Teacher Objectives: ☻ To introduce base, exponent and value. ☻ To deduce law of exponents by using the rational numbers. Product law. Quotient law. Power law. For zero exponent. For exponent negative integer. ☻ To explain the concept of power of integer that is (–a)n when n is even or odd integers. ☻ To demonstrate the law of exponents to evaluate expression. Learning out comes: Student should be able to: ☻ Know that he natural numbers 1,2,3......, are also called positive integers and the corresponding negative numbers -1,-2,-3...., are called negative integers. 0” is an integer which is neither positive nor negative. ☻ Recognize integers. ☻ Represent integers on number line. ☻ Know that on the number line any number lying
CSS Primary Standard “Mathematics” 95 to the right of zero is positive to the left of zero is negative, to the right of another number is greater to the left of another number is smaller. ☻ Know that every positive integer is greater than a negative integer. ☻ Know that every negative integer is less than a positive integer. ☻ Arrange a given list of integers in ascending and descending order. ☻ Define absolute or numerical value of a number as its distance from zero on the number line and is always positive. ☻ Arrange the absolute or numerical values of the given integers in ascending and descending order. ☻ Use number line to display sum of two or more given negative integers, difference of two given positive integers, sum of two given integers. ☻ Add two integers (with like signs) in the following three steps: Take absolute values of given integers Add the absolute values Give the result the common sign ☻ Add two integers (with unlike signs) in the following three steps. Take absolute values of given integers Subtract the smaller absolute value from the larger. Give the result the sign of the integer with the larger absolute value. ☻ Recognize subtraction as the inverse process of addition. ☻ Subtract one integer from the other by changing the sign of the integer being subtracted and adding according to the rules for addition of integers. ☻ Recognize that the product of two integers of like signs is a positive integer. the product of two integers of unlike signs is a negative integer. ☻ Recognize that division is the inverse process of multiplication. ☻ Recognize that on dividing one integer by another. If both the integers have like signs, the quotient is positive. If both the integers have unlike signs, the quotient is negative. ☻ Know that division of an integer by “0” is not possible. Teacher materials. CSS Primary Standard Mathematics Book 6. Writing Board.
CSS Primary Standard “Mathematics” 96 Marker. Eraser. Classroom Activity: Match the columns. Column A Column B 3 × 3 × 3 × 3 444 333 1111 2222 a × a × a (–5) × (–5) 3 4 3 (–5)2 3 4 4 1 2 a 3 Solution: 3 × 3 × 3 × 3 = 34 3 4 4 4 4 3 3 3 3 4 1 1 1 1 1 2 2 2 2 2 a × a × a = a3 (–5) × (–5) = (–5)2 Hence Column A Column B 3 × 3 × 3 × 3 444 333 1111 2222 a × a × a (–5) × (–5) 3 4 3 (–5)2 3 4 4 1 2 a 3
CSS Primary Standard “Mathematics” 97 Second Term Week 1 Exercise 4a Q1. Separate positive and negative integers. Ans: Negative integers: –8, –339, –44, –91, –635, –435, –1100, –1432, –1072. Positive Integers: 11, 71, 88, 447, 834, 647, 839, 942, 1240, 1342, 4234. Q2. Draw on number line by selecting proper scale and show the integer on it. (i) 10 and 70 Ans: (ii) 45 and 55 Ans: (iii) 150 and 400 Ans: (iv) –200 and –600 Ans: (v) –300 and –200 Ans:
CSS Primary Standard “Mathematics” 98 (vi) –450 and +300 Ans: Q3. Write the absolute value of the given integers. Ans: |–7321| = 732 |–4375| = 4375 |–432| = 432 |–5389| = 5389 |472| = 472 |–3742| = 3742 |832| = 832 |–2314| = 2314 |941| = 941 |–7100| = 7100 |–182| = 182 |–8432| = 8432 |1001| = 1001 |–71105| = 71105 |2375| = 2375 |–83942| = 83942 Q4. For the following numbers write ascending and descending order and also arrange the absolute value of integers in descending order. (i) 430, 474, 894, –1140 Ans: Ascending order: –1140, 430, 474, 894 Descending order: 894, 474, 430, –1140 Absolute value in descending order: 1140, 894, 474, 430 (i) 430, 474, 894, –1140 Ans: Ascending order: –1140, 430, 474, 894 Descending order: 894, 474, 430, –1140 Absolute value in descending order: 1140, 894, 474, 430 (ii) –110, 730, –940, 940, 344, 7440 Ans: Ascending order:
CSS Primary Standard “Mathematics” 99 –940, –110, 344, 730, 940, 7440 Descending order: 7440, 940, 730, 344, –110, –940 Absolute value in descending order: 7440, 940, 940, 730, 344, 110 (iii) 8390, 11432, 37184, 74291, –3745, –4752 Ans: Ascending order: –4752, –3745, 8390, 11432, 37184, 74291 Descending order: 74291, 37484, 11432, 8390, –3745 –4752 Absolute value in descending order: 74291, 37184, 11432, 8390, 4752, 3745 Q5. Which is greater? Ans: –41004, –41104, –4114 –4114 is greater than other two numbers. Q6. Which one is smaller? Ans: –30001, –3001, –301 –30001 is smaller than other two numbers. Exercise 4b Q1. Find the sum of following integers on the number line. (i) 7 + 8 Ans: 7+ 8 = 15 (ii) 50 + 30 Ans: 50 + 30 = 80 (iii) 6 + (–10) Ans: 6 – 10 = –4 (iv) 20 + (–10) Ans: = 20 – 10 = 10
CSS Primary Standard “Mathematics” 100 (v) (–3) + (–5) Ans: = –3 – 5 = – 8 (vi) (–30) + (–60) Ans: = –30 –60 = –90 Q2. Find the difference of following integers on a number line. (i) (+10) – (+7) = +3 Ans: (ii) (+40) – (+20) = +20 Ans: (iii) (+200) – (+100) = +100 Ans: