ARITHMETIC 101 37 ×10 0 0 +370 370 287 ×100 000 0000 +28700 28700 37 × 0 0 0 37 × 10 370 287 × 0 000 287 ×00 0000 287 ×100 28700 3479 ×1000 0000 00000 000000 +3479000 3479000 3479 × 0 0000 3479 ×00 00000 3479 ×000 000000 3479 ×1000 3479000 Multiply : 1. (a) 37 × 10 (b) 59 × 10 (c) 392 ×100 (d) 3790 ×100 (e) 87800 ×300 Multiply : 2. (a) 370 ×1000 (b) 580 ×1000 (c) 2078 ×1000 (d) 2398 ×1000 (e) 9847 ×1000 A stalk of bananas has 37 bananas. A farmer collects such 10 hands of bananas. How many bananas does he collect ? 8.3 Multiplying by 10, 100 and 1000 EXERCISE 8.3 Your mastery depends on practice. Practice like you play. Read, Think and Learn When a number is multiplied by 10 or multiple of 10, the product contains the number followed by the number of zeros in the multiple of 10.
102 The Leading Mathematics - 4 Multiply by ones. Multiply by tens. Multiply by hundreds. Carryovers 287 ×437 2009 8610 +114800 150890419 64 287 ×7 2009 2 2 287 ×30 8610 3 2 287 ×400 114800 Multiply : To multiply by the larger multiplicands, multiply by ones, tens, hundreds ... etc. and the products so obtained. In compact form we have, Carryovers when multiplied by hundreds Carryovers when multiplied by tens Carryovers when multiplied by ones Multiply by ones 287 × 7 Multiply by tens 287 × 30 Multiply by hundreds 287 × 400 3 2 2 2 6 4 287 ×437 2009 8610 +114800 125419 Multiplication of product of 287 × 437 8.4 Multiplying by 3-digit Numbers Lattice (Napier's Bones) Multiplication Method 2 8 7 1 1 2 1 0 8 3 2 2 8 4 2 0 6 2 4 2 1 3 5 1 4 5 6 4 9 7 4 1 9 \ 287 × 437 = 125419 Read, Think and Learn
ARITHMETIC 103 283 × 6 283 ×20 283 ×400 283 ×426 + (b) 761 × 8 761 ×90 761 ×300 761 ×398 + (c) 2 3 5 2 0 0 2 0 3 0 5 1 2 0 6 2 4 1 0 2 9 0 8 1 2 2 0 4 1 4 0 \ 235 × 124 = 29140 1. Multiply the following numbers completing the following steps. 235 × 4 235 ×20 235 ×100 235 ×124 + (a) EXERCISE 8.4 Your mastery depends on practice. Practice like you play. Read, Think and Learn
104 The Leading Mathematics - 4 2. Carry out the following multiplication. (a) 276 ×521 (b) 821 ×482 (c) 257 ×973 (d) 892 ×125 (e) 253 ×526 (k) 324 ×212 (l) 347 ×310 (m) 856 ×320 (n) 972 ×300 (o) 344 ×321 (f) 217 ×289 (g) 432 ×389 (h) 712 ×805 (i) 305 ×927 (j) 768 ×102 (p) 307 ×201 (q) 483 ×873 (r) 999 ×999 (s) 820 ×380 (t) 682 ×123 (u) 873 ×872 (v) 903 ×500 (w) 451 ×123 (x) 829 ×342 (y) 872 ×987 Count the total pages of one of your books. If a box contains 279 such books, what is the total pages in these all books? Find it. Prepare a report and present it in your classroom. PROJECT WORK
ARITHMETIC 105 Example 1 A box has 245 packets of biscuits. How many packets are there in 278 such boxes ? Solution : Here, Number of boxes = 278 Number of packets of biscuits in a box = 245 \ Total number of packets of biscuits in 278 boxes = 278 × 245 Carryovers when multiplied by hundreds Carryovers when multiplied by tens Carryovers when multiplied by ones Multiply by ones 278 × 5 Multiply by tens 278 × 40 Multiply by hundreds 278 × 200 Sum 1 1 133 134 278 ×245 1390 111 2 0 +55600 68110 Thus, there are 68110 packets of biscuits in 278 boxes. Example 2 The cost of a calculator is Rs. 785. What is the cost of 579 such calculators ? Solution : Here, Cost of 1 calculator = Rs. 785 Number of calculators = 579 \ Total cost of 579 calculators = Rs. 785 × 579 8.5 Verbal Problems on Multiplication Read, Think and Learn
106 The Leading Mathematics - 4 Carryovers when multiplied by hundreds Carryovers when multiplied by tens Carryovers when multiplied by ones Multiply by ones 278 × 5 Multiply by tens 278 × 70 Multiply by hundreds 278 × 500 Sum 342 553 774 785 ×579 7065 54950 +392500 454515 Thus, the cost of 579 calculators is Rs. 32878515. EXERCISE 8.5 Your mastery depends on practice. Practice like you play. 1. A chalk box has 86 chalk pieces. How many pieces will be there in (a) 600 chalk boxes (b) 586 chalk boxes (c) 947 chalk boxes. 2. A box has 156 lipsticks. How many lipsticks are there in (a) 27 boxes (b) 378 boxes (c) 896 boxes. 3. The monthly salary of Hari $ 278. How much salary will be there in (a) 12 months (b) 273 months (c) 456 months 4. A radio costs Rs. 947. What is the cost of : (a) 36 radios (b) 782 radios (c) 308 radios 5. A human body has 206 pieces of bones. How many pieces of bones are there in 378 human bodies ?
ARITHMETIC 107 6. There are 365 days in a year. How many days are in 273 years ? 7. The speed of a bullet train is 603 km per hour. How long distance will it travel in 475 hours? 8. An active mathematics book has 288 pages. How many pages are there in 345 such books ? 9. An electric fan rotates 596 times in one minute. How many rotations will it make in 8 hours ? 10. The distance between Kathmandu and Jomsom is 358 km. If a bus makes 409 tips between them in a year, how long distance does the bus cover in all ? 11. There are 3600 seconds in an hour. How many seconds are there in 6 days ? 12. Find the product of the greatest numbers of 3 digits and 2 digits. 13. The length and breadth of the football ground are 394 feet and 295 feet respectively. Find the product of its length and breadth. 14. A tennis court needs 936 inches length and 324 inches breadth. What is the product of its length and breadth ? 15. The cost of a watch is Rs. 758. What is the cost of such types of 9 dozen of watches ? 16. There are 368 pages in The Leading Mathematics Pocket Dictionary. How many pages are there in 23 dozen of such dictionaries.
108 The Leading Mathematics - 4 CHAPTER 9 Division How many apples and coloured pencils are there in the above picture? How many boys and girls are there in the above picture? How many apples does each boy get in equal ? How many apples does each girl get in equal ? How many coloured pencils does each boy get in equal ? How many coloured pencils does each girl get in equal ? WARM-UP Lesson Topics Pages 9.1 Review on Dividing by 1-digit Numbers 109 9.2 Review Dividing in Standard Form 111 9.3 Dividing 3-digit Numbers by 2-digit Numbers 113 9.4 Dividing by 10, 100 and 1000 115 9.5 Dividing 4 and 5-digit Numbers by 2-digit Numbers 116 9.6 Dividing 3-digit Numbers 118 9.7 Simple Problems on Multiplication and Division 120 9.8 Verbal Problems on Division 122
ARITHMETIC 109 9.1 Review (A) on Dividing by 1-digit Numbers Read, Think and Learn Divide 24 by 6. i.e. 24 ÷ 6 = ? = = In the other hand, 24 ÷ 6 = 4 6 can be subtracted from 24 for 4 times. 2 4 – 6 1 8 – 6 1 2 – 6 6 – 6 0 1 time 2 times 3 times 4 times 6 24 4 –24 × 4 24 6 –24 × Since 4 × 6 = 24, So, 24 ÷ 6 = 4 and 24 ÷ 4 = 6 Here, 24 ÷ 6 = has the same meaning 6 × = 24. Since, 6 × 4 = 24, so 24 ÷ 6 = 4 In the other hand, 24 ÷ 6 = 24 6 = 2 × 2 × 2 × 3 2 × 3 = 4 To divide by a number is to multiply by its reciprocal. How many apples does a boy get when 24 apples are equally distributed among 6 boys ? Oh! I remembered division is short form of repeated subtraction. It is not commutative. Oh! Therefore, 4 groups of 6.
110 The Leading Mathematics - 4 1. In each of the following, write the equivalent multiplication sence and find the replacement for . (a) 28 ÷ 7 = has the same meaning as 7 × = 28. (b) 64 ÷ 8 = has the same meaning as 8 × = 64. (c) 135 ÷ 9 = has the same meaning as 9 × = 135. (d) 2375 ÷ 5 = has the same meaning as 5 × = 2375. (e) 30726 ÷ 6 = has the same meaning as 6 × = 30726. 2. Find the quotient by using the concept of inversible multiplication. e.g. 15 ÷ 3 = 3 × 5 3 = 5 (a) 65 ÷ 5 = (b) 84 ÷ 7 = (c) 90 ÷ 6 = (d) 184 ÷ 8 = (e) 144 ÷ 4 = (f) 702 ÷ 9 = (g) 1086 ÷ 3 = (h) 3682 ÷ 7 = (i) 1290 ÷ 5 = (j) 3471 ÷ 3 = (k) 24246 ÷ 6 = (l) 16387 ÷ 7 = 3. Find the quotient by using the concept of multiplication as the inverse of division. e.g. 345 ÷ 5 = 3 × 5 × 23 5 = 69 (a) 39 ÷ 3 = (b) 148 ÷ 4 = (c) 972 ÷ 6 = (d) 1325 ÷ 5 = (e) 3648 ÷ 8 = (f) 4109 ÷ 7 = (g) 4578 ÷ 7 = (h) 3033 ÷ 9 = (i) 78272 ÷ 8 = (j) 14500 ÷ 4 = (k) 18920 ÷ 8 = (l) 48258 ÷ 7 = EXERCISE 9.1 Your mastery depends on practice. Practice like you play.
ARITHMETIC 111 7 938 134 28 –7 23 –21 7 437 062 17 –0 43 –42 –28 –14 Remainder Remainder \ 934 ÷ 7 = 134 r 0 \ 437 ÷ 7 = 62 r 3 v Divide 938 by 7. v Divide 437 by 7. 0 3 Quotient Quotient Here, in 24 ÷ 6 = 4, 24 is dividend, 6 is divisor and 4 is quotient. Also, 6 × 4 = 24 i.e., Divisor × Quotient = Dividend But, in this division, 24 ÷ 5 = Here, since 5 > 4, so 5 can not be subtracted from 4. Then, 4 is remainder. \ 24 ÷ 5 = 4 r 4 \ 24 = 5 × 4 + 4 Divisor + Quotient + Remainder = Dividend 2 4 – 5 1 9 – 5 1 4 – 5 9 – 5 4 1 time 2 times 3 times 4 times 9.2 Review (B) Dividing in Standard Form Basic Operations 75 7 938 134 28 –7 23 –21 7 437 062 17 –0 43 –42 –28 –14 Remainder Remainder \ 934 ÷ 7 = 134 r 0 \ 437 ÷ 7 = 62 r 3 v Divide 938 by 7. v Divide 437 by 7. 0 3 Quotient Quotient Here, in 24 ÷ 6 = 4, 24 is dividend, 6 is divisor and 4 is quotient. Also, 6 × 4 = 24 i.e., Divisor × Quotient = Dividend But, in this division, 24 ÷ 5 = Here, since 5 > 4, so 5 cannot be subtracted from 4. Then, 4 is remainder. \ 24 ÷ 5 = 4 r 4 \ 24 = 5 × 4 + 4 Divisor + Quotient + Remainder = Dividend Remainder Divisor 3.4 (B) Review (B) Dividing in Standard Form Read, Think and Learn 2 4 – 5 1 9 – 5 1 4 – 5 9 – 5 4 1 time 2 times 3 times 4 times Read, Think and Learn Remainder Divisor
112 The Leading Mathematics - 4 1. Divide and verify : Divisor × Quotient = Divident e.g. 45 ÷ 5 = 5 × 9 = 45 \ Divisor × Quotient = Dividend (a) 85 ÷ 5 = (b) 76 ÷ 4 = (c) 184 ÷ 8 = (d) 504 ÷ 9 = (e) 168 ÷ 7 = (f) 3472 ÷ 8 = (g) 7392 ÷ 6 = (h) 3934 ÷ 7 = (i) 2190 ÷ 6 = (j) 20504 ÷ 8 = (k) 34371 ÷ 3 = (l) 53780 ÷ 5 = 2. Divide and verify that Divisor × Quotient + Remainder = Dividend e.g. 275 ÷ 6 = 6 × 45 + 5 = 275 \ Divisor × Quotient + Remainder = Dividend (a) 37 ÷ 5 = (b) 78 ÷ 6 = (c) 98 ÷ 8 = (d) 360 ÷ 8 = (e) 245 ÷ 8 = (f) 348 ÷ 7 = (g) 7536 ÷ 6 = (h) 2304 ÷ 9 = (i) 1460 ÷ 4 = (j) 4958 ÷ 6 = (k) 4578 ÷ 9 = (l) 98765 ÷ 5 = 5 45 9 × – 45 6 275 45 5 –24 35 –30 EXERCISE 9.2 Your mastery depends on practice. Practice like you play.
ARITHMETIC 113 1. Divide : 255 ÷ 15 Solution : \ 255 ÷ 17 Also, 15 × 17 = 225 Therefore, Divisor × Quotient = Dividend 2. Divide : 198 ÷ 16 Solution : \ 198 ÷ 16 = Q12 R6 Also, 16 × 12 + 6 = 198 Therefore, Divisor × Quotient + Remainder = Dividend 15 255 Since 2 < 15, so it can't divide 2. Take 2 digits as 25. The first 2 digits in 105 make 10 which is less than 15. Therefore, divide 3-digit number 105 by 15. 17 × –15 105 –105 15 × 1 = 15 15 × 2 = 30 15 × 3 = 45 15 × 4 = 60 15 × 5 = 75 15 × 6 = 90 15 × 7 = 105 16 198 Since 1 < 16, so take 19 which is greater than 16. Divide 19 by 16 at once. Down 8 and since 38 > 16. Divide 38 by 16 at 2 times. 12 6 –16 38 –32 16 × 1 = 16 16 × 2 = 32 16 × 3 = 48 9.3 Dividing 3-digit Numbers by 2-digit Numbers Read, Think and Learn
114 The Leading Mathematics - 4 1. Divide 11 44 (a) 17 51 (b) 18 72 (c) 13 78 (d) 22 89 (e) 24 99 (f) 39 90 (g) 49 84 (h) 23 95 (i) 12 88 (j) 13 95 (k) 69 99 (l) 2. Divide : 14 476 (a) 13 338 (b) 15 345 (c) 28 476 (d) 33 695 (e) 42 790 (f) 67 808 (g) 78 710 (h) 36 252 (i) 47 425 (j) 56 455 (k) 99 999 (l) 3. Divide and verify : Divisor × Quotient = Dividend (a) 57 ÷ 19 = (b) 84 ÷ 21 = (c) 78 ÷ 26 = (d) 87 ÷ 29 = (e) 65 ÷ 13 = (f) 80 ÷ 16 = (g) 182 ÷ 26 = (h) 180 ÷ 12 = (i) 391 ÷ 17 = (j) 782 ÷ 34 = (k) 952 ÷ 56 = (l) 456 ÷ 57 = 4. Divide and verify : Divisor × Quotient + Remainder = Dividend (a) 95 ÷ 23 = (b) 99 ÷ 18 = (c) 87 ÷ 15 = (d) 78 ÷ 40 = (e) 99 ÷ 67 = (f) 94 ÷ 47 = (g) 236 ÷ 26 = (h) 478 ÷ 35 = (i) 394 ÷ 59 = (j) 892 ÷ 65 = (k) 984 ÷ 75 = (l) 999 ÷ 99 = Count the bricks of a wall of any room of your home or neighbouring home. Also, count the number of bricks in a line of the wall. How many lines are there in the wall ? Find it. Prepare a report and present it in your classroom. PROJECT WORK EXERCISE 9.3 Your mastery depends on practice. Practice like you play.
ARITHMETIC 115 \ 3847 ÷ 10 = 384 r 7 Quotient = 384 Remainder = 7 \ 3847 ÷ 100 = 38 r 47 Quotient = 38 Remainder = 47 \ 3847 ÷ 1000 = 3 r 847 Quotient = 3 Remainder = 847 If the divisor is 10, the last digit of the dividend is the remainder and the number formed by the earlier remaining digits of the dividend is the quotient. If the divisor is 100, the number formed by left two digits of the dividend is the remainder and the number formed by earlier digits of the dividend is the quotient. If the divisor is 1000, the number formed by the last three digits of the dividend is the remainder and the number formed by the remaining digits of the dividend is the quotient. 3847 ÷ 100 3847 38 –300 847 47 –800 100 3847 ÷ 1000 3847 3 –3000 847 1000 Let’s divide 3847 by 10,100 and 1000 separately. Divide and write down the quotient and the remainder. 1. (a) 32 ÷ 10 (b) 473 ÷ 10 (c) 9912 ÷ 10 2. (a) 124 ÷ 100 (b) 4788 ÷ 100 (c) 78762 ÷ 100 3. (a) 4742 ÷ 1000 (b) 5878 ÷ 1000 (c) 2478 ÷ 1000 (e) 5689 ÷ 1000 (f) 5768 ÷ ÷ 1000 (g) 98489 ÷ 1000 3847 ÷ 10 3847 384 –30 84 47 –80 –40 7 10 9.4 Dividing by 10, 100 and 1000 EXERCISE 9.4 Your mastery depends on practice. Practice like you play. Read, Think and Learn
116 The Leading Mathematics - 4 9.5 Dividing 4 and 5-digit Numbers by 2-digit Number Divide 4212 by 78. 4 < 78 and 42 < 78. So, take 421 for dividing. 31 < 78 and down 2. 78 4212 54 –390 312 –312 × 67 8782 8 < 67. So, take 87 for dividing. 131 –67 208 –201 72 –67 5 Down 8. 208 > 67 Down 2. 72 > 67 5 < 67. So, 5 is remainder. \ 8782 ÷ 67 = 131 r 5 and 67 × 131 + 5 = 8782 i.e., Divisor × Quotient + Remainder = Dividend Divide 8782 by 67. Read, Think and Learn \ 4212 ÷ 78 = 54 and 78 × 54 = 4212 i.e., Divisor × Quotient = Dividend
ARITHMETIC 117 EXERCISE 9.5 Your mastery depends on practice. Practice like you play. 1. Divide and write the quotient. (a) 15 4785 (b) 38 2648 (c) 75 73950 (d) 81 99954 (e) 64 20800 (f) 79 51745 2. Divide and write the quotient and remainder. (a) 27 6617 (b) 49 1137 (c) 64 9999 (d) 66 99999 (e) 77 27259 (f) 38 38875 3. Divide and check it by using Divisor × Quotient = Dividend. (a) 1288 ÷ 23 (b) 4455 ÷ 45 (c) 55917 ÷ 57 (d) 58990÷ 85 (e) 60168÷ 92 (f) 64582÷ 98 4. Divide and check it by using Divisor × Quotient + Remainder = Dividend. (a) 3308 ÷ 14 (b) 10000 ÷ 99 (c) 80000 ÷ 49 (d) 99999÷ 89 (e) 51015÷ 78 (f) 55100 ÷ 97 5. Find the dividend if : (a) Divisor = 27 and quotient = 19 (b) Divisor = 52 and quotient = 49 (c) Divisor = 79, quotient = 123 and remainder = 5 (d) Divisor = 99, quotient = 537 and remainder = 98 (e) Divisor = 86, quotient = 254 and remainder = 85 (f) Divisor = 96, quotient = 287 and remainder = 47
118 The Leading Mathematics - 4 Divide 5987 by 243. Divide 38070 by 568. Divide 47201 by 652. \ 5987 ÷ 243 = 24 r 155 Quotient = 24 Remainder = 155 5987 24 –486 1127 155 – 972 243 38070 67 –3408 3990 14 – 3976 568 47201 72 –4564 1561 257 – 1304 652 243 × 1 = 243 243 × 2 = 486 243 × 3 = 729 243 × 4 = 972 243 × 5 = 1215 568 × 1 = 568 568 × 2 = 1136 568 × 3 = 1704 568 × 4 = 2272 568 × 5 = 2840 568 × 6 = 3408 568 × 7 = 3976 568 × 8 = 4544 652 × 1 = 652 652 × 2 = 1304 652 × 3 = 1956 652 × 4 = 2608 652 × 5 = 3260 652 × 6 = 3912 652 × 7 = 4564 652 × 8 = 5216 \ 38070 ÷ 568 = 67 r 14 Quotient = 67 Remainder = 14 \ 47201 ÷ 652 = 72 r 257 Quotient = 72 Remainder = 257 Read, Think and Learn 9.6 Dividing 3-digit Numbers
ARITHMETIC 119 1. Divide and write down the quotient and the remainder. (a) 234 2878 (b) 575 3589 (c) 375 20250 (d) 602 45950 (e) 724 31132 (f) 789 99999 2. Divide and check by using the relation Divisor × Quotient + Remainder = Dividend . (a) 347 902 (b) 878 999 (c) 789 9468 (e) 8278 ÷ 275 (f) 9587 ÷ 437 (g) 9895 ÷ 678 (h) 4878÷ 946 (i) 30625 ÷ 555 (j) 35890 ÷ 365 (k) 99999 ÷ 985 (l) 99999 ÷ 999 (m) 23475 ÷ 652 3. Find the dividend in each of the following conditions : (a) Divisor = 153 and quotient = 38 (b) Divisor = 378 and quotient = 23 (c) Divisor = 623, quotient = 13 and remainder = 5 (d) Divisor = 873, quotient = 29 and remainder = 565 4. 25875 apples are beared in a garden. (a) Write the relation between dividend, divisor, quotient and remainder. (b) If a gardener packets them in 345 boxes, how many apples are contained in one box? (c) If the gardener wants to packet them in 325 boxes, how many apples are left after full packs of the boxes? (d) If the gardener wants to packet 95 apples in one box, how many total boxes does he need and how many apples are left after full packs of the boxes? EXERCISE 9.6 Your mastery depends on practice. Practice like you play.
120 The Leading Mathematics - 4 47 × 28 = ÷ 28 = 47 123 × 239 = 29397 ÷ 123 = 25 × = 125 125 ÷ = 25 587 × = 14675 14675 ÷ = 587 × 67 = 4355 1467 ÷ = 67 × 123 = 84747 ÷ 123 = 689 Can you do ? 7 9 × ÷ = = 256 26 × = = Here, 7 × 9 = 63 and 63 ÷ 9 = 7. Also, 256 × 26 = 6656 and 6656 ÷ 26 = 256 \Multiplication and division are inverse to each other Example 1 Find the value of a if 27 × a = 6912 Solution : Here, 27 × a = 6912 or, 27 × a 27 = 6912 27 or, a = 256 ÷ 9.7 Simple Problems on Multiplication and Division Read, Think and Learn CLASSWORK EXAMPLES
ARITHMETIC 121 EXERCISE 9.7 Your mastery depends on practice. Practice like you play. 1. Find the value of a if : (a) 37 × a = 999 (b) 257 × a = 771 (c) a × 59 = 531 (d) a × 27 = 945 (e) a × 36 = 576 (f) a × 23 = 213 (g) a × 45 = 405 (h) a × 25 = 7800 (i) 12 × a = 900 2. Find the value of k if : (a) 299 ÷ k = 27 (b) 6939 ÷ k = 27 (c) k ÷ 25 = 782 (d) k ÷ 217 = 125 (e) 949 ÷ k = 73 (f) k ÷ 23 = 213 (g) k ÷ 327 = 45 (h) k ÷ 59 = 569 (i) k ÷ 564 = 36 3. (a) What must be multiplied to 78 to make it 936 ? (b) What must be multiplied to 96 to make it 864 ? (c) What must be divided to 986 to make it 17 ? (d) What must be divided to 928 to make it 58 ? (e) If a number is divided by 896, the result is 64. Find the number. (f) If a number is multiplied by 87, it becomes 957. Find the number. Example 2 What must be divided to 30726 to make it 54 ? Solution : Let the number to be divided be a. Then, 30726 ÷ a = 54 or, 30726 a = 54 or, 30726 a × a = 54 × a or, 30726 54 = 54 × a 54 or, 569 = a
122 The Leading Mathematics - 4 Example 1 The cost of 85 pencils is Rs. 935. Find the cost of each pencils. Solution : Here, The cost of 85 pencils = Rs. 935 or, The cost of 1 pencil = Rs. 935 ÷ 85 = Rs. 11 Thus, the cost of each pencil is Rs. 11. Example 2 How many 75 rupee notes are in a deck of 1 thousand rupees ? What amount will be left in the deck of notes ? Solution : Here, Total amount = 1 thousand rupees = Rs. 1000 Amount of each note = Rs. 75 For calculating the number of Rs. 75 notes in Rs. 1000 Rs. 1000 ÷ Rs. 75 = 13 r 25 Hence, there are 13 pieces of Rs. 75 notes in the deck of 1 thousand rupees and Rs. 25 is left in it. EXERCISE 9.8 Your mastery depends on practice. Practice like you play. 1. The cost of 1 Doko of 89 apples of Manang is Rs. 979. How much does each apple cost ? 2. The cost of 28 Illustrated maths books is Rs. 896. Find the cost of each Illustrated maths book. 1000 13 –75 250 25 – 225 75 935 11 –85 85 × – 85 85 9.8 Verbal Problems on Division Read, Think and Learn
ARITHMETIC 123 3. 715 apples were distributed among 65 persons equally. How many apples did each get ? 4. Rs. 882 was collected by 42 persons contributing equally. How much did each person contribute ? 5. A typist can type 72 words per minute. How long will it take to type a catalogue of 864 words ? 6. A transistor costing Rs. 945 was paid in monthly installment of Rs. 35. How many months will be required to clear up the loan ? 7. A radio costs Rs. 984. How many month will be required to clear up the loan if it is purchased in an installment of Rs. 82 per month ? 8. A grocers brought 35 boxes to pack up 980 oranges. How many oranges are packed in a box if each box holds equal number of oranges ? 9. A dealer brought 25 pairs of socks paying Rs. 975. How much did he pay for each pair of socks ? 10. A biscuit factory produces23 cartoons of biscuits in one hour. How many hours will be needed to produce 598 cartoon of biscuits ? 11. A man earns Rs. 840 in a day. What is his income in an hour ? 12. Houses are built in the area of 78 square meter each. How many houses could be built in 936 square meter of land ? 13. An airline flies at an speed of 68 km per hour. How long will it take to cover a journey of 816 km ?
124 The Leading Mathematics - 4 CHAPTER 10 Simplification How many apples are there in each box ? How many total apples are there in all boxes ? If a girl takes two apples, how many apples will remain? If a boy eats one apple from it, how many apples will remain? If you go to market with Rs. 3000, you buy a T-shirts of the amounts Rs. 1250 and a shirt of the amount Rs. 1435, how much amount will you have now? WARM-UP Lesson Topics Pages 10.1 Addition and Subtraction Together 125 10.2 Verbal Problems on Addition and Subtraction Together 126 10.3 Simplification Having Brackets ( ) 127 Rs. 1250/- Rs. 1435/-
ARITHMETIC 125 I know a + b = b +a and a + (–b) = (–b) + a Simplify the following : 1. (a) 424 + 216 – 31 4 (b) 576 + 247 – 738 (c) 529 – 307 + 477 (d) 928 – 807 + 370 (e) 432 – 123 – 204 + 249 (f) 789 – 527 + 230 – 179 (g) 4789 – 4734 + 3709 (h) 9872 – 4729 – 3892 (i) 7082 – 1234 – 4321 (j) 2992 + 1990 + 2787 – 4789 (k) 8782 – 3897 – 4325 + 1234 (l) 98762 – 34567 + 12345 – 24680 (m) 9999 – 4444 + 7777 – 8888 (n) 100000 + 278401 – 3784 – 987 (o) 347892 – 302987 + 2801 – 15 (p) 978 – 870 + 478294 – 237892 Example 1 Solve : 324 + 578 – 689 Solution : Here, 324 + 578 – 689 = 902 – 689 = 213 Example 2 Solve : 3780 – 2189 – 4683 + 6049 Solution : Here, 3780 – 2189 – 4683 + 6049 = 3780 – 2189 + 6049 – 4683 = 1591 + 1366 = 2957 At first add 324 and 578. 1 1 3 2 4 + 5 7 8 9 0 2 Subtract 689 from the sum 902. 8 9 12 9 0 2 – 6 8 9 2 1 3 6 17 10 3 7 8 0 – 2 1 8 9 1 5 9 1 5 9 14 6 0 4 9 – 4 6 8 3 1 3 6 6 1 1 5 9 1 + 1 3 6 6 2 9 5 7 10.1 Addition and Subtraction Together EXERCISE 10.1 Your mastery depends on practice. Practice like you play. Read, Think and Learn
126 The Leading Mathematics - 4 There are 2523 students in a school. Among them, 1076 students are boys and 1367 are girls. Find how many students are there of third sex. Solution : Here, Total number of students = 2523 Number of boys = 1076 Number of girls = 1367 \ Number of third sex = 2523 – 1076 – 1367 = 1447 – 1367= 80 Hence, there are 80 students of third sex. 2 5 2 3 –1 0 7 6 1 4 4 7 –1 3 6 7 8 0 1. Find the sum of 144 added to the difference of 278 and 197. 2. Add 378 with the difference of 900 and 789. 3. There are 4810 fish in a pond. A farmer adds 2599 fish in the same pond. If 1567 fish are died, how many fish are left in the pond ? 4. Radha has Rs. 4789 and her father gives Rs. 4372. If she spends Rs. 7058, how much money is left with her ? 5. Samiksha had Rs. 10000. She bought a T–shirt for Rs. 1350 and a pair of shoes for 3409. How much money is left with her ? 6. Two pieces of wires of the lengths 2345 m and 3295 m were cut down from a wire of 8296 m long. Find the length of the remaining wire. 7. The dealer had 98795 boxes of noodles. 23456 boxes of noodles were sold on the first day, 1985 boxes of noodles were sold on the second day and 2005 boxes of noodles were sold on the third day. How many boxes of noodles were left with the dealer ? 8. Ram deposits Rs. 29875 in a bank and withdraws Rs. 2555 by check. Again, he deposits Rs. 3579 on next day. Find the total deposited amount in the bank. 10.2 Verbal Problems on Addition and Subtraction Together EXERCISE 10.2 Your mastery depends on practice. Practice like you play. Read, Think and Learn
ARITHMETIC 127 10.3 Simplification Having Brackets ( ) Read, Think and Learn Example 1 Binod has Rs. 1000. He buys a calculator for Rs. 299 and a book for Rs. 447. (a) Express the given information in algebraic notation. (b) How much does he expense ? Find it. (c) How much will a shopkeeper return to him when he gives Rs. 1000?? Solution : Here, total amount = Rs. 1000, price of a calculator = Rs. 299, price of a book = Rs. 447 (a) The algebraic notation of the given information is as, 1000 – (299 + 447) (b) Expending amount by him = 299 + 447 = 746 (c) Return amount = 1000 – 746 = Rs. 254. Example 2 Simplify : 349 – (246 + 101) Solution : Here, 349 – (246 + 101) = 349 – 347 = 2 Example 3 Simplify : (272 + 123) – (347 – 259) Solution : Here, (272 + 123) – (347 – 259) = 395 – 88 = 307 246 +101 347 3 4 9 –347 002 272 +123 395 347 –259 88 395 –88 307
128 The Leading Mathematics - 4 Simplify the following : 1. (a) (3 + 7) – 2 (b) 20 – (12 + 3) (c) 29 – (28 – 21) (d) 50 – (25 + 14) 2. (a) (37 – 25) – 8 (b) (27 – 20) + 2 (c) (27 – 20) + 3 (d) (27 – 22) + (23 + 5) 3. (a) (37 + 3) – 35 (b) (50 + 20) – 68 (c) (39 + 41) – 64 (d) (57 + 43) – 89 4. (a) 89 + (39 + 47) (b) 120 – (34 + 27) (c) 150 – (94 – 47) (d) 200 – (125 – 45) 5. (a) 54 – (27 + 15) (b) (37 + 28) – 62 (c) (372 – 28) + 89 (d) (452 – 145) + 246 6. (a) (278 + 29) + 478 (b) (682 – 39) – 598 (c) (372 – 29) – 78 (c) (542 – 123) – 125 7. (a) (372 – 123) + 143 (b) (378 – 89) – 187 (c) (879 – 625) – 89 (d) (975 – 458) – 123 8. (a) (3478 – 471) – 592 (b) (8523 + 1357) – 8278 9. (a) 1467 – (845 + 623) (b) 7825 + (3847 – 2796) 10. (a) 9347 – (3890 – 1005) (b) (4789 – 4788) + (3824 – 1234) 11. (a) (3478 + 5392) – (3879 – 2147) (b) (4789 – 4702) + (3762 – 3713) EXERCISE 10.3 Your mastery depends on practice. Practice like you play.
ARITHMETIC 129 Rs. 339.50 0 2 0 0. Petrol price is 169.75/ltr. FRACTION, DECIMAL AND PERCENTAGE UNIT IV Estimated Working Hours : 23 COMPETENCY solution of the simple behavior problems related to fraction, decimal and percentage CHAPTERS 11 Fraction 12 Decimal 13 Percentage LEARNING OUTCOMES After completion of this content area, the learner is expected to be able to: compare the fractions with the same denominators. separate proper fraction, improper fraction and mixed fraction. represent the tenths and hundredths in figure, fraction and decimal. establish the relation between fraction, decimal and percentage.
130 The Leading Mathematics - 4 CHAPTER 11 Fraction How much pizza is divided ? How much pizza is Aftab eating ? How much pizza is remaining on the plate ? How much pizza is John eating ? How much pizza is remaining on the plate ? Who ate more pizza Aftab or John? How much pizza is Rita eating ? How much pizza is remaining on the plate ? WARM-UP Lesson Topics Pages 11.1 Review on Fractions 131 11.2 Addition of Like Fractions 133 11.3 Addition of Like Mixed Fractions 136 11.4 Verbal Problems on Addition of Fractions 138 11.5 Subtraction of Like Fractions 140 11.6 Subtraction of Like Mixed Fractions 142 11.7 Word Problems on Subtraction of Fractions 144 11.8 Addition and Subtraction of Like Fractions 146 11.9 Comparison of Like Fractions 147 Aftab John Rina
ARITHMETIC 131 A mother equally divides a piece of bread into four equal parts and gives one piece to her son. How many quantity of bread can her son eat? How many parts of the bread are left ? Write it in fraction. Son eats ...... ...... bread, one-forth bread. The remaining parts is ...... ...... bread, three-forths bread. How many parts is the pizza divided into in the picture? A girl eats one piece. How much quantity of pizza does she eat? How many parts of the pizza are left ? She eats ...... ...... pizza. The remaining parts is ...... ...... pizza. A teacher folds a rectangular paper once in horizontally and two times vertically and he unfolds it. How many parts does it divide into? If he colours 1 part with red and 3 parts with green, what is the fraction of red and green coloured parts? The fraction of red colour is ...... ...... parts, one-eighth. The fraction of green colour is ...... ...... parts three-eighths, where .......... is numerator and .......... is denominator. 11.1 Review on Fractions 88 Allied Mathematics-IV 4.1 Review on Fractions Read, Think and Learn A mother equally divides a piece of bread into four equal parts and give one piece to her son. How many quantity of bread can her son eat? How many parts of the bread is left ? Write the in fraction. Daughter eats ...... ...... bread, one-forth bread. The remaining parts is ...... ...... bread, three-forth bread. In the picture, how many parts is the pizza divided ? A girl eats one piece. How many quantity of pizza does she eat? How many parts of the bread is left ? She eats ...... ...... bread. The remaining parts is ...... ...... bread. A teacher folds a rectangular paper in once in horizontal and two times in vertical and he unfolds it. How many parts does it divide ? If he colours 1 part with red and 3 parts with green, what is the fraction of red and green coloured parts? The fraction of red colour is ...... ...... bread, one-eighth. The fraction of green colour is ...... ...... bread three-eighth. where .......... is numerator and .......... is denominator.
132 The Leading Mathematics - 4 1. Write the fractions of the shaded parts of the following pictures. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) 2. Write the numerator and denominator of the following fractions. (a) 1 3 (b) 9 11 (c) 2 5 (d) 3 8 (e) 3 7 3. Write the following fractions into words. (a) 1 2 (b) 3 8 (c) 2 5 (d) 3 4 (e) 3 7 4. Write the following words into fractions. (a) one-third (b) half (c) three-fifths (d) five-tenths EXERCISE 11.1 Your mastery depends on practice. Practice like you play.
ARITHMETIC 133 Like Fractions Unlike Fractions 1 4 3 4 1 4 1 3 e.g. 1 4 , 3 4 , 5 4 , 8 4 , 201 4 , etc. e.g. 1 4 , 1 2 , 2 5 , 100 23 , etc. Denominators are the same. Denominators are not the same. Fractions with the same denominators are called like fractions. Fractions with different denominators are called unlike fractions. Add + = 3 8 2 8 5 8 3 8 + 2 8 = 5 8 One-sixth Two-sixth Two-sixth + + = One-sixth + Two-sixth + Two-sixth = Five sixth Five-sixth 1 6 2 6 2 6 5 6 1 6 + 2 6 + 2 6 = 1 + 2 + 2 6 = 5 6 11.2 Addition of Like Fractions Read, Think and Learn
134 The Leading Mathematics - 4 Rules for adding like fractions Step1 : Add the numerators of the fractions in numerator. Step 2 : Write the common denominator in the denominator. Sum of like fractions = sum of numerators Common denominator e.g. 2 9 + 5 9 = 2 + 5 9 = 7 9 33 50 + 17 50 + 9 50 = 33 + 17 + 9 50 = 59 50 = 1 9 50 EXERCISE 11.2 Your mastery depends on practice. Practice like you play. 1. Study the given figures, colour and fill in the blank spaces. (a) (b) (c) 1 4 + + = = 3 4 4 + + = 1 4 + + = = 2 4 4
ARITHMETIC 135 2. Add : (a) 2 4 + 1 4 (b) 3 5 + 1 5 (c) 2 6 + 3 6 (d) 3 10 + 2 10 (e) 7 15 + 6 15 (f) 3 20 + 9 20 (g) 31 30 + 17 30 (h) 33 50 + 41 50 (i) 11 67 + 23 67 (j) 29 70 + 21 70 (k) 43 75 + 12 75 (l) 61 85 + 7 85 3. Find the sum of : (a) 3 5 + 1 5 + 2 5 (b) 2 10 + 1 10 + 6 10 (c) 2 27 + 5 27 + 4 27 (d) 11 22 + 7 22 + 23 22 (e) 31 40 + 7 40 + 3 40 (f) 45 47 + 13 47 + 20 47 (g) 23 50 + 11 50 + 8 50 (h) 14 57 + 7 57 + 2 57 + 3 57 (i) 24 65 + 8 65 + 7 65 + 3 65 (j) 23 84 + 8 84 + 7 84 + 5 84 You and your two friends ate 1 3 , 2 9 and 1 9 pieces of an orange respectively. How many pieces of orange did you eat ? Prepare a report and present it in your classroom. PROJECT WORK
136 The Leading Mathematics - 4 Method of adding like mixed fractions Method 1: Changing into improper fractions Method 2 : Separating whole numbers and fractions 1 1 4 + 2 2 4 1 1 4 + 2 2 4 Step 1 : Convert into improper fractions. Step 1 : Separate whole numbers and fractional parts. = 1 × 4 + 1 4 + 2 × 4 + 2 4 = 4 + 1 4 + 8 + 2 4 = 5 4 + 10 4 = 1 + 1 4 + 2 + 2 4 = (1 + 2) + 1 4 + 2 4 Step 2: Add the numerators keeping denominator common. Step 2 : Add whole numbers and fractions. = 5 + 10 4 = 15 4 = 3 3 4 = 3 + 1 + 2 4 = 3 + 3 4 = 3 3 4 15 4 –12 3 4 3 3 4 11.3 Addition of Like Mixed Fractions + = 1 + = 1 4 2 2 4 3 3 4 Read, Think and Learn 1 1 4 + 2 2 4 = 3 3 4
ARITHMETIC 137 1. Add the following mixed fractions by changing into improper fractions. (a) 3 1 3 + 3 1 3 (b) 1 2 5 + 3 1 5 (c) 5 2 7 + 4 3 7 (d) 3 2 9 + 5 5 5 (e) 10 2 5 + 12 1 5 (f) 27 1 13 + 12 5 15 (g) 2 25 28 + 4 1 28 (h) 34 1 3 + 20 1 3 (i) 5 1 8 + 2 3 8 + 5 2 8 (j) 7 1 7 + 2 2 7 + 5 3 7 (k) 12 3 7 + 2 2 7 + 5 3 7 (l) 24 2 17 + 20 5 17 + 25 3 17 2. Add the following mixed fractions by separating whole numbers and fractions : (a) 4 2 5 + 2 1 5 (b) 7 2 9 + 1 5 9 (c) 4 3 7 + 2 2 7 (d) 3 2 11 + 5 3 11 (e) 12 7 15 + 7 11 15 (f) 24 3 19 + 19 10 19 (g) 37 12 23 + 40 15 23 (h) 52 4 51 + 17 31 31 (i) 2 1 7 + 3 2 7 + 4 3 7 (j) 7 2 13 + 1 5 13 + 9 5 13 (k) 5 2 15 + 4 5 15 + 3 7 15 (l) 20 2 19 +22 3 19 + 25 5 19 3. In the adjoining rulers, 1 cm is divided into 10 equal parts. Write the length of each pencil in mixed fraction. Then find their total length if they are joined one to end. EXERCISE 11.3 Your mastery depends on practice. Practice like you play. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 5 4 3 2 1
138 The Leading Mathematics - 4 1. Hari spends 3 13 of his money for buying a toy 5 13 and for buying a copy. How much does he spend altogether ? 2. Alex travels 2 8 km of the road by a bus and 3 8 km by a bike. How long distance does he travel ? Sagar and his wife went for shopping. Sagar spent 5 8 of his income to buy clothes and shoes and his wife spent 1 8 of her income to buy saree and kurta. How much did they spend ? Solution : Given, Spent amount to buy clothes and shoes = 5 8 of money Spent amount to buy saree and kurta = 1 8 of money \ Total spent amount = 5 8 + 1 8 = 5 + 1 8 = 6 8 = 2 × 3 2 × 4 = 3 4 Hence, they spent 3 4 of their income. 11.4 Verbal Problems on Addition of Fractions EXERCISE 11.4 Your mastery depends on practice. Practice like you play. Read, Think and Learn
ARITHMETIC 139 3. Amar ate 15 part of an apple before lunch and 25 parts after lunch. How much of apple did he eat altogether ? 4. Sita drank 3 3 10 of a packet of Yummy juice and 1 4 10 of a packet of Nice juice. How many packets of juice did she drink in all ? 5. Rojan and his brother mixed two-seventh of a can of yellow paint and three-seventh of a can of red paint to put on their bedroom walls. How much cans of paint did they use on the walls ? 6. There are nine pieces of pizza. Joseph ate four parts, Jesus ate one part and Krishna ate 2 parts. How much pizza did they eat in all ? 7. Kamal planted the rice in 2-tenths of land in the morning, 3-tenths in the afternoon and 1-tenth in the evening. In how much land did he plant the rice altogether ? 8. A sugarcane is divided into 15 equal parts. Ganga eats 2 parts, Jamuna eats 4 parts and Saraswoti eats 1 part. How many parts of the sugarcane do they eat in all ?
140 The Leading Mathematics - 4 1. Study the given figures, color and fill in the blank spaces : (a) ..... 7 ..... 7 ..... ..... – – = = 11.5 Subtraction of Like Fractions Read, Think and Learn – – = 5 = 8 2 8 3 8 Rules for subtracting like fractions Step -1 : Subtract the numerators of the fractions in numerator. Step - 2 : Write the common denominator in the denominator. Difference of fractions = Difference between numerators Common denominator Which colour is more and how much ? e.g. 3 7 – 1 7 = 3 – 1 7 = 2 7 and 13 11 – 5 11 – 2 11 = 13 – 5 – 2 11 = 6 11 EXERCISE 11.5 Your mastery depends on practice. Practice like you play.
ARITHMETIC 141 (b) – – = 15 16 – – = 2. Subtract : (a) 2 3 – 1 3 (b) 5 7 – 2 7 (c) 13 11 – 2 11 (d) 4 9 – 2 9 (e) 37 25 – 13 25 (f) 42 53 – 12 53 (g) 58 87 – 28 87 (h) 99 101 – 33 101 (i) 65 119 – 28 119 (j) 83 35 – 58 35 (k) 86 178 – 54 178 (l) 82 191 – 56 191 3. Find the difference of : (a) 5 7 – 2 7 – 1 7 (b) 9 11 – 5 11 – 2 11 (c) 22 19 – 12 19 – 7 19 (d) 24 28 – 15 28 – 5 28 (e) 32 37 – 22 37 – 9 37 (f) 58 67 – 27 67 – 25 67 (a) 15 17 – 12 17 – 2 17 (b) 47 24 – 15 24 – 21 24 (c) 72 81 – 52 81 – 17 81 (d) 124 48 – 105 48 – 5 48 (e) 302 73 – 202 73 – 19 73 (f) 508 97 – 127 97 – 25 97 16
142 The Leading Mathematics - 4 Method of subtracting like mixed fractions Method 1 : Changing into improper fractions Method 2 : Separating whole numbers and fractions e.g. 2 3 5 – 1 1 5 e.g. 2 3 5 – 1 1 5 Step-1 : Convert into improper fractions. Step-1 : Separate whole numbers and fractional parts. = 5 × 2 + 3 5 – 1 × 5 + 1 5 = 10 + 3 5 – 5 + 1 5 = 13 5 – 6 5 = 2 + 3 5 – 1 + 1 5 = (2 – 1) + 3 5 – 1 5 Step-2 : Subtract the numerator and keeping denominator common. Step 2 : Subtract whole numbers and fractions. = 13 – 6 5 = 7 5 Step 3 : Express into mixed fractions. = 1 2 5 = 1 + 3 – 1 5 = 1 + 2 5 = 1 2 5 7 1 –5 2 5 1 2 5 2 3 5 1 1 5 1 2 5 – – = = 11.6 Subtraction of Like Mixed Fractions Read, Think and Learn
ARITHMETIC 143 1. Subtract the following mixed fractions by changing into improper fractions : (a) 3 2 3 – 2 1 3 (b) 5 2 5 – 2 1 5 (c) 6 4 7 – 5 2 7 (d) 8 5 9 – 2 4 9 (e) 10 2 5 – 5 1 5 (f) 14 5 13 – 11 2 13 (g) 24 5 17 + 19 4 17 (h) 45 24 37 – 42 12 37 (i) 7 4 9 – 3 2 9 – 2 1 9 (j) 8 7 8 – 3 3 8 – 2 1 8 (k) 12 7 12 – 4 5 12 – 1 12 (l) 23 15 17 – 12 2 17 – 4 4 17 (m) 18 9 13 – 5 7 13 – 6 13 (n) 25 13 21 – 11 4 21 – 5 3 21 2. Subtract the following mixed fractions by separating whole numbers and fractions : (a) 4 3 4 – 2 2 4 (b) 6 3 5 – 4 2 5 (c) 12 10 13 – 10 9 13 (d) 15 7 16 – 12 4 16 (e) 36 2 3 – 21 1 3 (f) 37 6 21 – 29 2 21 (g) 13 7 11 – 8 4 11 – 4 1 11 (h) 8 8 13 – 4 4 13 – 3 2 13 (i) 26 8 9 – 18 2 9 – 7 1 9 (j) 52 22 29 – 23 10 29 – 5 7 29 (k) 28 4 7 – 19 5 7 – 9 3 7 (l) 46 23 25 – 55 15 25 – 8 48 25 EXERCISE 11.6 Your mastery depends on practice. Practice like you play. Express the obtained marks by you and your friend in the full marks 100 into fraction. Who secured more marks in fraction by how many? Find it. Prepare a report and present it in your classroom. PROJECT WORK
144 The Leading Mathematics - 4 v Abraham had 5 8 of a pizza. He ate 2 8 of them. How many pieces of pizza did he have now ? Solution : Here, Quantity of pizza with Abraham = 5 8 Quantity of eaten pizza by him = 2 8 \ Quantity of left pizza = 5 8 – 2 8 = 5 – 2 8 = 3 8 Hence, he has 3 8 of pizza now. 11.7 Word Problems on Subtraction of Fractions EXERCISE 11.7 Your mastery depends on practice. Practice like you play. Read, Think and Learn 1. Krishna had 12 13 of money and he spent 5 13 of it. Find the amount of remaining money. 2. Jasmin bought 7 8 metre of cloth and she used 5 8 metre of it. Find the remaining cloth.
ARITHMETIC 145 3. A cylinder had 13 16 kg of gas. 9 10 kg of gas is used. How much gas is left? 4. Shushil had 3 5 of the cake. He gave 2 5 of the cake to his sister. What fraction of the cake is left with him ? 5. Road Division office planned threequarter of a road to be black-topped. If the quarter of it was finished, what fraction of the road is remaining for black topping ? 6. Among 7 13 parts of a land, Usha cultivates 4 15 parts with tomatoes and 2 15 parts with pumpkins. How many parts of land were there left ? 7. Out of the total students in a class, 12 13 passed the examination in which 3 13 passed in the first division and 5 13 passed in the second division. How many students passed in the third division ? 8. Sristi has 55 7 of ribbon. She cuts down 23 4 of it. Find the remaining quantity of the ribbon.
146 The Leading Mathematics - 4 – + = + = = 5 6 4 6 1 6 1 6 1 6 2 6 1 6 – + = + = = Simplify : 5 7 – 3 7 + 2 7 Solution : Here, 5 7 – 3 7 + 2 7 = 5 – 3 7 + 2 7 = 2 + 2 7 = 4 7 Alternatively, Here, 5 7 – 3 7 + 2 7 = 5 – 3 + 2 7 = 2 + 2 7 = 4 7 1. Simplify : (a) 5 7 – 4 7 + 1 7 (b) 7 9 – 4 9 + 2 9 (c) 3 5 – 2 5 + 1 5 (d) 8 13 – 5 13 – 1 13 (e) 12 15 – 7 15 – 1 15 (f) 14 15 – 7 15 – 1 15 (g) 24 17 + 23 17 – 45 17 (h) 57 67 – 27 67 – 35 67 2. Simplify : (a) 2 1 5 + 12 5 – 2 2 5 (b) 5 5 7 + 2 2 7 – 33 7 (c) 15 13 + 1 3 13 – 3 7 13 (d) 106 7 – 85 7 + 32 7 (e) 12 4 21 – 6 3 21 – 5 1 21 (f) 2715 17 – 18 9 17 – 9 8 17 11.8 Addition and Subtraction of Like Fractions EXERCISE 11.8 Your mastery depends on practice. Practice like you play. Read, Think and Learn
ARITHMETIC 147 Which is greater 1 3 or 2 3 ? = 1 3 One part is shaded among 3 parts. This is less than 2 3. = 2 3 Two parts are shaded among 3 parts. This is greater than 1 3 . \ 1 3 < 2 3 \ 2 3 > 1 3 Rules to remember! In like fractions, the fraction with the greater numerator has a greater value. e.g. compare 4 9 or 2 9. 4 and 2 are numerator, Since 4 > 2, so 4 9 > 2 9. 11.9 Comparison of Like Fractions Read, Think and Learn 3. (a) Kamal has 7 8 of money and he spends 3 8 of it. If his father gives him 1 8 of more money, how much money does he have now ? (b) A container has 12 25 litre of oil and 7 25 litre of oil is added in it. If 8 25 litre of oil is used, how much oil is left in the container ? (c) There is 25 7 10 kg of rice in the kitchen. A cook-man use 16 3 10 kg of rice for dinner and the house owner adds 9 5 10 kg of rice. Find the quantity of rice in the kitchen.
148 The Leading Mathematics - 4 Alternatively : 1 3 or 2 3 By cross multiplication, 1 3 or 2 3 1 × 3 or 2 × 3 = 3 or 6 Clearly, 3 < 6. So, 1 3 < 2 3 or 2 3 > 1 3 (1) If a b or c d (2) Find cross-products a×d and c × b. (3) Compare a × d and c × b. (4) If a × d is greater than c × b, a b > c d. (4) If c × b is greater than a × d, c d > a b. CLASSWORK EXAMPLES Example 1 Arrange the given fractions in the order of smaller to the greater: 3 13 , 5 13 and 2 13 Solution: Here, the given fractions are 3 13 , 5 13 and 2 13 . 3, 5 and 2 are the numerators of the given like fractions. Since 2 < 3 < 5 so, 2 13 , 3 13 , 5 13 . EXERCISE 11.9 Your mastery depends on practice. Practice like you play. 1. Write the correct sign < or > or = in empty boxes : (a) 2 3 3 5 (b) 5 7 6 7 (c) 2 11 2 11 (d) 7 17 9 17 (e) 9 19 7 19 (f) 11 15 17 15 (g) 24 23 28 23 (h) 25 27 25 27 (i) 43 49 47 49
ARITHMETIC 149 2. Compare the following fractions and write greater and smaller fractions : (a) 2 5 or 3 5 (b) 7 9 or 5 9 (c) 5 17 or 2 11 (d) 18 23 or 81 23 or 19 23 (e) 4 95 or 8 95 or 9 95 (f) 28 47 or 82 47 or 18 47 3. Arrange the following fractions in the order of smaller to the greater. (a) 2 7 , 8 7 , 5 7 (b) 14 17 , 41 17 , 4 17 (c) 14 23 , 18 23 , 11 23 (d) 32 37 , 8 37 , 25 37 (e) 25 47 , 301 47 , 84 47 (f) 81 57 , 18 57 , 118 57 4. Arrange the following fractions in the order of larger to the smaller. (a) 8 13 , 6 13 , 12 13 (b) 24 25 , 23 25 , 28 25 (c) 42 57 , 34 57 , 35 57 (d) 86 75 , 68 75 , 112 75 (e) 47 85 , 53 85 , 49 85 (f) 24 91 , 34 91 , 15 91 5. (a) Amir ate 2 5 of a bread and Samir ate 4 5 of the same bread. Who ate more ? (b) Radha has 7 9 parts of a rope and Gita has 5 9 parts of the same rope. Who has longer rope? (c) 13 21 parts of a tower is in red and 11 21 is white in colour. Which part is taller ? (d) Ram travels 17 25 parts of a road by bus and 13 25 parts of the road by bike. By which vehicle does he travel longer? A bowl has 30 marbles. Your two friends take out some marbles from it once by own hand and the remaining marbles for you. Who take more marbles and who take less marbles and how many ? Compare the taking marbles in fractions form. Prepare a report and present it in your classroom. PROJECT WORK
150 The Leading Mathematics - 4 CHAPTER 12 Decimal What time does Athletics Bolt cover 100 m running ? How much rupees and paisa do you have ? What is the cost of petrol per litre? What amount is shown in the price tags? What is the length and breadth of the book? What is your weight? WARM-UP Lesson Topics Pages 12.1 Tenths Decimal Numbers 151 12.2 Hundredths Decimal Numbers 154 12.3 Place Value of Decimal Number 156 12.4 Changing Fraction into Decimal 157 12.5 Changing Decimal into Fraction 159 Bolt, 100 m in 9.58 sec Rs. 339.50 0 2 0 0.