Chapter 1: Number and Numeration

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3 Chapter : Number and Numeration Exercise. Refer answers at the end of book. Exercise.2 3. Greatest 6 digit number = Greatest 5 digit number = Total 6 digit numbers = Greatest 6 digit number Greatest 5 digit number = = Refer answers at the end of book Refer answers at the end of book. Exercise.3-.4 Refer answers at the end of book. Exercise Refer answers at the end of book. 4. To write the greatest 7 digit number we select the greater 7 digits from given digits they are 3, 2, 7, 8, 4, 6 and 5. Now place them in such a way that the greatest digit occupy the greatest place value i.e., is the greatest seven digit number. Similarly to form smallest seven digit number, we place them in such a way that the smallest come at the highest place value i.e., is the smallest seven digit number. Similarly for eight digit the greatest numeral is and the smallest numeral is (b) 0, 2, 4,, 3, 6, 8, 9. Greatest seven digits: Seven greater digits are 9, 8, 6, 4, 3, 2 and Hence greatest seven digit number = and Smallest seven digit number is = Greatest eight digit number using 0, 2, 4,, 3, 6, 8, 9 are Smallest eight digit number = Remember that 0 can not be placed at crore s place as it will become an seven digit number Refer answers at the end of book. 7. Smallest 8 digit number = Greatest number using digit 3, 8, 6, 5,, 2, 0 is Difference = Smallest number using digits 3, 8, 6, 5,, 2, 0 is TH Easy Maths 5 Price : `

4 Difference = Greatest 8 digit number = Greatest 7 digit number = Greatest 8 digit number = Smallest 7 digit number = Exercise Refer answers at the end of book. Chapter 2: Roman Numerals Exercise Refer answers at the end of book. 6. (a) XXXVIII = 38 (b) LXXXVI = 86 XXV = 63 XI = Sum = 63 Sum = = LXIII 97 = XCVII (c) XC = 90 (d) XXIII = 23 CX = 0 XXVII = 27 Sum = 200 Sum = = CC 50 = L 7. Refer answers at the end of book. Chapter 3: Addition and Subtraction Exercise (a) 35,27, , One crore seven lakh thirty one thousand eight hundred ten. (b) Twenty two lakh eighty seven thousand seven hundred ninety nine. 4 TH Easy Maths 5

5 (c) Fifty two lakh sixty six thousand two hundred sixteen. Exercise Refer answers at the end of book. 3. (a) Fourteen crore ninety three lakh fourty five thousand two hundred ninety one. (c) Two crore ten lakh seventy seven thousand four hundred ten. (d) Seventy one lakh ninety eight thousand one hundred seventy eight. (b) Eight crore two lakh fourteen thousand two hundred fifty two. (d) Fourteen crore eighty one lakh sixty seven thousand one hundred fifty five. Exercise 3.4. (a) Production of toys in = Production of toys in = Total (b) Production of toys in = Production of toys in = Total Total production of toys in = Answer of (a) + Answers of (b) = Cost of house = ` Cost of office = + ` Total ` Total money spent by Mohan Lal is ` TH Easy Maths 5 5

6 3. Books sold in st week = Books sold in 2nd week = Total books sold Total books sold at the end of two weeks is Number of copies sold in January = Number of copies sold in February = Number of copies sold in March = Total copies sold Total copies sold in three months is Money allocated in 200 = ` Money allocated in 20 = ` Money allocated in 202 = + ` Total money allocated ` Total money allocated is ` Exercise 3.5. (a) Actual sum Estimated sum Difference between the actual sum and estimated sum is = 2. (b) Actual sum Estimated sum Difference between the actual sum and estimated sum is = 7. (c) Actual sum Estimated sum Difference between the actual sum and estimated sum is = 4. 6 TH Easy Maths 5

7 (d) Actual sum Estimated sum Difference between the actual sum and estimated sum is = (a) Actual sum Estimated sum Difference between the actual sum and estimated sum is = 40. (b) Actual sum Estimated sum Difference between the actual sum and estimated sum is = 47. (c) Actual sum Estimated sum Difference between the actual sum and estimated sum is = 5. (d) Actual sum Estimated sum Difference between the actual sum and estimated sum is = (a) Actual sum Estimated sum Difference between the actual sum and estimated sum is = 340. TH Easy Maths 5 7

8 (b) Actual sum Estimated sum Difference between the actual sum and estimated sum is = 65. (c) Actual sum Estimated sum Difference between the actual sum and estimated sum is = 389. (d) Actual sum Estimated sum Difference between the actual sum and estimated sum is = (a) Actual cost Estimated cost `378 `380 `549 `550 `352 `350 + `772 + `770 `305 `3050 Difference between actual cost and estimated cost is `( ) = `. Estimation is accurate. (b) Actual cost sum `378 `549 `352 + `772 `305 Estimated cost sum `400 `500 `400 + `800 `300 Difference between estimated cost sum and actual cost sum is `( ) = `49. Estimation is accurate. 8 TH Easy Maths 5

9 Exercise 3.6. Refer to the answer given 2. Refer to the answer given at the end of the book. at the end of the book. 3. (a) One of the number Difference Other number Exercise 3.7 Other number is (b) Sum One number should be added to to get (c) Greatest number of 8 digits Number should be added to to get greatest 8 digit number. (d) Money earned ` ` ` Money spent Money saved He saved ` (e) Greatest number Smallest number ` ` `58975 Difference between greatest and smallest number firmed using the digits 8, 5, 7, 0, 6, 4, 9 is (f) Production after 2 years ` Production initially ` ` was increase in the production. Refer answers at the end of book. TH Easy Maths 5 9

10 Exercise 3.8. First find the sum of and Now find the sum of and Now subtract from First find the sum of and Now find the sum of and First find the sum of and Now subtract from First find the sum of and Now subtract from Now subtract from Ans: Sum of and is greater than the sum of and by First find the sum of the children less than 0 years old and their find the number of people in the age group of 0 70 years Now subtract from There are whose age is more than 70 years. 0 TH Easy Maths 5

11 6. First add the number of students who voted for winner and who voted for loser Now subtract this sum from the total number of student voters students did not 7. First add the amount allocated in the first year and second year. st year 2nd year Total ` ` ` Now subtract this from the total annual allocation. ` ` ` The remaining amount due to be allocated in the third year is ` vote in the election. 8. To find the number of magazine sold in July, subtract from were sold in July. To find the number of magazine sold in August add to In the month of August Refer answers at the end of book. Chapter 4: Multiplication Exercise 4.. (a) (c) (b) (d) TH Easy Maths 5

12 (e) (g) (a) Cost of toy car = `462 Cost of 7 toy cars = `462 7 = ` Cost of 7 toy cars = ` (b) Cost of book = `46 Cost of 624 books = ` Thus cost of 624 books is ` (f) (h) (c) Cost of bicycle = `562 Cost of 322 bicycles = ` Thus cost of 322 bicycles is ` (d) To find the bill paid by Mr. Mohan add answers obtained in (i), (ii) and (iii). (i) Cost of dress = `536 Cost of 8 dresses = `536 8 = `4288 (ii) Cost of book = `326 Cost of 63 books = ` `20538 Total bill = He paid `44082 in total. (iii) Cost of pizza = `232 Cost of 83 pizzas = ` ` TH Easy Maths 5

13 (e) Cost of one chair = `486 Cost of 764 chairs = Cost of 764 such chairs is ` Exercise 4.2 Refer answers at the end of book. Exercise 4.3. (a) (d) (a) (d) (b) (e) (b) (e) (c) (f) (c) a.-b. Refer answers at the end of book. Exercise 4.4. Product of 3254 and 74 = = Greatest number formed by the Now digits 4, 7, 5, 3, 6, 8 is TH Easy Maths 5 3

14 2. Smallest three digit number using 5, 0, 7 is 507. Greatest five digit number Product of = Number of toys in one day = Number of toys in 24 days = Number of soap cakes in a carton = 450 Number of cartons = 585 To find the number of soap cakes in 585 cartons, multiply = There are soap cakes in 450 cartons toys are produced in 24 days. 5. Cost of shirt = `56 Cost of 3624 shirts = ` Cost of trouser = `867 Cost of 4567 trouser = ` Total money he made = ` ` = ` Cost of 75 bags of urea = ` = `62300 Cost of 24 bags of phosphorus = `45 24 = `8880 Total amount spent = `( ) = `50 7. Weight of bag = 50 kg Number of bags a truck can carry = 883 Weight a truck can carry = kg = kg Weight carried by 65 trucks = kg = kg 4 TH Easy Maths 5

15 8. Number of bags = 24 Weight of bag = 95 kg Total weight of 24 bags = kg = kg Cost of kg rice = `38 Cost of kg rice = = ` One day earning = `957 One month or 26 days earning = ` = `24882 One year (or 2 months) earning = ` = ` Exercise 4.6. Savings of 8 months = `48000 Savings of months = ` = `6000 Mohan saves `6000 in a month. 2. Number of pens fitted in a box = 250 Number of pens fitted in 40 boxes = = 0,000 0,000 pens can be fitted in 40 such boxes. 3. Money spent in 2 months (or year) = `0800 Money spent in month = `0800 = `900 2 Money spent in 6 months = `900 6 = `5400 Rohit spend `5400 in 6 months for maintaining the garden. 4. Cost of 6 books = `640 Cost of book = `640 6 = `40 Cost of 9 books = `40 9 = `360 Cost of 9 books is ` Distance covered in 8 minutes = 480 m. Distance covered in minute = (480 8) m = 60 m. Distance covered in 20 minutes = = 200 m. Athlete will cover 200 m in 20 minutes. 6. dozen = 2 Cost of 2 bananas = `48 Cost of banana = `48 2 = `4 Cost of banana is `4. 7. dozen = 2 Cost of 2 oranges = `24 Cost of orange = `24 2 = `2 Cost of 5 oranges = `2 5 = `30 8. Toys produced in 30 days = Toys produced in day = = 2748 Toys produced in 5 days = = toys are produced in 5 days. TH Easy Maths 5 5

16 Exercise 5.. (a) Chapter 5: Division (b) Q = 86 R = 0 Q = 9 R = 40 (c) (d) Q = 4 R = 96 Q = 224 R = 0 (e) (f) Q = 75 R = 0 Q = 96 R = 0 (g) (f) Q = 4 R = 224 Q = 6 R = (a) 2 objects = dozen 392 objects = = 326 There are 326 dozen if number of objects is 392. (b) Number of trees = 3256 Number of gardens = 37 Number of trees in each garden = = 88 Number of trees in each garden 88. (c) Number to be multiplied = = should be multiplied by 72 to give TH Easy Maths 5

17 (d) Cost of book = `26 Number of books that can be bought for `8424 = = books can be bought for `8424. (e) Cost of 54 kg rice = `5236 Cost of kg rice = ` = `34. Cost of kg rice is `34. Exercise 5.2. Refer answers at the end of book. 2. Refer answers at the end of book. Exercise 5.3. (a) Q = 97 R = 34 (b) Q = 632 R = 34 (c) Q = 5622 R = 30 Verification = Quotient Divisor + Remainder = = = Dividend Verification = Quotient Divisor + Remainder = = = = Dividend Verification = Divisor Quotient + Remainder = = = TH Easy Maths 5 7

18 (d) Q = 674 R = 44 Verification = Divisor Quotient + Remainder = = = (e) Q = 2532 R = 52 Verification = Quotient Divisor + Remainder = = = Dividend (f) Q = 8870 R = 29 Verification = Quotient Divisor + Remainder = = = = Dividend 8 TH Easy Maths 5

19 (g) Q = R = 5 (h) Verification = Quotient Divisor + Remainder = = = = Dividend Verification = Divisor Quotient + Remainder = = = = Dividend Q = 2804 R = (a) Dividend = Divisor Quotient + Remainder = = = 500 Dividend = 500 (b) Quotient = (Dividend Remainder) Divisor = ( ) 24 = = Quotient = (c) Dividend = Quotient Divisor + Remainder = = = Dividend = TH Easy Maths 5 9

20 (d) Dividend = Divisor = Q = R = 2 (f) Dividend = Divisor = Q = R = 4 Exercise 5.4. (a) Q = 233 R = 289 (e) Dividend = Divisor = Q = 95 R = 53 Checking Dividend = Quotient Divisor + Remainder = = = TH Easy Maths 5

21 (b) Q = 53 R = 57 (c) Q = 2072 R = 87 Checking Dividend = Quotient Divisor + Remainder = = = Checking Dividend = Quotient Divisor + Remainder = = = (d) Q = 82 R = 258 (e) Q = 9955 R = 2 Checking Dividend = Divisor Quotient + Remainder = = = TH Easy Maths 5 2

22 (f) Q = 8092 R = 240 Checking Dividend = Divisor Quotient + Remainder = = = (g) Q = R = 5 (h) Q = 5686 R = (a) Dividend = Divisor Quotient + Remainder = = = Dividend = Verification Dividend = Divisor Quotient + Remainder = = = Dividend = Divisor Quotient + Remainder = = = TH Easy Maths 5

23 (b) Dividend = Quotient Divisor + Remainder Q = 3252 R = 37 (c) Dividend = Divisor Quotient + Remainder = (Dividend Remainder) Quotient = Divisor = ( ) 5008 = Divisor = = Divisor 963 = Divisor (d) Dividend Divisor Quotient = Remainder = = Remainder = = Remainder = 84 = Remainder (e) Dividend = Quotient Divisor + Remainder = = = = Dividend Yes, the given sum is correct. Exercise 5.5. Divisor = 435 Quotient = 5643 Remainder = 46 Dividend = Divisor Quotient + Remainder = = = The number was TH Easy Maths 5 23

24 2. Apples in one carton = 563 Cartons required to pack apples = cartons are required to pack apples and 75 apples will be left. 3. Donation by 782 person = ` Donation by person = ` = `4356 Donation by 987 person = ` = ` person will donate ` in a month for CRY foundation. 4. To find the number that must be subtracted from so that the number is exactly divisible by 328 we need to find the remainder when is divided by must be subtracted from to make it exactly divisible by Greatest 6 digit number = Greatest 3 digit number using 7, 8 and 9 = 987 Now divide by 987 and subtract the remainder so obtained from to get the largest six digit number divisible by = is the largest six digit number exactly divisible by TH Easy Maths 5

25 = Sum of the given number is not exactly divisible by 257 and remainder is Number of students = 856 Total amount collected = paise = `3424 (Divide by 00) Amount donated by each student = ` = `4 Each student donated `4. 8. Selling price or cost of 275 bicycles = ` Selling cost of bicycle = ` = `745 Selling cost of 35 bicycles = ` = ` Total students = = 40 Total mess fees paid = `57080 Mess fees paid by one student = ` = `222 Each student paid ` Cost of 364 microchips = ` Cost of microchip = ` = `3456 Cost of 36 defective microchips = ` = `47006 Cost of remaining microchips = ` `47006 = ` TH Easy Maths 5 25

26 . Greatest 7 digit number = Greatest number using 3, 7, 4 = Divisor = 743 Quotient = 3458 Dividend = Remainder = 705 Dividend = Divisor Quotient + Remainder = Total consumption = Total days = August + September + October + November = = 22 Consumption per day = = kg kg vegetable is consumed per day. 3. To let students try by themselves. Exercise 5.6. (a) 396 is rounded to 400 (b) 84 is rounded to is rounded to is rounded to = = 3 (c) 79 is rounded to 720 (d) 49 is rounded to is rounded to is rounded to = = 3 (e) 2877 is rounded to 2880 (f) 2974 is rounded to is rounded to 80 3 is rounded to = = 99 (g) 4863 is rounded to 4860 (d) 5849 is rounded to is rounded to is rounded to = = 7 26 TH Easy Maths 5

27 Chapter 6: Multiples and Factors Exercise Refer answers at the end of book. 5. (a) (b) Since remainder is zero Remainder is 6 so 3 is not a hence 9 is a factor of 36. factor of 26. (c) is a factor of (a) 24 Factors of 24 are, 2, 3, 4, 6, 8, 2 and 24 (b) 36 Factors of 36 are, 2, 3, 4, 6, 9, 2, 8 and = (c) 08 Factors of 08 are, 2, 3, 4, 6, 9, 2, 8, 27, 36, 54 and = (a) Factors of 4 are, 2, 7, 4 Factors of 35 are, 5, 7, 35 Common factors of 4 and 35 are and 7. (b) Factors of 27 are, 3, 9, 27 Factors of 36 are, 2, 3, 4, 6, 9, 2, 8, 36 Common factors of 27 and 36 are, 3 and = (d) 225 Factors of 225 are, 5, 5, 45, 225, 3, 75, 9, = TH Easy Maths 5 27

28 (c) Factors of 48 are, 2, 3, 4, 6, 8, 6, 2, 6, 24 and 48 Factors of 32 are, 2, 4, 8, 6, 32 Common factors of 48 and 32 are, 2, 4, 8, 6. (d) Factors of 36 are, 2, 3, 4, 6, 9, 2, 8, and 36 Factors of 45 are, 3, 5, 9, 5 and 45 Common factors of 36 and 45 are, 3 and Refer answers at the end of book. Exercise 6.2. (a) 5 and 33 Factors of 5 are, 3, 5, 5 Factors of 33 are, 3,, 33 Common factors of 5 and 33 are and 3 5 and 33 are not coprime as they have 3 as common factor other than. (b) 24 and 29 Factors of 24 are, 2, 3, 4, 6, 8, 2, 24 Factors of 29 are, 29 Common factors of 24 and 29 is only. Hence they are coprime. (c) 34 and 57 Common factors of 34 are, 2, 7, 34 Common factors of 57 are, 3, 9, 57 Common factors of 34 and 57 is. Hence 34 and 57 are coprime. (d) 8 and 67 Factors of 8 are, 2, 3, 6, 9, 8 Factors of 67 are, 67 Common factors of 8 and 67 is. Hence 8 and 67 are coprime. (e) 4 and 52 Factors of 4 are, 2, 7, 4 Factors of 52 are, 2, 4, 3, 26, 52 Common factors of 4 and 52 is and 2. Hence they are not coprime. 2. (a) 36 is a composite number as it has more than 2 factors i.e.,, 2, 3, 4, 6, 9, 2, 8, 36 are its factors. (b) 37 is prime as it has only two factors and they are and 37. (c) 3 is a prime as its has only two factors and they are and 3. (d) 59 is a prime as it has only two factors and they are and 59. (e) 29 is a prime number as it has only two factors and they are and Refer answers at the end of book. Exercise 6.3. Refer answers at the end of book. 28 TH Easy Maths 5

29 2. (a) 4623 (b) 9000 (c) 438 (d) 7596 (e) 8875 unit digits are 3 and 5 so it is not divisible by 2. (f) 2004 has units digits as 0, 8, 6 and 4 so they all are divisible by (a) 323 = = 9 (b) 4826 = = 20 (c) = = 27 (d) = = 25 (e) 7632 = = 9 Sum of digits of (a) and (d) is divisible by 3 hence 3, 23 and is divisible by (a) 486 (b) 52 (c) 4920 (d) (e) 9636 (f) 7773 The number formed by last two digits of b, c and e i.e., 2, 20, and 36 are divisible by 4. Hence b, c and e are divisible by (a) 592 (b) (c) (d) 7732 Since 92, 224 are divisible by 8, So the number 592 and are divisible by (a) = = 38 (b) 6987 = = 30 (c) 8424 = = 8 (d) 9405 = = 8 Sum of digits of 8424 and 9405 is divisible by 9, So 8424 and 9405 are divisible by (a) = 7 + A number greater than 7 divisible by 3 is 8 so 8 7 = should be there in the box as the smallest digit. The number so formed is divisible by 3. (b) = is divisible by 3 so the smallest digit that can be filled in the blank is 0. (c) 59 6 = Smallest = 20 + but the smallest number greater than 20 but divisible by 3 is 2 so 2 20 = should be the digit at the blank space. TH Easy Maths 5 29

30 (d) = 3 + The smallest number greater than 3 divisible by 3 is 5 so 5 3 = should be the digit at the blank space. 8. (a) as 08 or 8 is divisible by 4. (b) as 2 is divisible by 4. (c) as 52 is divisible by 4. (d) as 72 is divisible by (a) as 656 is divisible by 8. (b) as 264 is divisible by 8. (c) as 704 is divisible by 8. (d) 83 2 as 32 is divisible by (a) 572 = = 4 + A number greater than 4, divisible by 9 is 8. Hence 8 4 = 4 is the digit to be fitted in the blank space. (b) = = 24 + A number greater than 24 but divisible by 9 is 27. So = 3 is the digit to be fitted in the blank space. (c) 97 5 = = 22 + A number greater than 22, but divisible by 9 is 27 hence = 5 is the digit to be fitted in the blank space. (d) 4 2 = = 7 + A number greater than 7, but divisible by 9 is 9. Hence 9 7 = 2 so 2 is to be fitted in the blank space. Exercise 6.4. (a) 42, = = HCF (42, 84) = = 42. (b) 36, = = HCF (36, 63) = 3 3 = TH Easy Maths 5

31 (c) 2, 8, = = = HCF (2, 8, 27) = 3 (e) 25, 65, = = = 5 9 HCF 25, 65, 95 = 5 (g) 25, = = HCF (25, 90) = 5 (i) 64, 80, = = = HCF (64, 80, 20) = = 8 (d) 22, 66, = 2 66 = = HCF (22, 66, 2) = (f) 42, = = HCF (42, 63) = 3 7 = 2 (h) 8, 24, = = = HCF (8, 24, 32) = 2 (j) 80, 36, = = = HCF (08, 35, 52) = 2 2 = 4 TH Easy Maths 5 3

32 2. (a) 2, H.C.F. (2, 28) = 4. (b) H.C.F. (60, 420, 924) = 2. (c) 42, H.C.F. (42, 330) = 6. (d) 78, H.C.F. (78, 20) = 6. (e) 54, 770, H.C.F. (54, 770, 90) = (a) 24, H.C.F. (24, 35) =. 32 TH Easy Maths 5

33 (b) 36, H.C.F. (36, 252) = 36. (c) 8, 36, H.C.F. (8, 36, 45) = 9. (d) 20, 420, H.C.F. (20, 420, 540) = 30. (e) 90, 40, H.C.F. (90, 40, 20) = 0. (f) 45, 25, H.C.F. (45, 25, 65) = 5. TH Easy Maths 5 33

34 Exercise 6.5. (a) 28, = = 5 7 LCM = = 40 LCM (28, 35) = 40 (c) 22, = 2 66 = 2 3 LCM (22, 66) = 2 3 = 66 (e) 25, 80, = = = LCM (25, 8, 20) = = 3500 (b) 48, = = HCM = = 44 (d) 36, 48, = = = LCM (36, 48, 96) = = 288 (f) 98, 26, = = = LCM (98, 26, 360) = = TH Easy Maths 5

35 2. (a) 20, 35, , 35, , 7, 9 2 2, 7, 9 7, 7, 9 3,, 9 3,, 3,, LCM (20, 35, 45) = = 260 (c) 36, 64, 72, 96, , 64, 72, 96, , 32, 36, 48, , 6, 8, 24, , 8, 9, 2, 5 2 9, 4, 9, 6, 5 3 9, 2, 9, 3, 5 2 3, 2, 3,, 5 3 3,, 3,, 5 5,,,, 5,,,, LCM (36, 64, 72, 96, 20) = = 2880 (e) 27, 45, 60, 72, , 45, 60, 72, , 5, 20, 24, , 5, 20, 8, 32 5, 5, 20, 8, 32 2,, 4, 8, 32 2,, 2, 4, 6 2,,, 2, 8 2,,,, 4 2,,,, 2,,,, LCM (27, 45, 60, 72, 96) = = 4320 (b) 0, 25, , 25, , 5, 3 5, 5, 3 3,, 3,, LCM (0, 25, 65) = = 650 (d) 42, 60, 84, , 60, 84, , 30, 42, , 5, 2, , 5, 7, 9 3 7, 5, 7, 3 7 7, 5, 7, 5, 5,,,,, LCM (42, 60, 84, 08) = = (a) 30, , , 5 2 2, 5 5, 5, LCM (30, 75) = = 50 TH Easy Maths 5 35

36 (b) 45, , , , 5 5,,, LCM (45, 66) = = 990 (d) 44, , , , , 5 3 9, 5 3 3, 5 5, 5, LCM (44, 20) = = 720 (f) 36, 63, , 63, 8 3 2, 2, , 7, 9 3 4, 7, 3 7 4, 7, 2 4,, 2 2,,,, LCM (36, 63, 8) = = 2268 (h) 62, 270, , 270, , 35, , 45, 8 3 9, 5, 6 3 3, 5, 2 5, 5, 2 2,, 2,, (c) 35, , 75, 3 27, , , 35 5, 35 7, 7, LCM (35, 75) = = 4725 (e) 20, 25, , 25, , 5, 2 2 2, 5, 6 5, 5, 3 3,, 3,, LCM (20, 25, 60) = = 300 (g) 2, 42, , 42, , 4, 35 2, 2, 5 5,, 5,, LCM (2, 42, 05) = = 20 LCM (62, 270, 08) = = TH Easy Maths 5

37 Exercise 6.6. LCM of 8, 6, and 24 is 48 Now divide greatest number of 6 digit by The greatest six digit number divisible by 8, 6 and 24 is = LCM of 48, 60 and 64 is 960. Greatest 4 digit number = = 9600 is the largest 4 digit number divisible by LCM of 8, 24, and 36 = 72 Greatest 5 digit number = Now divide by ( ) + 7 = is the greatest 5 digit number which leaves a remainder 7 when divided by 8, 24 and LCM of 2, 6, 24 and 36 = 44 Greatest 4 digit number = 9999 Now divide 9999 by ( ) + 5 = is the greatest 4 digit number which when divided by 2, 6, 24 and 36 leaves a remainder 5. TH Easy Maths 5 37

38 = = = 630 Now find the HCF of 345, 630 and is the greatest number that divides 036, 347 and 633 leaving remainders, 2, and 3 respectively = = = 536 Now find the HCF of 368, 480 and HCF of 368, 480, 536 = 8 8 is the greatest number that divides 373, 484 and 542 leaving remainders 5, 4, and 6 respectively. 7. LCM of 8, 5 and 24 = , 5, , 5, 2 3 2, 5, 6 2 2, 5, 2 5, 5,,, = = 20 Smallest 5-digit number = 0000 Now, divide 0000 by TH Easy Maths 5

39 m 25 cm = 425 cm 5 m 50 cm = 550 cm 6 m = 600 cm 425, 550 and and 80 is Hence 36 is the largest number of students among whom 08 chocolates and 80 cookies can be distributed equally. 0. LCM of 20, 80 and 240 is (20 40) = 0080 is the smallest 5-digit number which is exactly divisible by 8, 5 and Hence 25 cm is the length of the longest tape that can be used to measure exactly the dimensions of the given hall. Now to find the number of chocolates and cookies each students will get, divide the number of cookies and chocolates by 36. i.e., Chocolates Cookies Hence each students will get 3 chocolates and 5 cookies litres is the capacity of the greatest container that can be used to measure 20 litres, 80 litres and 240 litres of oil exactly. TH Easy Maths 5 39

40 . ` = 00 paise `.25 = 25 paise and `50 = 5000 paise. Now find the LCM of 25 and , , , 200 5, 40 8, 8, Exercise 6.7. We know that HCF LCM = st number 2nd number = 35 2nd number 2nd number = = HCF LCM = st number 2nd number 3 20 = 5 2nd number 2nd number = 3 20 = HCF LCM = st number 2nd number 6 80 = 36 2nd number 2nd number = 6 80 = HCF LCM = st number 2nd number = 89 2nd number nd number = = LCM HCF = HCF = HCF = = HCF LCM = Product of the numbers LCM 6 = 432 LCM = = HCF LCM = Product of the numbers LCM 7 = 735 LCM = = 05 LCM of 25,5000 = = 5,000 Amount in paise = 5,000 Amount in rupees = 5, = `50 The number of days = `50.25 = 40 days 40 TH Easy Maths 5

41 Chapter 7: Fractions Exercise 7.. Equivalent fractions are obtained by multiplying the numerator and denominator of the given fraction by the same number. (a) = 4 6 ; = 5 20 ; = 6 24 (b) = 4 20 ; = 5 25 ; = 6 30 (c) = 4 32 ; = 5 40 ; = 6 30 (d) = 4 36 ; = 5 45 ; = (a) In like fractions, the fraction with greater numerator in greater 4 > (b) Since = = = 3 (c) Convert unlike fractions into like fractions by finding LCM of 9 and , 2 3 3, 4 4, 4, Now 5 9 = = > 5 36 LCM = = 36 and or 5 2 = = > 5 2 In a given pair of fractions whose numerators are same the fraction with greater denominator is smaller. (d) Find the LCM of 35 and , 5 LCM = = 05 7, 3 Now 2 35 = = 36 0 and 05 5 = = < (e) 3 45 = 3 45 or 2 35 < 0 5 TH Easy Maths 5 4

42 (f) 6 = and = or 3 5 = = (a) Divide 8 by = = (b) Divide 37 by 6, = 6 6 (c) (c) (e) (f) (a) Find the LCM of 5, 20, 0 LCM = = , 20, 0 2, 4, 2, 2, Now 3 5 = = 2 20 ; 5 20 = 5 20 ; 2 0 = = 4 20 Arranging in ascending order: 4 20 < 5 20 < 2 20 or 2 0 < 5 20 < TH Easy Maths 5

43 (b) LCM of 5, 0, 20 is 20. Now 2 5 = = 8 20 ; = 4 20 ; 6 20 = 6 20 = < 6 20 < 8 20 or 2 0 < 6 20 < 2 5 (c) LCM of 2, 4, 8 = 8 Now 2 = = 4 8 ; = 2 8 ; 8 = 8 = 8 8 < 2 8 < 4 8 or 8 < 4 < 2 5. (a) As per the reason given in Answer 2(a). 3 4 > 2 4 > 4 (b) As per the reason given in Answer 2(c). 4 > 6 > 9 (c) LCM of 4, 8, 6 = = = 8 6 ; = 0 6 ; 6 = 6 = 6 Hence 6 > 0 6 > 8 6 or 6 > 5 8 > (a) Number of players allowed to play at one time = Total number of players = 6 Hence the fraction of the team that played the match = 6 (b) Dividing 32 students in 4 equal groups i.e = 8 students 3 groups of 8 students each includes = 3 8 = 24 students Hence, 24 students are less than 0 years old. (c) Improper fraction (d) 3 3 (3 4) + 3 = = = (4 2) + 7 (e) Tina jumped = 4 ft or = ft Meena jumped = 4 (3 6) + ft or = 8 + = ft Changing both fractions into like fractions, we get 9 6 = 9 2 = 38 and Since 55 2 > 38 2 or > TH Easy Maths 5 43

44 Since the whole number 4 is greater than > 3 6 Hence Tina jumped further. Exercise 7.2. To reduce the fraction in lowest fraction we divide the numerator and denominator by common factor. The process is continued till the common factor of numerator and denominator is. (a) 0 5 = = 2 3 (c) = = = 5 8 (e) = = = 2 3 (g) = = 2 5 (i) = = (a) 2 4 = = 2 (c) = = = 3 (e) = = 4 5 (b) = = 2 3 (d) = = = 3 4 (f) = = 7 9 (h) = = 5 8 (j) 2 28 = = (b) 20 = = 3 0 (d) 2 6 = = (f) 6 = = 4 3. (a) 6 3 = = 2 (b) 9 3 = = 3 (c) 8 2 = = 4 (d) 4 7 = = 2 (e) 25 5 = = 5 (f) = = (g) 6 4 = = 4 (h) 30 6 = = 5 (i) 49 7 = = 7 4. Dividing numerator and denominator by common factors. (a) 9 27 = = 3 (c) = = 3 8 (b) 24 = = 3 (d) = = 44 TH Easy Maths 5

45 (e) = = 6 5. (a) 2 4 (2 7) + 4 = = = (5 0) + 9 (c) 5 = = = (e) 5 ( 8) + 5 = 8 8 = = 3 8 (f) 3 5 = = 5 (b) 3 7 (3 9) + 7 = = = (d) 5 (5 9) + = = 45 + = (f) 3 3 (3 4) + 3 = = = Exercise 7.3. (a) = (b) = (a) = 9 5 When we have like fractions, we simply add numerators keeping the denominator same. (d) = = 8 (f) = = 3 3 (e) (h) = = (i) = = (j) = = = = 5 5 or (g) = = 7 7 or 4 7 = = = = 4 + = (4 + ) + = 5 + = 5 (k) = = = = (7 + ) = or 8 3 (l) = = = 3 + = 4 3 (m) = (2 + 7) = = (n) = (4 + 6) = = When denominators are not same we change them into like fraction by LCM method. TH Easy Maths 5 45

46 (o) = LCM of 8 and 4 is = = = = = or = (p) = (3 + 8) Since LCM of 3 and 9 is 9 3 = = Now = = (q) = ( ) = = = 4 9 (r) = ( ) Since LCM of 6, 8, 2 is = = 0 6 and 2 = = 8 6 Now, or = = = LCM of 5, 0 is 3 5 = = (a) Fraction of money spent on books = 2 = = or = or 22 5 Fraction of money spent on snacks and drinks = 4 Total fraction of money spent = LCM of 2 and 4 is 4 2 = = 2 4 Now, = TH Easy Maths 5

47 (b) Apples purchased = 2 2 kg Oranges purchased = 4 kg Grapes purchased = 3 4 kg Total weight of fruits purchased = LCM of 2 and 4 is 4 2 = = 2 4 Now = ( ) = = 6 + = 7 kg. (c) Distance jogged on Monday = km Distance jogged on Tuesday = 5 3 km Distance jogged on Wednesday = km Total distance jogged = km = ( ) = = = or km. (d) Part of cake eaten by friends = 4 9 Part of cake eaten by family members = 2 9 Total part of the cake eaten = = = Changing 2 into lowest form = 2 is the total part of the cake eaten. 3 TH Easy Maths 5 47

48 (e) Part of book read on Monday = 4 9 Exercise 7.4. (a) Part of book read on Tuesday = 2 9 Part of book read on Wednesday = 9 Part of the book finished reading = = = Meera = = = 72 5 = (b) 5 8 = or as = 8 8 = 88 8 = 83 8 or (c) Here, (d) Here, or 47 8 = 8 8 = 88 8 or = = (e) or = Here, = = = = = or 7 2 or = = 4 8 or (f) = (9 6) + 3 = (g) or Here, = 5 = 35 5 Now, = = or 3 3 or TH Easy Maths 5

49 (h) Since fractions are like fractions we simply subtract the numerators and write the answer over the common denominator. 7 4 i.e., = or = 3 (i) = 5 9 = (j) or = = 5 4 (k) = = (l) = = = = 4 4 or 2 2 We subtract the whole number and fractions separately. = (9 6) = = or (m) Changing mixed numbers into improper fractions, = = 75 9 and = 34 5 LCM of 9 and 5 is = Now, (n) and = = = Changing into improper fractions, = 2 9 and = 43 2 LCM of 9 and 2 is = = Now, and = = or or = = or TH Easy Maths 5 49

50 (o) Changing into improper fractions, 9 2 = 09 2 ; 7 9 = 6 9 LCM of 2, 9 and 6 is 36. Now, 09 2 = = and 6 = = = ( ) (p) = and = Changing into improper fractions or 29 5 = = 343 and 2 6 = Now, LCM of 5, 2 and 6 = = = = = ( ) = = = (a) Sohan ate = of cake 5 or 7 6 = = = So, or = = Now, or Mohan ate = of cake 6 Comparing the two fractions 5 6 = 6 > 5 Hence, 5 >. Sohan ate more TH Easy Maths 5

51 Changing fractions into equivalent fractions 5 = = 6 30 and Now = = 30 Sohan ate more by of the cake = = 5 30 (b) Fraction of pizza Rahul ate = 2 3 Fraction of pizza Abhay = 2 Changing into like fractions LCM of 3 and 2 = 6 Since 4 > = = > 3 6 and (i) True (ii) False (iii) False 2 = = 3 6 Rahul has more pizza. (c) Total length of wire = 2 3 or m. Length of wire cut off from it = 5 5 or 0 0 m. 08 Remaining length of the wire = m. Changing into like fractions 08 5 = = m = m = 65 0 m or m or 6 2 m (d) = LCM of 5 and 2 = 0 or 36 5 = = = = 45 0 TH Easy Maths 5 5

52 Now, = = or (e) = (29 5) (9 4) = = = 20 = = = = (35 3) (28 2) = = 8 6 Since 8 > > is greater. 3 (f) Other number = = 6 4 (6 4) = = 4 64 = or 3 4 (g) Fraction of black marbles = 3 Fraction of white marbles = 2 Fraction of marbles not green = (h) Total length of cloth = m ( 2) + ( 3) = = = Pieces cut off from cloth = 2 2 m m Cloth left = m = = = LCM of 6 and 4 = = Now, m = = 39 6 m or 2 7 m cloth is left 6 TH Easy Maths 5

53 (i) Total flour used to make both cakes = kg = kg LCM of 2 and 4 is = = 4 4 Now, kg = = kg or kg Flour bought by the baker = 5 kg Flour left after making cakes = (60 23) = kg = kg 4 4 = 37 4 kg or 9 4 kg kg Exercise 7.5. Refer answers at the end of book. 2. (a) Pizzas eaten by girls = 3 2 Pizzas eaten by boys = 7 2 Total pizzas eaten = = (3 + 7) = = 0 + = pizzas (b) Paint bought = 2 2 litres or 5 2 litres Paint used = 3 2 litres Paint left = litres = = 2 litres or litre 2 TH Easy Maths 5 53

54 (c) White flour needed for recipe = 2 3 cups Whole wheat flour needed for recipe = 2 3 cups Total flour needed = cups = = = 3 cups = = 2 + (d) Age of dog Cat is younger than dog by Age of cat = (5 4) = = 5 2 years = 4 3 years = years = + 6 years or 6 years (e) Since 5 > 2 hence, > 2 4 Dad ate more by = buns = (5 2) = = = buns or buns (f) Number of cups of water needed to drink = Number of cups of milk needed to drink = 2 4 Total fluid intake = cups = (8 + 2) = 0 + = = (0 + ) = cups 54 TH Easy Maths 5

55 Exercise 7.6. (a) Subtracting 9 from 5 9, i.e., = 4 9 Again subtracting 9 from 4 9, i.e = 3 9 or 3 Hence degree of closeness of 5 9 to is 2. 3 (b) Subtracting 6 from 5 6, i.e = 4 6 Again subtracting 6 from 4 6. i.e = 3 6 Hence degree of closeness of 5 6 to 3 is 2. 6 (c) Subtracting 5 from 3 5, = 3 = Again subtracting 5 from 2 5, i.e., = 5 Hence, degree of closeness of 3 5 to is 2. 5 (d) Subtracting 8 from 7 8, Hence, degree of closeness of 7 8 to 3 is (a) To find degree of closeness of 3 8 to 2. Add 8 to 3 8 i.e., = 4 8 or 2 Hence, degree of closeness of 3 8 to is. 2 TH Easy Maths 5 55

56 To find degree of closeness of 3 8 to 4. Subtract 8 from i.e., 8 8 = 2 or 8 4 Hence, degree of closeness of 3 8 to is. 4 As degree of closeness is same in both cases 3 8 to 2 and 4. is equally closer (b) To find degree of closeness of 7 6 to 2, we add 6 to 7 6. i.e., = 8 6 or. Hence it is 2 To find degree of closeness of (DOC) of 7 6 to 4, we subtract 6 from 7 6 i.e., Hence DOC is or 4 We can say 4 6 is closer to 2 than to 4. (c) To find DOC of 5 2 to 3, we subtract 3 from 5 2. i.e., = 4 2 Hence, DOC = or To find the DOC of 5 2 to 2 3, we add 2 to 5 2. i.e., Hence, DOC is or 2 3 So, we can say that 5 2 is closer to 3 than to TH Easy Maths 5

57 Exercise 7.7 (d) To find DOC of 6 to 2 we subtract 6 from 6. i.e., = or 2 Hence, degree of closeness is 2. To find DOC of 6 to 3, we add 6 from 6. i.e., = 2 6 Hence, DOC is. or So we can say that 6 is closer to 3 than to = = 5 or = = 5 or = = = = = = or 2 2 Exercise 7.8. (a) = 5 5 = 25 (b) = 6 4 = 24 (c) = 2 2 = 4 (d) 8 40 = 5 (e) = 3 7 = or 2 5 (f) = 6 7 or (g) = 4 9 = or (a) week = 7 days 7 of a week = days = day (h) = 6 2 = or TH Easy Maths 5 57

58 Exercise 7.9 (b) day = 24 hours, hour = 60 minute, minute = 60 second Now, 24 of a day = 24 hours = hour of hour = 60 min = min of a min = s = s Hence, 60 of 60 of of a day = s 24 (c) Denominator = 4 Numerator = Hence, fraction = 4 (d) Numerator = 5 Denominator =? Since the fractions is equivalent to = 5 70 Hence, denominator = 70 (e) Numerator = Denominator = 4 = 4 Hence, fraction is 4. (a) 2 3 of 5 = = 2 5 = 0 (b) of 2 = 3 4 (c) 4 5 of 0 = = 4 2 = 8 (d) of 2 = (a) = = or (b) = = = 3 3 = = 6 3 = 8 58 (c) = = 6 (d) 3 2 = = (e) 5 = = or (f) = = 7 26 = 82 or (g) = = 5 23 = 5 or (h) = = 3 5 = 45 4 (i) = = = 49 or TH Easy Maths 5

59 (j) = = = 2 or (k) = = = 23 or (l) = = = 28 or (m) = = = 9 or (n) = 8 7 = 56 or (o) = = 56 or (a) Perimeter of park = 2 3 km or 7 3 km. Number of rounds taken = 3 7 Total distance run by the boy = 3 = 7 km 3 (b) Earning in a month = `0,000 Fraction spent on house rent = 5 Money spent on house rent = of `0,000 5 = 0, = `2,000 Fraction of earning spent on personal expenses = 2 Money spent on personal expenses = of `0,000 2 = 0, = `5,000 2 (c) Total students = 50 Fraction of girls = 5 Number of girl students = of 50 5 = 50 0 = 0 girls students 5 TH Easy Maths 5 59

60 (d) Number of bags received = 2 Fraction of bags containing vegetables = 2 Number of vegetables bags = of 2 2 = = 56 bags Fraction of potato bags = 7 Number of potato bags = 7 of 56 = 7 (e) Total number of pages = = 8 bags Fraction of book read = 5 Number of pages read = of = = 50 pages Number of pages left = (250 50) pages = 200 pages (f) Chocolates brought = 8 9 of a kg = 8 9 kg Fraction of chocolates Jessica ate = 3 Amount of ate = 3 of 8 9 kg = = 8 27 Amount of chocolates left = kg = kg = 6 kg of chocolate in left with Jessica. 27 Exercise 7.0 (Making denominator same). (a) 9 4 (b) 5 2 or 5 4 (c) 6 5 (d) 29 3 (e) 3 9 (f) 4 (g) 3 25 (h) 5 49 (i) 5 22 (j) TH Easy Maths 5

61 2. (a) 2 3 = 7 3 Hence Multiplicative Inverse (MI) of 7 3 is 3 7. Exercise 7. (b) 6 MI of 6 is (c) 6 2 = 3 Hence, MI of is 2 3. (d) 00 MI of 00 is 00. (e) 9 MI is (f) = = MI of is (g) = = 377 Hence, MI of is (h) = = Hence, MI of is (a) 2 = = 0 We have successively subtracted from and 2 times 2 2 = 2 2 = 2 (b) 3 = = 3 3 = 3 or 3 = = 0 3 (c) 2 2 = 2 2 = = 2 3 Hence 2 2 = 4 or 2 2 = 4 (d), (e) and (f) are done in the same manner. 2 2 = (a) 4 as done is Question 4 Rest of the parts are done in the same manner. Exercise 7.2. (a) 4 3 = 2 3 = 2 3 = 6 ( reciprocal of 3 is 3 ) (b) = 4 2 = = 2 (c) = = = 9 90 TH Easy Maths 5 6

62 (d) = = 3 5 = 5 (e) = = = or 3 5 (f) = = 9 5 = or 67 2 (g) = = = 5 7 or (h) = = 5 (i) = 3 6 = 8 (j) = = = (k) = = = 2 8 or (l) = 5 2 = 7 3 = (m) = = or 35 (n) = 35 8 = (o) = 22 4 = 2 2 = (a) Cost of kg of rice = ` or 3 3 Cost of kg rice = ` = 87 ` = ` 87 or (b) = 00 paise `3.50 = 3.50 paise `0 = 000 paise Hence, the fraction is = TH Easy Maths 5