Example 3 : Find the length of the rectangle, if its area is 300 cm2 and breadth 12 cm.Solution : Here, Area (A) = 300 cm2Breadth (b) = 12 cmLength = l (let)Now, Area (A) = 300 cm2or, l × b = 300or, l × 12 = 300or, l = 30012or, l = 25Hence, length of rectangle is 25 cm.Classwork1. Count the square and calculate the area of the given figures:(one square room = 1 cm2)a. b. c.8 cm2d. e. f.g. h. i.12 cm ?300 cm2Acme Mathematics 5 201
j. k. l.m. n. o.2. Count the square and calculate the area of the given shaded figures:(one square room = 1 cm2)a. b. c.5 cm × 5cm = 25 cm2d. e. f.202 Acme Mathematics 5
g. h. i.Exercise 3.61. Study the given rectangle and fill in the blanks.DCAB1 cm1 cm(a) Length of rectangle ABCD is ......... cm.(b) Breadth of rectangle ABCD is ......... cm.(c) Area of rectangle ABCD is ......... cm2.2. Find the area of these rectangles:(a) (b)(c) (d) 2 cm 3 cm 2 cm 8 cm 2.5 cm 4 cm 3 cm 8 cm Acme Mathematics 5 203
(e) (f)3. Find the area of these squares:(a) (b) (c)4. Calculate the area of the following rectangular objects:(a) (b) (c)(d) (e) (f)1 cm 6 cm 15 cm 4 cm 1.5 cm 1.5 cm 2 cm 2 cm 3 cm 3 cm 15 cm20 cm 18 cm35 cm 8 cm8 cm17 cm15 cm40 cm72 cm13 cm17 cm204 Acme Mathematics 5
5. Calculate the area of the rectangles whose length (l) and breadth (b) are given:(a) l = 10 cm and b = 8 cm (b) l = 15 cm and b = 10 cm(c) l = 8 cm and b = 18 cm (d) l = 30 cm and b = 20 cm6. Calculate the area of the square whose length of each sides are given:(a) l = 16 cm (b) l = 9.5 cm(c) l = 7.5 cm (d) l = 11 cm7. Study the given irregular field and calculate the total area of the field. 5 m3 m3 m3 mA1 = ................ × ................ = ................A2 = ................ × ................ = ................Total Area = ................(a)10 m10 m4 m8 mA1 = ................ × ................ = ................A2 = ................ × ................ = ................Total Area = ................(b)5 m5 m7 m 12 mA1 = ................ × ................ = ................A2 = ................ × ................ = ................Total Area = ................(c)8. A rectangle is 15 cm long and 4.5 cm board. What is the area of the rectangle?9. The length of each side of a dice is 2 cm. Find the area of the one face.10. My study room is 4 m long and 3 m board. Find its area in square cm.2 cm 2 cm 2 cm Acme Mathematics 5 205
11. Find the area of a grassy field whose length is 25 m and breadth is 15 m.12. If the area of a floor is 48 m2 and its breadth is 6 m, what is its length ?13. If the area of this frame is 1200 cm2,calculate the breadth of the given frame, .14. A rectangular field with yellow and green shaded part is given alongside. Calculate the area of the yellow part.15. Calculate the area of the given square:(a) (b) (c)16. Measure the length and breadth of your math's book. Answer the following questions.(a) How long is your Maths book?(b) How wide is your Maths book?(c) How much space does it cover?40 cm 50 cm30 cm20 cm 30 cmPerimeter16 cmPerimeter20 cmPerimeter40 cm206 Acme Mathematics 5
1. Objective : To find the area. 2. Materials required :Graph paper, A-4 size paper, Glue, A pair of scissors3. Activities: Make 10 cm × 10 cm or 20 cm × 20 cm or 5 cm × 5 cm or any size of graph paper. Draw any five figures. Cut the shape you make. Paste on A-4 size paper. Count the square room and find the area. [Note: Remember not to count squares less than half room]4. An example is done for you:Its area is 32 Sq. cm.Project WorkAcme Mathematics 5 207
Look at the following shape and their sides carefully and get idea about the volume.Look at the figure alongside. It is cube.All the faces of it are equal. Its length, breadth and height all are 1 cm.Its volume is 1 cubic centimetre. It is written as 1 cc or 1 cm3.We use this size as a unit to measure the volume of an object.Classwork1. Count the number of the cubes and write the volume of each block [Note : volume of each cube is 1 cm3](a) (b) (c)6 cm3 Volume = cm3 Volume = cm3 Volume =(d) (e) cm3 Volume = cm3 Volume =(f) (g) cm3 Volume = cm3 Volume =1 cm31 cm 1 cm 1 cm7 Volume208 Acme Mathematics 5
Exercise 3.71. Fill in the blanks : (Count the unit cube.)(a) (b)V = .................. cm3 V = .................. cm3(c) (d)V = .................. cm3 V = .................. cm3(e) (f)V = .................. cm3 V = .................. cm3(g) (h)V = .................. cm3 V = .................. cm3Acme Mathematics 5 209
2. Count the cubes and write the total volume................ cm3 ............... cm3 ............... cm3............... cm3............... cm3............... cm3............... cm3............... cm3............... cm3= 1 cm3(g) (h)V = .................. cm3 V = .................. cm3210 Acme Mathematics 5
3. Count the block and write the volume of the figure.= 1 cm34. Unit cube is used for the following cuboids. Study the cuboids and fill in the blanks:(a) Length of cuboid = ...................................Breadth of cuboid = ....................................Height of cuboid = ....................................Volume of cuboid = ....................................(b) Length of cuboid = ...................................Breadth of cuboid = ....................................Height of cuboid = ....................................Volume of cuboid = ....................................(c) Length of cuboid = ...................................Breadth of cuboid = ....................................Height of cuboid = ....................................Volume of cuboid = ................................................... cm3 ............... cm3 ............... cm32 Units1 Unit5 Units10 Unit cubes. (2×5=10)Acme Mathematics 5 211
1. Objective: To construct different solid shapes.2. Materials required : Pencil, scale, dotted graph paper3. Activity: Draw lines to get different shapes.An example is given below:Project Work212 Acme Mathematics 5
1. Objective: To construct a cube2. Materials required : card board pair of scissors, pencil, scale, colours, gum, etc.3. Activity: Here is a net of cube. Use it to make cube.Each side is 4 cm.Project WorkAcme Mathematics 5 213
1. Study the given rectangle.(a) Measure the length and breadth of the given object.(b) How long is your hand ? Measure in cm.2. Guess the followings (a) How high is your room?(b) How long is your math book?4 inch9 cm4 cmPerimeter = .......... cm Perimeter = .......... inch 3. I am 57 years old now.(a) How old was I, 9 years ago?(b) Convert it to months.(c) How old are you? Convert your age to days.4. Kundan is 26 years 9 month and 18 days old today.(a) Find his birthday.(b) Convert the age into days.(c) Divide the age of Kundan by 6.5. If the weight of a bag is 50 kilogram, find the weight of 120 such bags.AB CDMixed Exercise214 Acme Mathematics 5
6. A rectangle has its sides 30 cm and 5 cm.MPNO30 cm5 cm(a) How long is its length than its breadth?(b) Calculate the sum of its length and breadth.(c) Calculate the perimeter.7. A square is 60 m long. A man runs around it 5 times daily.(a) Calculate its perimeter.(b) How much distance is covered by the man in one round?(c) Calculate the distance covered by the man in two days.8. Study the given rectangle.D 16 cm CA B 8 cm(a) Write the perimeter of rectangle ABCD.(b) Write the area of rectangle ABCD,9. A rectangular garden has length 12 m and breadth 8 m.(a) Find the perimeter of given rectangular garden.(b) Find the length of fencing wire that goes 3 times round the garden.10. Observe the given figure.(a) The perimeter of the plane figure is __________ .(b) Find the perimeter of given figure.15 cm15 cm15 cm15 cmDA BCAcme Mathematics 5 215
11. What is the area of square? Whose lenth is 'l' unit?(a) l × b (b) 4l (c) l2 (d) 2(l + b)12. In the given figure, what is the volume of cube?(a) 1 cm3 (b) 11 cm3(c) 3 cm (d) 3 cm313. Find the volume of given cuboids and cube.(a) (b)14. A rectangular field is 30 m long and 18 m wide.(a) Write the definition of the perimeter of square.(b) Find the perimeter of the given rectangular field.(c) Find the length of the fencing material that goes 5 times round the field for safety.15. (a) Write formula to calculate area of rectangle.(b) Find the length of rectangle if Area (A) = 100 cm2 and Breadth (b) = 10 cm16. (a) What is the formula to find out the perimeter of square?(b) Find the perimeter of square whose length is 6 cm.(c) Find the perimeter of given rectangle.17. A rectangular swimming pool is 60 m long and 40 m broad.(a) Write the formula to find the perimeter of a rectangle.(b) Find the perimeter of the rectangular swimming pool.(c) If the rate of cost of fencing the swimming pool is Rs. 50 per meter, find the cost of fencing it.1 cm 1 cm5 cm4 cm2 cm2 cm2cm2 cm20 cm10 cm1 cm216 Acme Mathematics 5
18. The perimeter of a square ground is 320 m.(a) Find the length of square ground.(b) Write the formula of area of square.(c) Find the area of square ground.19. From the given figure answer the questions.(a) Name the figure.(b) Write the formula to calculate volume of given cuboid.(c) Find the volume of give cuboid.20. Afarmer is cultivating paddy in a rectangular field having 100 meter length and 45 meter breadth. He bought 4 bundles of wire of equal weight from the market to fence the field 3 rounds with the wire to protect it from cattle.(a) When length and breadth of a rectangle are given, what should be done to find its area?(b) If the total weight of the wire is 3 quintal 40 kilogram, what is the weight of 1 bundle of wire? (c) While fencing the field 4 rounds, the farmer has 15 meters wire left, how many meters of wire did he purchase?21. A hall is paved with 1 square meter tiles. The length and breadth of the hall are 15 m and 10 m.(a) How many tiles are needed?(b) If one tile costs Rs. 75.50, find the cost of tiling.(c) Is Rs. 11000, enough for tiling?3 cm4 cm5 cmAcme Mathematics 5 217
EvaluationTime: 19 minutes Full Marks: 81. (a) Find the perimeter of the given square. [1] (b) A rectangle has a length of 20 cm and breadth is 15 cm. Find its area. [2](c) A cuboid has length \"l\" ,breadth 'b' and height 'h' . Find the volume of the cuboid. [1]2. (a) Find the perimeter of the given rectangle. [1] (b) What is the area of the given rectangle. (Each room is 1cm2) [1] (c) Find the volume of the solid. [2] 4 cm 5 cm3 cm3. A rectangular land is 30m long and 18m broad. (a) Find the perimeter of the land. [2] (b) Find the area of the land. [2] 218 Acme Mathematics 5
STATISTICS CHAPTER41 BillWarm Up Test1. Read the given bill and answer the questions given below:(a) Who is the buyer?(b) Who is seller?(c) Where is the shop?(d) What is the total amount?(e) When was the bill issued?2. Read the given bill and answer the questions given below:(a) Where is the buyer from? (b) Who is the seller?(c) What is the bill number? (d) What is the total amount?(e) What is the address of the Fashion Store? S. N. Particulars Qty.Rate (Rs.)AmountRs. Paisa1. Jackpot biscuits 6 pcs 12 72 002. 5-star chocolate 1 pc 12 12 003. Ice cream 3 pcs 15 45 004. Milk 3 litre 50 150 00Two hundred and seventy nine rupees only. In words: ................................................................................Grand total: 279.00............................. Seller/fd'JSK StoreBill no. 0134 Date: 083/08/17Name: .................................... Address: .................................Bharatpur - 11, ChitawanHom Nath Bharatpur - 7Ph: 056 - 522418Mo: 9845107849D-Next Fashion StoreHetauda, MakawanpurM/S .......................................... Address : ..................................Item Qty Price Cost (Rs.)BeltJacketT-shirtTrouserPantShirt21311275025308901260170013401500/–2530/– 2670/–1260/-1700/-2680/-Total 12340/– SignatureBill No. : 0215Padma Shrestha Hetauda - 17, HaityaIn Word : Twelve thousand three hundred forty only.RajakDate : 083-09-15PAN: 456789123PAN:984903772Acme Mathematics 5 219
Look at the following carefully:Swagat StoreHetauda, 2, MakawanpurM/S ............................................................Item Qty Price Cost (Rs.)BiscuitS.F. OilCoconutDaal2 packet5 Ltr.2 kg1.5 kg3514232015670/-710/– 640/–234/-Total 1654/– Sudhir LamichhaneThe above information is related to the buying and selling the things. We buy according to the need. The shopkeepers buy and sell the things and issue the bill.Generally, bills have the following details.1. Name and address of the shop 2. The bill number3. Name and address of the costumer 4. Date of issue of bill5. The rate of the items 6. The quantity of the items7. The sum of the prices. 8. PAN or VAT numberNow, let's look at a few samples of bills.Wisdom StationaryBharatpur, ChitwanM/S .....................................................Item Qty Price Cost (Rs.)Exe. BookPencilBall penGlue stickCorrection pen6 pc.1 doz.6 pc.2 pc.3 pc.2585254065150/-85/– 150/–80/-195/-Total 660/– Discount 5% 33/-Payable Amt. 627/-SignaturePAN Dipesh LamaFamily RestaurantBagbazar, KathmanduM/S .......................................................Item Qty Price Cost (Rs.)Veg. momoAalu SadekoCoffee3238065105240.00130.00315.00Total 685.00Service Charge 10% 68.50Payable Amt. 753.50Seven hundred fiftythree rupees and fifty paisa only.Binita ThapaliyaSignatureNote : If PAN or VAT numbers is not included the bill is not valid for official proposePAN: 980058733PAN 985103390PAN 985103391220 Acme Mathematics 5
This is a specimen copy of the bill given to the customer. Check the bill and answer the following questions.(a) Who is the customer ?(b) Where is the Designing house ?(c) What is the total bill ?(d) What is the rate of rubber seal ?(e) When was the bill issued ?Acme Mathematics 5 221
1. The price list of the 'Prakriti Stationary' is given below:Now answer the following questions:(a) Which has the least cost ?(b) Which is the most expensive ?(c) How much should be paid while buying 2 board marker ?(d) Where is the stationery ?Prakriti StationaryHetauda, MakawanpurPRICE LIST1. Pencil Rs. 5 2. Pencil cutter Rs. 4 3. Copy (No. 50) Rs. 10 4. Acme Maths book – 5 Rs. 250 5. Better Maths class – 10 Rs. 200 6. Ball (small) Rs. 20 7. Ball (big) Rs. 50 8. Glue stick (small) Rs. 25 9. Glue stick (big) Rs. 45 10. Board marker Rs. 22 11. Scale (6 inch) Rs. 10 1. Study the given bill and fill in the blanks(a) Name of shop is ....................(b) .................... items are sold.(c) Total bill amount is ....................(d) Date of bill issued is ....................BL StationeryBagbazar, KathmanduM/S ............................ Date : .................Item Qty Price Cost (Rs.)Exam BoardStaplerColour pencilPaper cutter6 pc.3 doz.5 pac.4 pc.5025075125300/-750/– 375/–500/-Total 1925/– Discount 200/-Payable Amt. 1725/-SignaturePAN :984592315 Bill No.2083-2-120123AP StationeryClassworkExercise 4.1222 Acme Mathematics 5
2. Make bill for the following purchase. Use the price list given in question number 1.(a) (b)(c) (d)3. Make the bill for the following.(a) Ramesh went to 'Baral Kirana Store' and bought 3 kg of potatoes at Rs. 35 per kg, 10 kg of rice at Rs. 52 per kg, 1 litre of sunflower oil at Rs. 85 per litre and 500 gram of jeera at Rs. 300 per kg.(b) Suntali went to fruit market. She bought 5 apples at the rate of Rs. 10 per apple, 3 oranges at Rs. 8 per orange, 1 kg of grapes at Rs. 150 per kg and 4 bananas at R. 5 per bananas.(c) Sridhar went to the Prasim Books and Stationery in Birgunj and bought the following items. 2 pencil - Rs 10 per pcs. 5 Ball pen - Rs 15 per pcs.7 Book Cover - Rs. 75 per pcs. 1 Math Book - Rs 412 per 4. Find out the mistakes in each bill:(a)2 Pencils3 Copy (No. 50)3 Compass1 Chinese pen1 Pencil2 Acme Maths book - 52 Ball (small)1 Glue stick (big)2 Board marker1 Pen (flame)1 Scale2 Better Maths class - 102 Pencil cutter1 Ball (big)2 Glue stick (small)1 ProtractorSuruchi StoreBirgunj, ParsaM/S .............................Address.........................Item Qty Price Cost (Rs.)Sugar RiceDalBhujiya3 kg 5 kg1 kg2 kg70 5010060200/–200/– 100/–120/–Total 620/– Bill No.:PAN Date:Acme Mathematics 5 223
(b)5. Write 'T' for true sentences and 'F' for false sentences for the following:The bill includes : (a) Name and address of the shop.(b) Bill number(c) Date of buying and selling(d) Name and address of the buyer(e) Rate of the items(f) Name of items and their quantities(g) PAN (Permanent Account Number) or VAT (Value Added Tax)New Fashion StoreNewroad, PokharaM/S .............................Address.........................Item Qty Price Cost (Rs.)T-shirt PantBeltMufflerTrouser21121400700500129300800/–700/– 500/–129/–600/-Total 620/– Bill No.:PAN Date:224 Acme Mathematics 5
Project Work1. Objective : To know about different types of bill.2. Materials required : Different types of bill Gum Scissors3. Activity : Collect different types of bill from different shop and paste them.Suruchi StoreBirgunj, ParsaM/S ...........................................Address..................................Item Qty Price Cost (Rs.)Sugar RiceChocolate4 kg 3 kg5 pc.70 5025280/–150/– 125/–Total 555/– Surendra Chaudhari BirgunjBill No.:Pan Date: 2082-10-11 98511370310Acme Mathematics 5 225
The monthly income and expenditure of a family is given below.Income (Rs) Expenditure (Rs)Source Amount Heading Amount1. Salary2. House rent3. Interest4. Farming35,000/-7,000 /-1,000/-1,200/-FoodEducationClothesTransportationMedicineTaxes12,500 /-7,000/-6,000/-2,500/-2,000 /-1,150/-Total 44,200 /– Total 31,150 /–The table is the budget of the family.Budget includes income and expenditure of the respective people, office, etc.Now, answer the following questions.(a) What is the total amount of income ?(c) Is there any saving ?(b) What is total expenditure of the family ?(d) What is amount for food ?Budget is planning of income and expenditure.Classwork1. The monthly heading of income and expenditure of your family is given below.Income (Rs) Expenditure (Rs)Source Amount Heading AmountSalaryHouse rentInterestFarming41,500/-12,000 /-1,250/-1,425/-FoodEducationClothesTransportationMedicine15,500 /-11,300/-5,000/-3,500/-1,150/-2 Budget226 Acme Mathematics 5
(a) What is the total income ?(b) What is total expenditure of the family ?(c) Is there any saving ?(d) What is amount for food ?Exercise 4.21. The monthly budget of a school is given below. Study the budget and answer the questions given below:Incomes (Rs)Source AmountFee 2,00,000/–Interest 2,000 /–Rent 25,000/–Others 5,000/–Total 2,32,000 /–Expenditure (Rs)Heading AmountSalary 90,000 /–Chalk, Duster 14,000/–Water bill 6,000/– Electricity bill 10,000/–Educational material 30,000/–Others 26,000/–Total 1,76,000 /–(a) Which is the greater source of income?(b) In which heading the expenditure is so high?(c) How much is the saving?(d) How much is earned from rent?Acme Mathematics 5 227
2. Prepare your family monthly budget.Incomes (Rs) Expenditure (Rs)Source Amount Heading AmountTotal Total(a) Is there any saving?(b) Is the budget in loss?3. Talk to your friend and make a monthly budget of his family.Incomes (Rs) Expenditure (Rs)Source Amount Heading AmountTotal Total228 Acme Mathematics 5
1. Objective: To know about the budget2. Materials required: A-4 size paper3. Activity: Ask your father or mother and prepare your yearly budget.Our family budget 2083Income(Heading)Amount(Rs)Amount(Rs)Expenditure(Heading)........................Prepare byProject WorkAcme Mathematics 5 229
A. Tabulation of a DataIn a school, the students in class 5 have the following caste. Discus on it and try to find the conclusion.Gurung, Aryal, Bhandari, Magar, Aryal, Koirala, Magar, Poudel, Gurung, Shrestha, Bhandari, Gurung, Aryal, Magar, Magar, Aryal, Aryal, Poudel, Bhandari, Poudel, Gurung, Gurung, Gurung. Koirala, Shrestha, Bhandari. (a) How many students are 'Aryal' ?(b) In which caste the number of students are highest ?(c) Which caste has the equal number of students ?(d) How many students are there in the class ?(e) How many students are more than 'Magar' ?(f) Which caste is in 4th position ?Statistics is a branch of mathematics. It deals with \"Data\".The above information is a data. The information is also called observation.a. Data A collection of facts such as numbers, words, measurements etc are called data.There are two types of data. They are,i. Qualitative Dataii. Quantitative DataQualitative data give descriptive information of something whereas quantitative data give numerical information about something. b. What is data collection?In Statistics, data collection is a process of gathering information from all the relevant sources to find a solution of the problem. c. Tabulation of dataThe information about the caste of students are as follows.Gurung, Aryal, Bhandari, Magar, Aryal, Koirala, Magar, Poudel, Gurung, Shrestha, Bhandari, Gurung, Aryal, Magar, Magar, Aryal, Aryal, Poudel, Bhandari, Poudel, Gurung, Gurung, Gurung. Koirala, Shrestha, Bhandari.3 Bar Graph230 Acme Mathematics 5
This data can be arranged in the following way.GurungGurungGurung Gurung Gurung GurungAryalAryal Aryal Aryal AryalBhandari Bhandari BhandariBhandariMagar Magar Magar MagarKoirala KoiralaPoudel Poudel PoudelShrestha ShresthaArrayed data are in better form than in raw form, but it is also not much of use. It will be useful if they are presented in the form of table. This data can be tabulated in the following way.Caste Gurung Aryal Bhandari Magar Koirala Poudel Shrestha TotalNumber of students 6 5 4 4 2 3 2 26Solved ExampleExample 1 : Students were asked to name their favorite food item. The record is as follow.Burger, French-fry, Pani-puri ,Burger, Pizza ,French-fry, 'Chatpate', Samosa, French-fry, Samosa ,French-fry, Samosa, French-fry, Pizza, Samosa, 'Chatpate', French-fry, French-fry, Pani-puri, Burger, Panipuri, French-fry, French-fry, 'Chatpate', Pizza, Burger, 'Chatpate', Dosa, Pizza, Pani-puri, Pizza, 'Chatpate', Pizza, Dosa, Pizza, Dosa, PizzaSolution: The number of students and their favorite food items are presented in the table given below.Food Item French-fry Pizza Burger Samosa Pani-puri Dosa 'Chatpate'Number of students 9 8 4 4 4 3 5 d. Tally MarksWhen the number of observation is large, it may not be convenient to find the frequencies simply by counting. In such case, we use tally marks which are quite helpful to find the frequencies. Tallies are usually marked in a bunch of five for Acme Mathematics 5 231
ease in counting. The fifth tally in a bunch is usually marked diagonally across the earlier ( ). We shall illustrate the method of tally marks in the following example. Solved ExampleExample 1 : The marks scored by 24 students in a unit test of mathematics are given below: 10 12 10 12 13 10 12 13 12 13 14 1012 13 15 13 14 12 10 13 14 15 14 14 Solution: The number of students and their obtained marks are presented in the table given below.We can prepare a table by using tally marks as follow. Marks Tally Number of students10 | | | | 512 | | | | | 613 | | | | | 614 | | | | 515 | | 2Total 24Here, 5 students got 10 marks, 6 students got 12 marks and so on. Repetition of marks is also called the frequency of the marks. In general frequency is denoted by 'f'. 12 appears 6 times so its frequency is 6. Similarly, 13 appears 6 times, 14 appears 5 times and 15 appears 2 times. The frequency table without tally marks is as follows. Marks (x) 10 12 13 14 15 TotalNo of students(f) 5 6 6 5 2 24Example 2 : The following marks were obtained by class 5 students in a unit exam in mathematics:9, 10, 7, 5, 6, 5, 6, 9, 10, 5,6, 6, 5, 7, 8, 9, 10, 10, 7, 8,7, 9, 10, 5, 9, 8, 6, 5, 10, 6,9, 9, 9, 10, 6, 5, 7, 6, 6, 8(a) Prepare a frequency table.(b) How many students got 10 marks ?232 Acme Mathematics 5
(c) How many students got least marks ?(d) How many students were in the examination ?Solution: (a) Table of marks of students in unit exam in mathematics isgiven below.Marks Tally Marks Number of students5 76 97 58 49 810 7Total: 40(b) 7 students got 10 marks.(c) 7 students got least marks.(d) 40 students were in the examination.Exercise 4.31. Fill in the box :Observation Tally marks Frequency6732........................7........2. The average temperature of some towns of Nepal are given below. Study the table and answer the following questions.Town Kathmandu Chitwan Dharan BiratnagarTemperature 29oC 35oC 20oC 30oC(a) Which place has the highest temperature ?(b) What is the temperature of Birantnagar ?(c) Which place is very hot ?Acme Mathematics 5 233
3. The following are the height (in inch) of 15 students of class 5.55,53, 50,51,54,50,52,62,61,57,55,60,48,49,50.(a) Arrange the data in ascending order .(b) Prepare a table.(c) Which is the lowest height? (d) Which is the highest height? 4. The following are the marks of 15 students of class 5 in terminal examination.45, 43, 50, 31, 34, 50, 32, 32, 21, 27, 35, 40, 48, 49, 50.(a) Arrange the data in descending order .(b) Prepare a table.(c) How many students stood first in the examination? (d) How many students got least mark in the examination? 5. Study the following distribution table and answer the question given below. Age(in months) 48 60 62 65 67 72No. of students 2 7 10 8 7 3(a) How many students are there in all ?(b) How many students are there above 62 months age ?(c) How many years are difference between youngest and oldest students ?(d) Which age group students are more ?6. The record of veichals passes through \"Nahar Chowk\" on Sunday from 8 a.m. to 9 a.m. is as follows.Motorcycle, Bus, Car, Cycle, Truck, Truck, Cycle, Motorcycle, Bus, Car, Car, Motorcycle, Motor cycle, Cycle, Bus, Car, Motorcycle, Motorcycle, Cycle, Cycle, Cycle, Van, Van, Car, Van, Van(a) Construct the frequency table.(b) When was the information collected ?(c) Where was the information collected? (d) Which vehicle was mostly crossed ? 234 Acme Mathematics 5
7. The height of the students was recorded in the class.123cm, 127cm, 130cm , 125cm,135cm, 125cm, 127cm, 130cm, 123cm, 135cm, 123cm, 125cm, 127cm, 130cm and 137cm are the height. Construct a table of the height of the students.(a) Arrange the height in increasing order .(b) Prepare a table.(c) If Suvas is tallest in the class, what is his height? (d) How many students are there as near to the height of Suvas? 8. A survey was conducted on the occupation of different people in a community.doctor, teacher, carpenter, farmer, doctor, farmer, teacher, teacher, doctor, painter, painter, doctor, painter, carpenter, doctor, painter, carpenter, farmer, painter, carpenter, farmer, painter, doctor, teacher, painter, painter, farmer(a) Construct the frequency table.(b) How many people were participated in the survey?(c) In how many occupations the people were involved? (d) Write the number of farmer and teacher in the community? 9. Ask your friends to name their favourite fruit item and record them.(a) Construct the table.(b) How many of your friends are participated in the survey?(c) How many types of fruits are recorded ? (d) Which fruit is liked most?Acme Mathematics 5 235
B. Tabulation of InformationMarks obtained by six students of class four in Maths exam are given below.Name of students Kabir Karna Rajensh Rupa Tripti RakhiMarks 16 12 18 10 14 20This information is the tabulation form. From the table, we have the following information.(a) 20 is the highest marks.(b) 10 is the lowest marks.(c) Marks obtained by Kabir is 16 etc.The above information can be presented by another way also.Name of students081621018412202224614KabirMarksKarna Rajesh Rupa Tripti RakhiThe above diagram is called the bar graph. By using bar graph, we can compare the marks of all students easily.(a) How many marks are obtained by Kabir?(b) Who obtained the highest marks?(c) Who obtained 18 marks?236 Acme Mathematics 5
Graph help the reader to gather all the information that is required. Given below are examples of different kinds of graphs.03691215Pie chart Bar graph Line graph PictographThe table gives the record of students and their weight in kg.Name of students Dwarika Suman Rasmi KalikaWeight in kg 25 20 30 25This information can be presented in the form of graph as,Dwarika051015202530SumanName of the StudentsWeight in kgRasmi KalikaStudents and their weightThe above graphs are called the Bar graphs. Using the graph we can answer the questions such as:1. the highest weight is 30 kg.2. the lowest weight is 20 kg.3. the weight of Dwarika and Kalika are equal.4. the weight of Kalika is 25 kg and so on.Acme Mathematics 5 237
A bar graph is used to compare the same kind of information. A lot of information can be shown with the help of a bar graph.The procedure for drawing the bar graph is as follows:Step-1: Draw a horizontal line segment OX. Draw a vertical line segment OY.Step-2: Mark points at convenient intervals on the lines OX and OY as shown in the figure.O XYO XYStep-3: Draw bars of equal thickness for each class. The height of the bars show the number of observation.I know, height of the bar shows the information.Remember: Breadth of bar is same.Don't forgwt! Gap between two bars is sameB. How to construct the bar-graph?Step-1 Step-2238 Acme Mathematics 5
Step-4: Write the title of the bar graph.O XY10...........................Number of .......................................................305070204060O XYClasswork1. Colour the bar graph. Name of students04080105020603070MarksHarka Balen GopiExercise 4.41. The weight of 6 students of class 4 is as follows.Kamal = 28 kg, Kunti = 30 kg, Kanchan = 32 kg,Karma =29 kg, Ram = 26 kg, Narayan = 25 kgNow, tabulate the information (data) in(a) Increasing order (b) Decreasing orderMarks obtained by studentsStep-3 Step-4Acme Mathematics 5 239
2. Bishal's father is a farmer. He has a farm house. He has the following animals in the farm.Animals NumberBuffalo 20Goat 25Cow 10Hen 30Rabbit 20Draw the bar graph (use graph paper)3. The given table shows the number of students in different section of class-5. Draw the bar graph to show this information.Sections Daisy Lotus Lily RoseNumber of students 42 36 38 404. Study the following bar graph which shows the number of people who like FM radio of Chitwan.Name of FM04080105020603070Number of peopleKalika Synergy Triveni Madi Arpan(a) How many people like 'Kalika FM'?(b) How many people like 'Madi FM'?240 Acme Mathematics 5
(c) Which FM is liked by 60 people?(d) Which FM is liked by least people?(e) How many more people listen Triveni than Synergy?5. Draw the bar graph of Aman's marks and find his favorite subject according to height of bar.Subjects Nepali English Maths Science Social studiesMarks 15 12 20 8 66. Study the following bar graph which shows the number of students in a school.Classes04080105020603070 Number of studentsClass 8 Class 9 Class 10 Class 11 Class 12(a) How many students are there in class 8?(b) How many students are there in class 9 and 10??(c) In which class are there fewer students?(d) Which class has the largest number of students?(e) How many students are there all together?7. The marks obtained out of 50 by Sujan in different subjects is given below.Subjects Mathematics Nepali English Social ScienceMarks 50 30 40 35 45Acme Mathematics 5 241
Present the information in the bar graph.Name of students Kusum Kiran Kabir Kisor KanchanMarks obtained in Math 50 30 40 35 458. This table records the number of absentees in class V on a given week. Draw a bar diagram.Days Sunday Monday Tuesday Wednesday Thursday FridayNumber of absentees 4 5 3 2 1 109. The table shows the maximum temperature (in °C) of place over on week.Days Sun Mon Tue Wed Thu Fri SatTemperature (°C) 28° 32° 24° 30° 34° 26° 20°Present the information in the bar graph.10. Draw a bar graph to represent the following data (information).Subjects Nepali English Maths Science SocialMarks obtained 65 85 90 75 60242 Acme Mathematics 5
1. Study the budget of a family given below and answer the following questions:Income ExpenditureSn. Topic Amount Sn. Topics Amount1 Salary Rs 42500 1 Education Rs 265002 Business Rs 22300 2 Clothes Rs 305003 Rent Rs 23200 3 Food Rs 123004 Others Rs 12500 4 Others Rs 10050Total 100500 Total ................(a) What is the total income of the Family?(b) Which topic has least expenditure?(c) How much amount is gained from business?2. Study the given table on the monthly income and expenditure of a family.Income ExpenditureSn. Topic Amount Sn. Topics Amount1 Salary Rs 40500 1 Food Rs 350002 Rent Rs 20000 2 Education Rs 225003 Business Rs 60000 3 Clothes Rs 90004 Others Rs 15000 4 Others Rs 3500Total 135500 Total Rs 70000(a) From which topic does the family earn more?(b) Which topic has least expenditure?(c) How much amount is gained from business?Mixed ExerciseAcme Mathematics 5 243
3. Monthly budget of a family is given below:Income ExpenditureSn. Title Amount Sn. Topics Amount1 Salary Rs 25000 1 Food Rs 120002 Business Rs 30000 2 Education Rs 60003 Clothes Rs 140004 Others Rs 4000Total 55000 Total Rs 36000(a) From which title does the family earn more income?(b) What is the monthly saving of the family?4. The given table shows the grades of students in an exam.Grade → E D C B AClass ↓3 7 .3 7 23 104 4 6 19 26 45 3 4 8 24 17(a) How many students are there who secured grade A?(b) How many students are there in class 5?(c) In which class did the more students secure the grade B?5. Study the following table and answer the questions.Month January February March April Mayprice of tomato per kg (Rs.) 40 30 55 60 80(a) What is the highest price of the tomato?(b) What is the lowest price of the tomato?(c) On which month was tomato the cheapest?(d) On which month was tomato the most expensive?244 Acme Mathematics 5
6. Present the given data in table where number of students who played different games are given.Football 75, Cricket 40, Volleyball 42, Chess 107. Answer the following questions with the help of given bar-graph.05101520Apple Mango GrapesFruitsNo. of PeopleOrange253035404550(a) Which is the most popular fruits?(b) Which fruit items are liked by less than 30 people?(c) What is the total number of fruits?8. The marks obtained by Rijan out of 50 in different subjects are given below.Subjects Nepali English Science MathsMarks 20 38 43 45(a) Which axis is called horizontal line in the bar diagram.(b) Construct a bar diagram of given table.9. Study the given monthly budget of a family and answer the following questions.Income ExpenditureSources Amount Particulars AmountSalary 20,000 Food 15,000House Rent 5,000 Clothes 5,000Shop 5,000 Education 5,000Interest 10,000 Entertainment 2,000(a) How much does the family earn from food?(b) What is the monthly income of the family?(c) Find the monthly saving of the family.Acme Mathematics 5 245
10. In a unit test of mathematics, Class 5 students obtained the following marks out of 20 full marks.18 15 18 16 19 20 17 15 18 20(a) Write this information in a table.(b) How many students appeared in the unit test?(c) How many students obtained the full marks?11. Study the given table and draw a bar graph to show the given information.Games Football Cricket Basketball VolleyballNo. of students 15 12 10 612. Study the bill and answer the question:Sharma StationaryTandi, ChitwanBill No. 123 Date: 2083-01-05Coustomer's Name: AnujaAdress: TandiS.N. Particular Qty. Rate(Rs. Amount (Rs.)1. Exercise book 4 250 10002. Chart paper 5 20 1003. Geometry box 3 120 3604. Pencil 10 8 80Total 1540In words: One thousand five hundred forty only. ....................... .......................Customer's sign Sharma StationaryPAN : 123456789(a) Who is a purchaser?(b) How many exercise books were purchased?(c) What is the cost of a geometry box?(d) What is the total amount she has to pay to the shopkeeper?(c) After paying the bill amount, will the remaining amount be enough to buy 2 exercise book. If she gave shopkeeper Rs. 2000?246 Acme Mathematics 5
1. Objective: To construct the bar-graph.2. Materials required:A-4 size paper Graph paperA pair of scissors Colours3. Activity: Collect the data of the number of books of your classmates.Subjects English Maths Nepali Science ComputerNo. of Books Take graph paper and make bar graph. Use different colours to different bars. Cut the bars you made and paste on A-4 size paper. Put the heading.4. An example is given below:English010203040MathsSubjectsNumber of booksNepali Science Social StudiesDifferent subjects in the classProject WorkAcme Mathematics 5 247
EvaluationTime: 55 minutes Full Marks: 231. Read the price list of different items in a shop. Items Price (per kg)Basmati rice Rs.120Patato Rs.50Onion Rs.60Grams Rs.65Answer the following questions.(a) Which is the most expensive food? [1](b) What is the cost of 2 kg onion? [1](c) Which item cost Rs 50 per kg? [1](d) Which is the cheapest item? [1]2. Show the number of students who like different games in a tabular form. [2]Football-25, Volleyball-15, Cricket-30, Basketball-20, Table Tennis-10 3. The annual income and expenditure plan of a family is given below.Income Rs. Expenditure Rs.Salary 150000 Food 50000Vegetable 10000 Education 30000Hen 15000 Clothes 20000Milk 25000 Medicine 10000Answer the following questions. (a) Which sources gives maximum income? [1](b) What is the yearly income of the family? [1](c) What is the total expenditure of the family? [1] (d) What is the yearly saving of the family? [1]4. Present the following data in a bar graph . [2] Name of students Ram Shyam Sita Rita MinaMarks obtain in Maths 40 30 25 20 45248 Acme Mathematics 5
5. Answer the following questions using the given bill. ABC Pustak Pasal PAN No.: 123456789Khairahani, ChitwanInvoice No.: 0070 2082/10/22Costumer's Name: Samir AryalAddress: Khairahani, ParsaS.N. Item Qty Rate Amount1 Book set Class-5 1 Set 2285 2285/-2 Copy 2 (Dozen) 550 1100/-3 Pencil 1 (Dozen) 120 120/-4 Eraser 2 (pcs) 20 40/-5 Sharpener 2 (pcs) 15 30/-In words: Three thousand five hundred fiftyTotal Amount 3,575/-Discount 25/-Bill Amount 3,550/-(a) What is the name of thecostumer ? [1] (b) What is the total amount without discount ? [1] (c) If the customer gives Rs. 4000 to the shopkeeper. Then how much money should be returned by shopkeeper to the costumer. [2] 6. Study the given bar-diagram and answer the following questions. Classes04080105020603070 Number of studentsClass 8 Class 9 Class 10 Class 11 Class 12Acme Mathematics 5 249
(a) How many students are there in class II ? [1] (b) In which classes are equal number of students ? [1] 7. Study the bill below and answer the given questions.RAM GROCERY STOREPokhara Bill No.: 205 Date: 2082/10/11Costumer's Name: Isha AryalAddress: Lake sideS.N. Particulars Quantity Rate(Rs) Amount(Rs)1 Cauliflower 6kg 50 300/-2 Potato 5kg 43 215/-3 Tomato 3kg 30 90/-4 Pea 2kg 110 220/-5 Sugar 2 kg 80 160/-6 Flour 2kg 50 100/-7 Chocolate 3 packets 150 450/-8 oil 3 liter 150 450/-In words: One thousand nine hundred only.Total Amount 1,985/-Discount 85/-Bill Amount 1,900/-Seller Dipak Tamang ...................(a) What are the names of buyer and seller ? [2](b) How much money did Isha spend to buy cauliflower? [1](c) Which cost is more in between chocolate and potato and how much? (d) Which good has the highest cost ? [1](e) What is the total cost? [1]PAN No.: 105999851250 Acme Mathematics 5