Example 2 : Convert 69 days into weeks and days.Solution : We have, 69 days = 697 weeks = 9 weeks 6 days ∴ 69 days = 9 weeks 6 days.Example 3 : Convert 7 years 8 months into days. Solution : We have, 7 years = 7 × 365 days = 2555 days 8 months = 8 × 30 days= 240 days ∴ 7 years 8 months = (2555 + 240 days) = 2795 days1.3. Multiplication and division of the different units of timeStudy the following examples carefully.Example 4 : Multiply 8 hours 23 minutes by 15.Solution : We have, hour minute8 23× 15120 345125 45Example 5 : Multiply 7 years 3 month by 12.Solution : We have,years months7 3 × 1284 3687 07)69(9 –63 6weeksdays60) 345 (5 → hour -300 45 → minutes12) 36 (3 → years -36 0 → monthsAcme Mathematics 5 151
Example 6 : Divide 18 hours 30 minutes by 15.Solution : We have, 1 hour 14 minutes 15 18 hours 30 minutes– 15 3 hours + 30 minutes 210 minutes–15– 60 – 60 0Hence, 1 hour 14 minutes is the quotient.Example 7 : A micro bus takes 3 hours 45 minutes to reach Kathmandu from Narayangarh. If the microbus goes to Kathmandu from Naranyangarh 6 times per week, find the total time taken by the micro bus per week to reach Kathmandu from Narayangarh.Solution : The problem is related to the multiplication of time.We have,Example 8 : Kabir spent 45 hours 30 minutes per month to study and do the homework. Find his time to study and do the homework per day.Solution : The problem is related to the division of time.We have, 1 month = 30 days3 hours = 3 × 60 min = 180 min30 minutes+ 180 minutes210 minutes hours minutes3 45 × 618 27022 30Thus the micro bus takes 22 hours 30 minutes to reach Kathmandu from Narayangarh per week.152 Acme Mathematics 5
So,Hence, Kabir spent 1 hour 31 minutes to study and do the homework per day.1. Match the times:Eleven thirty five PMQuarter past nine AMthree twenty five PMQuarter to five AM 1 hour 31 minutes30 45 hours 30 minutes– 30 15 hrs = 900 minutes 930 minutes – 90030– 30060× 15300600900900 + 30 = 930It is givenClassworkAcme Mathematics 5 153
2. Write the time............................................................. ............................................................ 8 o'clock a.m............................................................. ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ............................................................Exercise 3.11. Fill in the blanks:(a) 24 hours = .........................days(b) 7 years = .........................month(c) 23 : 30 o'clock = ................pm(d) 18 : 00 o'clock = ................pm(e) 1 day and 5 hours = .........hours(f) 1 year and 3 months = ...... months154 Acme Mathematics 5
2. Study the activity and draw the hands on the clock.3. Change the following as indicated in the brackets:(a) 15 hours 12 minutes (minutes)(b) 4 days 7 hrs 16 min (minutes)(c) 2 weeks 5 days 6 hours (hours)(d) 2 months 2 week 3 days (days)(e) 455 days (week)(f) 54 months (year)(g) 3285 days (year)(h) 700 years (decades)Acme Mathematics 5 155
4. Tick the correct time.5. Multiply the following:(a) (b)(c) (d)(e) 7 months 15 days 6 hours by 7.(f) 10 years 8 months 7 days by 16.(g) 3 years 7 months 11 days 15 hours by 12(h) 12 years 0 months 20 days 21 hours by 15.(i) 8 decades 7 years 6 months by 10(j) 4 century 4 decade 4 years by 6.hours minutes seconds4 5 6× 15 days hours minutes2 7 50× 20weeks days hours7 3 6× 16decades years days7 9 25× 25156 Acme Mathematics 5
6. Divide the following:(a) 6 hrs 10 min by 5(b) 12 days 18 hrs by 6(c) 4 weeks 7 days by 7(d) 10 weeks 24 hrs by 8(e) 16 years 9 months 18 days by 9(f) 19 years 6 months 20 days by 11.(g) 7 months 13 weeks 9 days by 8.(h) 80 decades 5 years 0 months by 12(i) 40 century 4 decades by 107. The table below shows the departure time table of the difference buses from Narayangarh to Kalanki, Kathmandu :Narayangarh Bus – A Bus – B Bus – C1. Narayangarh 5:10 am 6:45 am 9:40 am2. Ramnagar 5:25 am 7:00 am 10:00 am3. Muglin 6:00 am 8:00 am 10:45 am4. Bishaltar 6:30 am 8:25 am 11:45 am5. Malekhu 7:00 am 9:00 am 12:30 pm6. Gajuri 7:20 am 9:30 am 1:00 pm7. Naubise 8:00 am 10:00 am 2:00 pm8. Kalanki 8: 30 am 11:00 am 2:45 pmNow, answer the following questions:(a) When does Bus A reach Bishaltar?(b) How much time later did C reach Malekhu than B?(c) Which bus takes less time to reach Kalanki?(d) When do the passengers of bus B reach to 'Malekhu'?Acme Mathematics 5 157
(e) Which bus do you choose to reach 'Naubise' at 2 o'clock in the afternoon?(f) Where is bus C when bus B is in 'Naubise'?(g) After what time does bus C reach 'Kalanki' than bus A.8. (a) How many days are there from 3rd Bhadra to 4th Falgun? Look up the calendar and answer it.(b) A school begins at 9:45 am and finishes at 4:15 pm. How many hours did the school run?(c) Krishna is 46 years 11 months 29 days old now, How old will he be after 5 years 3 months and 20 days ?(d) Basanti did her homework for 2 hours 30 minutes and 35 seconds per day. How much did time Basanti devote to do her homework for a month ?(e) The total school hours of a school is 6 hours 35 minutes. If there are 7 periods of equal interval and a tiffin break of 45 minutes, how many minutes are there in one period ?(f) A pipe can fill a water tank in 2 hours 20 minutes. How long does it take to fill such 12 water tank ?(g) I am 17069 days old now. Write my age in years months and days.9. Study the following time table and complete it :ActivityTime (12 hours format)Time (24 hours format)Wake up 5:30 amDo Yoga (Exercise) 6:00 amTake bath 7:00 amBreakfast 8:30 amGo to office 9:30 amLunch 1:00 pmReturn home 5:00 pmHave dinner 7: 30 pmGo to bed 9:30 pm158 Acme Mathematics 5
9:30 o'clock17:00 o'clock22:00 o'clock07:00 o'clockProject Work1. Objective : To know the time 24 hours. 2. Materials required :Sticker or picture related to daily activities.Scissors, Chart paper, Gum, colour pencils3. Activities: Collect the sticker or picture related to daily activities. Paste it on the Chart paper and show to your friends and teacher.An example is given below.Acme Mathematics 5 159
1. Fill in the blanks:(a) 3 cm = .............. mm (b) 10 cm = .............. mm(c) 10 mm = .............. cm (d) 20 mm = .............. cm(e) 200 cm = .............. m (f) 700 cm = .............. m(g) 3000 m = .............. km (h) 6000 m = .............. km2. Measure the length of the following objects:(a) (b)It is ..................... It is .....................(c) (d)It is ..................... It is .....................3. Estimate the length (use mm, cm, m or km):(a) Length of white board. .................. .(b) Length of your school building .................. .(c) Length of road near to your home. .................. .(d) Thickness of your eraser. .................. .(e) Height of your Maths teacher. .................. .A BWarm Up Test2 Distance160 Acme Mathematics 5
0 km3 km What is the length of your mathematics book ? How long is your pencil ? What is the length of your white or black board ?We use different units to measure different sizes of length. We use the different tools to measure different size of length.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 156 5 4 3 2 1Measuring tape 100 cmMeasuring tape 12 ft./3.5 mScale 15 cm2.1 Relation between different units of length10 millimetre (mm) = 1 centimetre (cm)100 centimetre (cm) = 1 metre (m)1000 metre (m) = 1 kilometre (km)A. Millimetre and centimetre10 mm = 1 cm1 cm = 10 mmcubitcenti multiply by 10milli divide by 10Is it?Acme Mathematics 5 161
Solved ExampleExample 1 : Convert 15 cm into mm.Solution : 1 cm = 10 mm15 cm = 15 × 10 mm = 150 mmExample 2 : Convert 400 mm into cm.Solution : 10 mm = 1 cm400 mm = 400 ÷ 10 cm= 40 cmExample 3 : Convert 96 cm into cm and mm.Solution : 10 mm = 1 cm96 mm = (96 ÷ 10) cmDivide 96 by 10Now,So, 96 mm = 9 cm and 6 mmB. Centimetre and meter100 cm = 1 meter (m)1 m = 100 cmSolved ExampleExample 1 : Convert 75 m into cm.Solution : 1 m = 100 cm75 m = 75 × 100 cm= 7500 cmDivide 40 by 10. 10 ) 9 6 ( 9 – 9 0 6It is cm.It is mm.cm m× 100÷ 100 Oh! meter is 100 times greater than cm.Remember 1 0 0 × 7 5 5 0 0 7 0 0 7 5 0 0162 Acme Mathematics 5
Example 2 : Convert 1900 cm into meter.Solution : 100 cm = 1 m1900 cm = (1900 ÷ 100) m= 19 mC. Meter and kilometre1000 m = 1 kilometre (km)1 km = 1000 mSolved ExampleExample 1 : Convert 17 km into meter.Solution : 1 km = 1000 m17 km = 17 × 1000 m= 17000 mExample 2 : Convert 12000 m into km.Solution : 1000 m = 1 km12000 m = (12000 ÷ 1000) km= 12 kmExample 3 : Convert 7423 m into kilometre and meter.Solution : 1000 m = 1 km7423 m = (7423 ÷ 1000) kmNow,So, 7423 m = 7 km and 423 m.Remember!× 1000 × 100 × 10km m cm mm÷ 10 ÷ 100 ÷ 1000mm cm m km 100 1 9 0 0 1 9 – 1 0 0 9 0 0 – 9 0 0 0m km× 1000÷ 1000 1000 1 2 0 0 0 12 – 1 0 0 0 2 0 0 0 – 2 0 0 0 0 1000 ) 7 4 2 3 ( 7 – 7 0 0 0 4 2 3Acme Mathematics 5 163
Try to understand the conversion cycle :km cm mm× 100÷ 1000× 100 × 10÷ 100 ÷ 10meter2.2. Multiplication and division of different units of lengthSolved ExampleExample 1 : Multiply: 121 m 3 cm by 5Solution :Example 2 : Divide : 107 km 560 m by 20Solution :Hence the quotient is 5 km 378 mm cm121 3 × 5 605 15 5 km 378 m20 1077 × 1000 +560= 7560156160-140-160- 60-100560×7000 + 560 = 7560 m7 km = 7000 m164 Acme Mathematics 5
Example 3 : A rope is 6 m 48 cm long, find the length of such 50 ropes.Solution : Here the problem is related to multiplication.Now,Thus, total length is 324 metre.Classwork1. Convert the following as indicated:(a) 30 mm (cm) (b) 90 m (cm) (c) 120 mm (cm)(d) 13 cm (mm) (e) 15 cm (mm) (f) 39 cm (mm)(g) 200 cm (m) (h) 700 cm (m) (i) 1900 cm (m)(j) 5 m (cm) (k) 11 m (cm) (l) 17 m (cm)(m) 8000 m (km) (n) 4 km (m) (o) 12 km (m)2. Convert as indicated in the bracket:(a) 5 cm 9 mm (mm) (b) 12 cm 7 mm (mm) (c) 7 m 12 cm (cm)(d) 8 m 80 cm (cm) (e) 1 km 200 m (m) (f) 3 km 500 m (m)3. Measure the length of following objects :Exercise 3.21. Convert the following as indicated:(a) 130 mm (cm) (b) 190 m (cm) (c) 1120 mm (cm)(d) 213 cm (mm) (e) 215 cm (mm) (f) 139 cm (mm)(g) 1200 cm (m) (h) 1700 cm (m) (i) 11900 cm (m)(j) 25 m (cm) (k) 211 m (cm) (l) 117 m (cm)(m) 9000 m (km) (n) 14 km (m) (o) 112 km (m)m cm6 48 × 50 300 2400 324 00Acme Mathematics 5 165
2. Convert as indicated in the bracket:(a) 15 cm 9 mm (mm) (b) 72 cm 7 mm (mm)(c) 9 m 12 cm (cm) (d) 28 m 80 cm (cm)(e) 31 km 200 m (m) (f) 43 km 500 m (m)3. Convert the following units as indicated:(a) 2 m (mm) (b) 13 m (mm) (c) 124 m (cm)(d) 35000 mm (m) (e) 2500 cm (m) (f) 58720 m (km)(g) 125 km (m) (h) 2.5 km (m) (i) 0.8 km (cm)4. Multiply the following:(a) 20 cm 5 mm by 10 (b) 42 m 60 cm by 12(c) 8 m 4 cm by 15 (d) 17 km 7 m by 20(e) 100 km 57 m by 24 (f) 202 km 57 m by 25(g) 335 km 8 m by 30 (h) 98 cm 3 mm by 505. Divide the following:(a) 20 cm 7 mm by 9 (b) 18 m 15 cm by 15(c) 17 m 16 cm by 11 (d) 850 km 540 m by 20(e) 100 km 56 m by 24 (f) 202 km 650 m by 25(g) 335 km 10 cm by 30 (h) 507 km 98 m 15 cm by 456. The speed of motorcycle is 60 km and 500 m per hour. What distance does it covers in 18 hours ?7. The length of a rectangular garden is 18 m and breadth is 14 m .What is the perimeter of the garden ?8. Measure the height of your Mathematics book and find the total height of the all Maths books that your friends have in your class.166 Acme Mathematics 5
9. A rope is 18 m 24 cm long. If it is cut into 12 equal pieces, find the length of each piece .10. Study the figure, a wall of 1 m 44 cm high. Find the height of each brick.11. A water pipe is 3 m 48 cm long. A plumber need 12 equal pieces from this pipe. How long is each piece ?12. In the figure given along side, the land is fenced around it by wooden strip 2 times. Length and breadth of land are 100 meter and 50 meter respectively. Calculate the total length of wooden strip.13. Pukar is a student. The distance from his house to school is given below in the picture. Now, calculate the distance covered by Pukar in 30 days. 800 m125 m100 m 50 mAcme Mathematics 5 167
Warm Up Test1. Fill in the blanks.(a) 2 l = ........... ml (b) 3 l = ........... ml(c) 3000 ml = ........... l (d) 5000 ml = ........... l(e) 1 l 200 ml = ........... ml (f) 2 l 700 ml = ........... ml(g) 5 l 15 ml = ........... ml (h) 7 l 9 ml = ........... ml(i) 2345 ml = ........... l ........... ml(j) 3047 ml = ........... l ........... ml2. Guess the capacity in l and ml.(a) (b) (c)........................ ........................ ........................(d) (e) (f)........................ ........................ ........................(g) (h) (i)........................ ........................ ........................3 Capacity168 Acme Mathematics 5
IntroductionWe measure liquid like water, oil, milk etc. in litres and millilitres using different vessels. The amount of liquid that any vessel can hold maximum is its capacity.3.1 Relation between different units of capacity1000 millilitres (ml) = 1 litres (l) 1000 litres = 1 kilolitre (kl) Solved ExampleExample 1 : Convert 5000 millilitres to litres .Solution : We have, 1000 millilitre = 1 litre5000 millilitre = 50001000 litresThus, 5000 millilitres = 5 litresExample 2 : Convert 14 litres to be millilitres.Solution : We have, 1 litre = 1000 millilitres14 litre = 14 × 1000 millilitresThus, 14 litre = 14000 millilitres3.2 Multiplication and Division of different units of capacityExample 3 : Multiply 32 litres 213 millilitre by 15Solution : l ml32 213 × 15 480 3195 483 195Acme Mathematics 5 169
Example 4 : Divide 22 litres 335 millilitre by 15.Solution : Here,Example 5 : My motorcycle tank can hold 14 litres 500 millilitres of petrol. I filled it 15 times. What is the total amount of petrol that I consumed ?Solution :Thus, I consumed 217 litre 500 millilitre of petrol.Example 6 : A can of milk contains 30 litre of milk. If a milkman distributes it among 12 houses every morning equally, how many amount of milk does each get?Solution : This problem is related to the division.Now,Thus, each got 2 litre 500 ml. l ml15 ) 22 335( 1 litre 489 ml – 15 7335 – 60 133 – 120 135 – 135 ×l ml14 500 × 15 210 7500 217 50012 ) 30 ( 2 litre 500 ml – 24 6000 [6 l = 6000 ml] – 60 00170 Acme Mathematics 5
Classwork1. Match the followings: 1l900ml700ml500ml300ml100ml800ml600ml400ml200ml1l900ml700ml500ml300ml100ml800ml600ml400ml200ml1l900ml700ml500ml300ml100ml800ml600ml400ml200ml1l900ml700ml500ml300ml100ml800ml600ml400ml200ml1l900ml700ml500ml300ml100ml800ml600ml400ml200ml1l900ml700ml500ml300ml100ml800ml600ml400ml200ml1l900ml700ml500ml300ml800ml600ml400ml100ml200ml1l900ml700ml500ml300ml100ml800ml600ml400ml200ml1l900ml700ml500ml300ml100ml800ml600ml400ml200ml1l900ml700ml500ml300ml100ml800ml600ml400ml200ml500 ml900 ml1 l100 ml300 ml600 ml800 ml400 ml700 ml200 mlAcme Mathematics 5 171
2. Read and write the level of juice in each jar.500 ml100 ml1 litre2 litre1500 ml500 ml100 ml1 litre2 litre1500 ml500 ml100 ml1 litre2 litre1500 ml500 ml100 ml1 litre2 litre1500 ml500 ml100 ml1 litre2 litre1500 ml500 ml100 ml1 litre2 litre1500 ml3. Fill in the blanks.160 ml 120 ml+ = ............. ml500 ml 500 ml+ = ............. ml600 ml 320 ml+ = ............. ml870 ml 330 ml+ = ............. ml172 Acme Mathematics 5
460 ml 940 ml+ = ............. ml1 l 580 ml+ = ............. mlExercise 3.41. Which container holds 1 litre?2. How much soup is in the jug? 250 ml 950 ml 800 ml 300 ml3. Which container holds more than 5 litre?1l500ml100mlAcme Mathematics 5 173
4. How many glasses of water were used to fill the jug?1l500ml100ml= 250 ml5. How many jugs of water are needed to fill the bucket?2 litre 4 litre 1 2 3 46. What is the capacity of the bowl?150 ml 100 ml 250 ml 750 ml 3 l7. Convert the following as indicated in the brackets:(a) 6 l (ml) (b) 9 l (ml) (c) 25 l (ml)(d) 4000 ml (l) (e) 23000 ml (l) (f) 900 ml (l)(g) 300 l (kl) (h) 5300 l (kl) (i) 12 l (kl)8. Multiply the following:(a) 12 l 32 ml by 20 (b) 17 l 322 ml by 18(c) 18 l 204 ml by 15 (d) 38 l 546 ml by 12(e) 6 kl 43 l 309 ml by 10 (f) 76 kl 350 l 160 ml by 8174 Acme Mathematics 5
9. Divide the following:(a) 9 liter 32 ml by 8 (b) 15 liter 324 ml by 12(c) 28 liter 110 ml by 15 (d) 738 liter 540 ml by 20(e) 3 liter 500 ml by 10 (f) 5 liter 264 ml by 810. Arun's family consumes 105 l of milk in a month:(a) What is the total consumption in 10 months ?(b) What is the consumption in a day ?11. Rama's family consumes 20500 l of water in a month:(a) What is the total consumption in a year ?(b) What is the total consumption in a day ?12. A car consumed 1 l 500 ml of petrol for 20 km. If the car covered the distance of 100 km, find the amount of petrol consumed by the car.13. A company provides 15 l 500 ml diesel for their officers per month. If there are 95 officers, find the amount of diesel per year.Acme Mathematics 5 175
Project Work1. Objective : To know the capacity of the object.2. Materials required : 10 different object that can hold liquid, measuring jar3. Activities: Fill the liquid to all the objects and measure its capacity with the help of measuring jar.SN Name of the Objects Capacity in litre and millilitre1.2.3.4.5.6.7.8.9.10.176 Acme Mathematics 5
1. Fill in the blanks:(a) 2 kg = ............... g (b) 4 kg= ............... g(c) 3000 g = ............... kg (d) 5000 g = ............... kg(e) 1 kg 500 g = ............... g (f) 2 kg 625 g = ............... g(g) 1234 g = ............... kg ............... g(h) 6789 g = ............... kg ............... g2. Guess the weight in kg or g:(a) (b) (c).................... .................... ....................(d) (e) (f).................... .................... ....................3. Study the given information and write the weight.Warm Up Test5 kg 3 kg 8 kg 2 kg4 WeightAcme Mathematics 5 177
178 Acme Mathematics 5
Revision What is the weight of your mathematics book ? What is your weight ? Can you guess the weight of your mathematics teacher ? We use different units to weigh different objects We use different tools to measure the weight of objects.4.1. Relation between different units of weightThe weight of different objects are given in different units but they are related to each other. Their relation is given below,1000 milligram (mg) = 1 gram (g)1000 gram (g) = 1 kilogram (kg)100 kilogram (kg) = 1 quintal (qt)10 quintal = 1 tonne (t) or, 1000 kg = 1 tonnetonne kg g mg× 10÷ 10× 100 × 1000 × 1000÷ 100 ÷ 1000 ÷ 1000QtSolved ExampleExample 1 : Convert 8000 mg to gram.Solution : We have, 1000 mg = 1 g8000 mg = 80001000 gThus, 8000 mg = 8gAcme Mathematics 5 179
Example 2 : Convert 12 kg to gram.Solution : We have, 1 kg = 1 × 1000 gram12 kg = 12 × 1000gramThus, 12 kg = 12000gramExample 3 : Convert 45000 kg to tonne :Solution : We have, 1000 kg = 1 tonne45000kg = 45×1000 kg = 45 tonne4.2. Multiplication and division of different units of weightExample 4 : Multiply 12 kg 223 g by 15.Solution :Example 5 : Find the weight of 230 shirts, if the weight of one shirt is 550 gram.Solution : Here, weight of 1 shirt = 550 g.weight of 230 shirt = 230 × 550 gweight of 230 shirt = 126500 g = 1265001000 kg = 126.5 kgThus, weight of 230 shirts is 126.5 kg.Oh ! I remembered :1000 kg = 1 tonnekg g12 223 × 15 180 3345 183 345180 Acme Mathematics 5
Example 6 : If the weight of 45 bag of rice is 1350 kilogram, find the weight of each bag.Solution : Here, weight of 45 bag = 1350 kilogramweight of 1 bag = 135045 kilogramweight of 1 bag = 30 kilogramThus, weight of each bag of rice is 30 kilogramClasswork1. Add the weight and tick the correct option.1 kg 12 kg 12 kg 12 kg 12 kg1 kg2 kg3 kg1 kg 14 kg 14 kg 14 kg 14 kg1 kg2 kg3 kg1 kg 1 kg 12 kg 14 kg 14 kg1 kg2 kg3 kg12 kg 12 kg 12 kg 14 kg 14 kg1 kg2 kg3 kgAcme Mathematics 5 181
2. Write the weight of the objects:1 kg1 kg1 kg1 kg1 kg 1 kg1 kg 1 kg 1 kg1 kg1. Write True or False for the following.(a) Milligram in smaller unit than kg.(b) A kg is equal to 1000 g.(c) A quintal is equal to 500 kg.(d) Thousand kg is equal to one tonne.2. Guess and write the weight.Exercise 3.3182 Acme Mathematics 5
3. Change the following as indicated in the bracket:(a) 15 kg (gram) (b) 8.2 kg (gram) (c) 0.12 kg (gram)(d) 120000 g (kg) (e) 22950 g (kg) (f) 550 g (mg)(g) 130 g (mg) (h) 2 kg (mg) (i) 305 kg (mg)(j) 130 kg (qt) (k) 30 qt (tonne) (l) 35 qt (kg)4. Multiply the following:(a) 291 g 76 mg by 18 (b) 43 kg 180 g by 15(c) 22 kg 25 g by 14 (d) 50 kg 45 g by 25(e) 12 qt 2 kg by 20 (f) 48 qt 187 kg by 22(g) 12 qt 7 kg by 30 (h) 45 tonne 5 qt by 355. Divide the following:(a) 290 g 70 mg by 9 (b) 180 g 130 mg by 10(c) 202 kg 25 g by 12 (d) 50 kg 40 g by 15(e) 102 kg 472 g by 8 (f) 48 qt 86 kg by 7(g) 202 qt 88 kg by 16 (h) 56 tonne 8 qt 5kg by 216. In a day, Manju's family needs 2 kg 350 g of rice. How much rice does the family need for 30 days?7. A bag contains 30 kg 700 gram of rice. Find the weight of such 123 bags.8. In a month, a hotel needs 32 kg 520 g of sugar . How much sugar does the hotel need for a day?9. Prem takes 62 kg 800 gram of fruits and distributes equally among 25 students. What is the share of each student?10. A chocolate factory produces 3 quintals of chocolates in a day. A packet can hold 750 gram only. How many such packets are needed to pack the chocolates?Acme Mathematics 5 183
1. Objective : To know the weight of the objects.2. Materials required : Weighing machine and some different objects.3. Activities: Collect 10 different objects around you. Take their weight and complete the tableSN Name of the Objects Weight in kg. and g.1.2.3.4.5.6.7.8.9.10.Play a Game(i) Take your students to your Math Lab.(ii) Show the weight of small object with digital weighing machine (balance) in mg.(iii) Let weigh some of the students' weight in kg.(iv) Then let them guess the other students' weight at first and then weigh their body.(v) Repeat such activity which makes students guess weight properly (near to correct).Project Work184 Acme Mathematics 5
1. Sita has Rs 3000 and her father gave her Rs 100.(a) Find the total amount of money she has.(b) If she gave Rs 2000 to her sister, how much money is left with her now?2. Answer the following questions.(a) How many days are there in a year?(b) Convert 2 hours 40 minutes into minutes.(c) Calculate your age in years, months and days.3. Karishma drives a car 2 hours 30 mins 50 sec everyday.(a) Find the time taken by Karishma in 1 day in seconds.(b) Find how much time she drives in 5 days.4. If 2 45 is a fractions.(a) Show the given fraction in diagram.(b) What kind of fraction is it?5. Rita bought 449 kg of oranges and 229 kg of apples. Find the total amount of fruits she bought.6. 45 and 35 are given fractions.(a) Write the types of fractions.(b) Find out which one is greater.7. Study the given information:Pokhara Muglin90 km 750 m 110 km 945 mKathmanduFind the total distance between Pokhara and Kathmandu.8. Rita's school is 2 km away from her house.(a) Calculate the distance in centimetres.(b) Multiply : 9 km 500 m 40 cm by 3.Mixed ExerciseAcme Mathematics 5 185
9. (a) Write 04:45 PM in 24 hour system.(b) Raj takes 2 hours 25 minutes to plant flowers in a garden. How long will he take to plant in such 3 gardens?10. Observe the given clock.(a) Write the time in 12-hour system.(b) Write the time in 24-hour system.11. (a) Multiply : 24 m 78 cm by 9.(b) Convert 128 l 250 ml into ml.(c) The weight of a sack of a flour is 12 kg 875 gm. Find the total weight of such 7 sacks.12. How many days are there in 5 weeks.(a) 25 (b) 35 (c) 45 (d) 5513. Add: 3 weeks 6 days and 4 weeks 3 days14. (a) Shreya works 6 hours and 30 minutes in a day. How much time does she work in 4 days?(b) The length of a stick is 78 cm 4 mm. If it is equal by divided into 7 parts, what is the length of each part?(c) Multiply : 46 l 800 ml by 3.(d) Divide : 38 kg 374 gm by 7.15. (a) Write 18 : 40 in 12 hour clock system.(b) Convert : 5 km 300 m into meter.(c) Add :16. (a) How many kg are there in 75,000 gram.(b) Convert : 1950 g into kg and g.17. (a) Divide : 130 paisa by 5.(b) Convert 21 days into weeks.(c) Add 750 ml and 675 ml(d) Convert 14 minutes 28 seconds into seconds.cm45mm2+ 3186 Acme Mathematics 5
18. Study the given road. 4 km 400 mABCD2 km 700 m 1 km 200 m(a) How far is place 'D' from place 'B'?(b) Which place is far from place 'B'?(c) How far is the place 'D' from place 'A'?19. Divide : 16 km 190 m and 19 cm by 9.20. Study the given rectangle.(a) Measure its length.(b) Measure its breadth.(c) How much longer is length than breadth?21. A sugar factory produces 45 quintals and 15 kg of sugar in a day. A sack can hold 35 kg only. (a) Convert production in kg.(b) Convert the capacity of a sack in the quintal.(c) How many such sacks are needed to pack the sugar per day?22. Angle's family consumes 105 litres of milk in a month:(a) What is the consumption in a day?(b) Calculate the total consumption in a year.(c) If a litre costs Rs 110, calculate expenditure in a week.23. Weight of the objects are given below.(a) Which is heavier?(b) Which is 100 g less than pineapple?(c) What is total weight?AB CD2 kg 100 g1 kg 400 g2 kg5 kg 700 gAcme Mathematics 5 187
24. Fill in the blanks.(a) 1 hour = ............ minutes.(b) 2 weeks = ............ days.(c) 24 months = .............. years.25. The table below shows the departure time table of the different buses from Narayangadh to Kalanki, Kathmandu.Narayangadh Bus - A Bus - B Bus - C1. Narayangadh 5:30 6:10 9:302. Muglin 6:20 7:00 10:103. Malekhu 7:00 9:10 12:354. Naubise 8:10 10:10 2:005. Kalanki 9:00 11:20 2:55(a) When did Bus - A reach Malekhu?(b) Where is Bus - C when Bus - B is in Naubise?(c) Which bus takes less time to reach Kalanki?(d) Which bus do you choose to reach 'Naubise at 2 o'clock in the afternoon?26. A story book is 20 cm 5 mm long and 15 cm 6 mm broad.(a) Convert its length in mm.(b) Convert its breadth in cm.27. (a) How many days are there in a year?(b) Convert 5 kg 265 gm into gm(c) Subtract the following:gm mg25 865– 13 296188 Acme Mathematics 5
EvaluationTime: 55 minutes Full Marks: 231. (a) How many months are there in 1 year? [1](b) How many minutes are there in 2 hours? [1](c) Write the time : Quarter past nine. [1]2. (a) Make a watch displaying one O'clock. [1](b) Madhu goes to school at 9:30 a.m. and returns back at 6:00 p.m. His lunch time is 12:00 noon to 12:45 P.M. Rewrite these timings in 24 hours clock format. [2](c) Add: Hrs. Min. Sec.5 35 50+ 4 15 20 [2](d) Multiply : 5 years 8 months 20 days by 5. [2]3. (a) How many minutes are there in 2 hours< [1](b) AddM m. cm. mm.6 35 50+ 4 50 15[2](c) A tap can fill a water tank in 30 minutes 45 second, Find the total time to fill such 5 tanks. [2](d) DivideM [2] 4. (a) Study the give watch and write the time in 12- hour clock system. [1] (b) How many weeks are there in a year ? [1] (c) A pot can hold 2 kg 150 gm of sugar. How much sugar will be held by 6 such pots altogether ? [2](d) Subtract: 25km 425m from 40 km 875m [2]3 8kg 400 gmAcme Mathematics 5 189
Warm Up Test1. What is the perimeter of each shape?[Note : length and breadth of each room is 1 cm.](a) (b)Perimeter = cm. Perimeter = cm.(c) (d)Perimeter = cm. Perimeter = cm.(e) (f)Perimeter = cm. Perimeter = cm.5 Perimeter190 Acme Mathematics 5
5.1.Perimeter of a rectangleObserve this rectangle. Its length is 10 cm and breadth is 8 cm. Its total length from A to A is given below.A to A = AB + BC + CD + DA= 8 cm + 10 cm + 8 cm + 10 cm= 2 × 8 cm + 2 × 10 cm= 16 cm + 20 cm= 36 cmThus, the total length (boarder) of the rectangle is 36 cm.The total length of the boarder of any plane figure is called its perimeter.Perimeter of a rectangular in terms of length (l) and breadth (b).Consider the given rectangle ABCD.Now,Perimeter of rectangle ABCD.= AB + BC + CD + DA= length + breadth + length + breadth= 2 × length + 2 × breadthThus, the perimeter of a rectangle = 2 (length + breath)5.2. Perimeter of a squareIn the figure, PQRS is a square. Its sides are PQ, QR, RS, SP and PQ = QR = RS = SP.Now, perimeter of square PQRS= PQ + QR + RS + SP= l + l + l + l= 4 × lengthThus, the perimeter of a square = 4 l8 cmA 8 cm BD C10 cm 10 cmD lengthA BClengthbreadth breadth= ===SP QRll(l= length)Acme Mathematics 5 191
Solved ExampleExample 1 : A rectangular piece of paper has length 16 cm and breadth 12 cm. Find its perimeter.Solution : Here,Length of paper = 16 cmBreadth of paper = 12 cmNow, Perimeter of rectangular piece of paper= Length + Breadth + Length + Breadth= AB + BC + CD + DA= 16 cm + 12 cm + 16 cm + 12 cm= 56 cmPerimeter of a paper is 56 cm.Example 2 : A rectangular park is 70 m long and 30 m wide. Find the distance covered by a man around it in 10 rounds.Solution : Here, Total distance = 10 × perimeter of the park.Length of park = 70 mBreadth of park = 30 mPerimeter = 2 × length + 2 × breadth= 2 × 70 m + 2 × 30 m= 140 m + 60 m= 200 mNow, 10 times perimeter = 10 × 200 m= 2000 m [1000m = 1 km]= 2 kmThus, the distance covered by a man is 2 km.12 cm16 cmDACB30 m70 mDACB192 Acme Mathematics 5
Classwork1. Write the perimeter of the following figures.perimeter = .......... cm perimeter = .......... cm perimeter = .......... cm 1 cm1 cmExercise 3.51. Write the perimeter of the given figures:(a) 3 cm3 cm2 cm 2 cmIts perimeter = ................. cm(b) 2 cm2 cm2 cm 2 cmIts perimeter = ................. cm2. Complete the table:Length (l) Breadth (b) l + b 2(l + b)2 cm 1 cm3 cm 2 cm4 cm 2 cmAcme Mathematics 5 193
4 cm 3 cm5 cm 3 cm3. Complete the table:Length (l) Breadth (b) 4 l 4 b4 cm 4 cm3 cm 3 cm5 cm 5 cm10 cm 10 cm12 cm 12 cm4. Calculate the perimeter of the given rectangles:(a) (b) (c)5. Calculate the perimeter of the given squares:(a) (b) (c) 6. Draw rough figure of rectangle from the given data and find the perimeter.(a) Length = 8 cm and breadth = 6 cm(b) Length = 12.5 cm and breadth = 8.5 cm(c) Length = 20 cm and breadth = 16.5 cm(d) Length = 50 cm and breadth = 45 cm7. Find the perimeter of the given squares when:(a) Side = 4.5 cm (b) Side = 6 cm8 cm5 cm4 cm6 cm12 ft10 ft3 ft5 ft6 ft194 Acme Mathematics 5
(c) Side = 15 cm (d) Side = 25 cm(e) Side = 16.5 cm (f) Side = 22.5 cm8. Find the perimeter of the given rectangular picture.[Hint : measure its sides]9. (a) Find the perimeter of the given rectangle.9 cm4 cm(b) Find the perimeter of the given chessboard.10. A man has 180 m of fence for a rectangular garden. If his garden is 10 m long and 8 m wide, how many times he can round it ?11. How long wire is needed to fence a square field of 12 m long 4 times ? 10 m8 mAcme Mathematics 5 195
1. Objective: To find the perimeter of objects by counting squares.2. Materials required: Scales Colours3. Activity: Join the dots and make different shapes. 4. An example is given below: (1 room = 1 cm2) Perimeter of figure A is 22 cm.AProject Work196 Acme Mathematics 5
Warm Up Test1. What is the area of each shape?[Note : Each small square room represents 1 square cm.](a) (b) (c)Area = Sq.cm Area = Sq.cm Area = Sq.cm(d) (e) (f)Area = Sq.cm Area = Sq.cm Area = Sq.cm(g) (h)Area = Sq.cm Area = Sq.cm6 AreaAcme Mathematics 5 197
2. Find the area of each shape.[Note :Each small square room represents 1 square cm.](a) (b) (c)(d) (e) (f)(g) (h) (i)(j) (k) (l)198 Acme Mathematics 5
IntroductionLook at the two carpets:Carpet-A Carpet-BBy which carpet the floor is covered more? Why?Carpet – A has covered the floor (surface) more.The amount of surface covered by the closed figure is called the area of the figure.Unit of areaTo measure small areas like a rectangle (book) or square we use a square of side 1 cm as the unit of area. Here is a square side 1 cm.We say that it has an area of 1 square centimetre.We also write this as 1 sq. cm (or 1 cm2). Here is a figure covered by 6 such squares.Therefore its area is 6 cm2.6.1. Area of a rectangleLet, ABCD be a rectangle. Divide AB into 5 equal parts such that each part is 1 cm. Divide AD in to 4 equal parts such that each part is 1 cm. The area of each small square is 1 cm2. The area of rectangle is 20 sq. cm (or 20 cm2).1 cm1 cm1 sq. cm.1 cm1 cm1 cm2 1 cm21 cm2 1 cm21 cm2 1 cm2Acme Mathematics 5 199
Quick way of calculating area of a rectangle.Here, Number of square along length = 5Number of square along breadth = 4Also we have, length × breadth = 5 × 4Area of rectangle = 20 sq. cm2Now, we know that :Area of a rectangle = length × breadthIn short, A = l × b6.2. Area of squareSquare is a rectangle whose length and breadth are equal.So, Area of square = length × length= (length)2In short, A = l2Solved ExampleExample 1 : The length and breadth of a rectangle are 12 cm and 10 cm. Find its area.Solution : Here, Length of rectangle (l) = 12 cmBreadth of rectangle (b) = 10 cmArea of rectangle (A) = ? Area (A) = Length (l) × breadth (b)= 12 cm × 10 cm = 120 cm2Thus, the area of rectangle is 120 sq. cm.Example 2 : Find the area of the given handkerchief whose each side is 20 cm long.Solution : Here, handkerchief is a square shape.So, Area of handkerchief = (side)2= (20 cm)2= 400 cm2 = 400 sq. cmThus, the area is 400 sq. cm.AD5 cm B4 cmCAD3 cm BC10 cm 12 cm 20 cm 20 cm 200 Acme Mathematics 5