Math Class IV Measurement Length Mass Volume PDF

os remem Chapter Four Conversion of large metric units of length into small units The measurements of length ca...

os remem Chapter Four Conversion of large metric units of length into small units The measurements of length can be converted from large metric Measurements of length, units to small units. The relationships of metric units of length are used in converting the units according to the needs. Use mass and volume multiplication (x) method when converting larger units to — units. Introduction ‘ YY In this chapter, you will learn the metric ements of length, mass, and volume. You will also lean Nodonvert add, Samet Convert 3 m into centimetres. ©* and subtract the measurements. The eons developed Solution © will be used in constructions, tailo ras ooking, hospitals, \ agriculture, designing and many other: plications. Use the relationship between metre andic timetre. 1m=100 ‘ma ideas oo we = 300 cm Therefore, 3 m is e x to:300 cm. S ys Conversion of méetri units of length wv The basic sta d metric unit of length is metre (m). Other commonly ws metric units of length are millimetres (mm), centime cm) and kilometres (km). Length measurements can be co: d from one metric unit to another. Cometh 250 m into metres. Solut ban. owing table shows the relationships of metric units of e relationship between kilometre and metre. Chitin \centimetre \decimetre| metre |\decametre |hectometre |kilometre 4 km = 1000m (mm) (sm) (dm) \(m) (dam) (hm) (km) X 5 km = 1000 x 5m 1 = 5000 m 10 [1 | | 100 10 dq | Add 5000 m and 250 m. Thus, 5000 m + 250 m = 5,250 m 1,000 100 10 {1 | Therefore, 5 km 250 m is equal to 5,250 m. 10,000 ~—- 1,000 100 10.1 | 100,000 10,000 1,000 100 100 4 1,000,000 100,000 10,000 1,000 100 10 11 eee  Revision Exercise. The length of a ruler is 100 centimetres. Whatis thisi.._ in metres? te [emt Lomb TAs) SAS! 330 600. Acontainer weighs 2 tonnes and 300 kilograms. Convert — 53 532 +130 800 this mass into kilograms.. A factory produces 345 litres of sunflower oil every. day. How many millilitres of oil will the factory produce in one 3. Lome km week? 731 116 12 349. A maize sack weighs 18250 grams. Convert this mass +123 882 +4 651 into kilograms. 14. Two cows produce milk as follows: the first cow produces 2 litres and 353 millilitres andthe second cow produces 5\ m cm km m cm 5 litres and 452 millilitres: Find the total volume of milk 240 64 14 700 00 produced by the two:cows. + 660 95 -13 860 95 15. Which measurement is the largest among 7500 grams, 3 tonnes, 4000.kilograms, and 2350 milligrams? Give reasons for your answer? 7 t. -kg kg g mg 12 555 19 552 701. Abucketof water has a volume of 10 litres. If 5534 millilitres of water have been added to the bucket, how many more - 8 227 = 41 910 900 millilitres of water are needed to fill the bucket? mals A trader purchased products with the following masses: 76320 grams of flour, 61000 grams of rice, and 7200 grams 9. t kg g mg of salt. What is the total mass of the products purchased? 15 821 800 697 + 83 260 333 222 ihe L mL 8. L mL 9. L mL | Exercise 13 100 100 330 800 75 426 —15 900 -—130 600 — 53 532. Agas cylinder has a volume of 18 litres. If 13 litres are _— used, how many litres will remain? 2. How many 500 mL water bottles are needed to fill a 20-litre oe mL 4.0 Lomb 12a Le me bucket? us 41 20 93 90 ~ 180 3. A1 litre bottle contains 750 mL of milk. How much more is - 8 74 -— 16 37 -45 382 needed to fill the bottle? 4. Lina, Sanka, and Imani filled a water bucket. If Lina put in 5 litres, Sanka 2 litres and Imani 3 litres, what is the total volume of water in millilitres that they all put in together? Word problems involving measurements of volume 5. Mbale drank 3 litres of water and Senga drank 2,000 Word problems involving measurements of volume highlight the millilitres of water. Find the difference in the amount of water use of metric units of volume in real-life situations. They reflect they drank. the activities performed every day. 6. A water well produces 24,758 litres and 580 millilitres of water per day. If 17,900 litres and 846 millilitres are used every day, how much water remains? A cow produces 20 litres of milk every day. How many millilitres of milk will the cow produce in 3 days? Learning measurements of length, mass and Solution volume through reliable online materials 1 Day: 20 litres Description 3 days =3 x 20L=60L Use various reliable programs such as Khan Academy to learn more about measurements of length, mass and volume. Convert 60 L into millilitres as follows. 1L=1000 mL 60L=60 x 1000 mL Summary =60000 mL 1. The basic unit of length is metre (m) 2. The basic unit of mass is gram (g) So, the cow will produce 60,000 millilitres of milk in 3 days. 3. The basic unit of volume is litre (L)  6L 550 mL + 3 L 160 mL= L mL 2. Subtract litres: 80 L- 45 L = 35 L. 80 370 Solution Write 35 in the L column. E mL -— 45 160 6 550 35 210 +3 160 Therefore, the answer is 35L 210mL. 9 710 Exercise 11 He E mL L mL 2. Lome 15 350 415 205 600 40 78 426 — 10 370 + 27 8 + 350. 250 +55 542 4 L ombL Lo omL 6 Lomb Solution 4 750 17 800 20 920 L mL 316 250 + 3 366 14 112 14 1350 + 15 101 +13 126 - 10 370 4 980 Subtraction of measurements of volume Metric units of volume with the same measurements can be Ey 10 subtracted. Start by subtracting smaller units followed by larger units. LomL L mL 3. L mL 66 89 500 50 68 423 -52 48 — 300 250 -41 544 L 80mL 370-—L 45mL160 = Solution Steps L; mL L mL L mL 6. L mL 1. Subtract millilitres: 80 370 45 513 46 48 72 490 370 mL -—160 mL =210mL. — 16 701 -—33 35 -37 541 — 45 160 Write 210 in the mL column. 210 Measurements of volume | Exercise 10 The basic metric unit of volume is the litre (L). Other commonly i. How many millilitres are in the following volumes? used metric unit of volume is millilitre (mL). The following is the (a) 9 litres (b) 12 litres (c) 3 litres (d) 5 litres relationship between the two units. 2. Convert the following volumes into litres. 1 litre (L) = 1,000 millilitres (mL) (a) 14,000 mL (b) 6,000 mL (c) 2,000 mL (d) 8,500 mL Conversion of measurements of volume 3. A bucket has a volume of 20 litres. What is this volume in The metric measurements of volume can be converted based on millilitres? the relationship between the given units. 4. Awater tank is filled with 6 buckets of 20 litres each. How many millilitres of water does the tank hold? How many millilitres are in 9 litres? Addition of measurements of volume Metric units of volume with the same measurements can be Solution added. Start by adding smaller units followed by larger units. Use the relationship between millilitres and litres. To convert litres to millilitres; multiply the number of litres by 1000. 1 litre = 1000 mL 9L=9x1000mL Therefore, there are 9000 millilitres in 9 litres. Solution Steps oo L mL~ | 1.Add millilitres: How. many litres are in 18000 millilitres? 3 600 600 mL + 450 mL = 1050 mL. Convert Diivtion 4 450 1050 mL to get 1 Land 50 mL. a — ; a ait Ww Write 50 in the mL column and take1 litre To convert millilitres to litres, divide the number of millilitres | 50 from theliie colon by 1000. 1000 mL =1 litre L ml 2 Add litres: 1+ 3L+4L=8L. Write 8 Multiply by 18 both sides to obtain 3 600 in the column of L. 18 x 1000 mL=18L +4. 450 18000 mL = 18L 7 =18L 8 ___50 _ Therefore, there are 18 Lin 18000 mL. _ Therefore, the answer is 8 L 50 mL.  Solution (a) Mass of rice = 54 kg 1. t omg 8 kg g Mass of wheat = 49000 g 220 26 = 3370 14 239 Convert the mass of the sack of rice into kilograms as follows. -—4 114 -— 13 250 -12 910 1kg=1000g 54kg =54x1000g = 54000 g 4. t kg 9% kg dag 6. kg g The sack of rice weighs 54000 g while that of whéat weighs 4 54 20 600 16 = 860 49000 g. Therefore, the sack of rice is heavier than that of -2 340 -6 560 -13 900 wheat. (b) The difference in their masses is 54000 g—49000 g=5000 g. 7. t kg cg & 9Q mg 9. hg g Therefore, the difference in mass is 5000 g. 10 143 64 40 720 15 85 im 337 27 -15\y~670 -12 90 Exercise 9 1. Which is heavier between 2,000 g of salt and 20 kg of 10. kg cg mgvii-* t g mg 12. hg g cg cotton? 70 40 60 6 800 660 4 31 12 2. A fisherman caught fish weighing 3 kg and 500 g. What is -15 12.38 -3 280 830 -1 81 4 the mass of the fish in grams? 3. Elia weighs 32 kg, Zawadi weighs 300 hg and Furaha weighs 30,750 g. (a) Who has the greatest mass? Word problems involving measurements of mass (b) Find the difference in mass between Elia and Furaha in Word problems in measurements of mass show how the metric grams. units are used in real-life situations. 4. Buholo bought 2 kg of millet flour, 1 kg of sugar, and 500 g Examp le } of powdered milk. How many grams of items did she buy?... l 5. Find the total mass of five loaves of bread in grams if each A sack of rice weighs 54 kg while a sack of wheat weighs loaf has a mass of half a kilogram : 49,000 g. 6. The mass of a chicken is 3 kg. After preparing it for cooking, (a) Which of the two sacks is heavier? its mass was 2 kg 750 g. How many grams did its mass (b) Find the difference in their masses. decrease? Give reasons for the decrease in mass. Guam) Solution t kg g Steps 1. Subtract grams: tonne kg 6 199 1550 550 g-750 g, it is not sufficient. 12 740 _9 300 750 Take 1 kg from 200 kg and -6 420 es convert it into 1000 g. = Add grams: 1000 g + 550g = 1550 g. Solution Steps Then, subtract grams: 1550 g — 750 g = 800g. Write 800 t kg 1. Subtract kilograms: in the g column..Remember that, 12 740 740 kg — 420 kg = 320kg. 199 kg remained in the kg column -6 420 Write 320 in the kg column. 320 t kg g 2. Subtract kilograms: 5 200 1550 199 kg - 300 kg; is not sufficient. —~2 300 750 Take 1 tonne from 6 tonnes and t kg 2. Subtract tonnes: 899 800 convert it into 1000 kg. 12 740 12 tonnes — 6 tonnes =6 tonnes. TO Add kilograms: -6 420 Write 6 in the tonnes column. 1000 kg + 199 kg = 1199 kg. 6 320 Then, subtract kilograms: 1199 kg — 300 kg= 899 kg. Write Therefore, the answer is 6 tonnes 320kg. 899 in the kg column. Remember that, 5 tonnes remained in the tonnes column.. t kg g 3. Subtract tonnes: tonne kg g 5 1199 1550 5 tonnes — 2 tonnes = 3 tonnes. 6 200 550 _2 300 750 Write 3 in the tonnes column. -2 300 750 3 899 800 Therefore, the answer is 3 tonnes 899 kg 800g.  | Exercise 7 Solution | Steps t kg | 1.Add kilograms: 1. t kg 2 kg dag 3. g mg 6 750 4 715 2 175 a 850 850 kg + 350 kg=1200 kg. Convert +5 250 +8 25 +3 945 1200 kg to get 1 tonne. Write 200 in the +3 350 kg column. Take 1 tonne to the tonnes es column. 4. hg dg 5. t dag 6 kg g t kg | 2.Add tonnes: 19 375 4 500 3 800 + ao 1 tonne + 4tonnes + 3. tonnes =8 tonnes. + 14 765 +7 660 +3 434 Write 8 in the tonnes column. +3 350 8 200 kg g 8 t_. eg mg Therefore, the answer is 8 tonnes 200 kilograms. 3 460 12/216 9 50 90 10 +1 630 +/5- 801 6 25 70 30 + 20 55 30 t kg ie t kg g 10. 470 40. 80 30 14 365 9 896 735 +17 675 71. 14 40 9 475 +8 250 289 +20 22 70 +3 300 Solution t kg Subtraction of measurements of mass 10 470 +17 675 Metric units of mass of the same measurement can be subtracted. Start by subtracting smaller units followed by larger units. In 28 145 regrouping the units, the relationship between the given units should be considered. (b) Use the relationship between grams and kilograms. Addition of measurements of mass 1000 g =1kg Metric units of mass of the same measurement can be added. Start 6 x 1000 g=6 x 1kg by adding smaller units followed by large units. The relationship between the given units should be considered. =6 kg Therefore, 6,000 g=6 kg. Convert the following measurements: (a) 89 kilograms into grams (b) 58,000 grams into hectograms (c) 6,500 kilograms into tonnes Solution Steps (d) 4 tonnes into kilograms g9 mg 1. Add milligrams: A farmer harvested maize weighing 5,070,000 grams. a ovo 225 mg + 370 mg =595 mg. What is this mass in.kilograms? —— Write 595 in the mg column. A vehicle has a mass of 15 tonnes. Convert this mass 595 into hectograms. g mg 2. Add grams: A car carries. 1,200 kilograms of beans and maize which 4 225 49+4g=8g. weighs 5 tonnes, find the difference between the mass of beans and that of maize in kilograms and grams. +4 \370 Write 8 in the g column. Mwanaisha is going to prepare three different sorts of 8 595 biscuit. The following are the recipes. _ Therefore, the answer is 8 g 595 mg. Chocolate biscuits Oat biscuits Nut biscuits sugar 120g sugar 140g sugar 110g butter 60 g butter 170 g butter 160 g wheat flour 100 g oats flour 80 g wheat flour 230 g cocoa powder 20 g powdered milk 30 g nuts powder 60 g (a) What is the total mass of the ingredients for each recipe. (b) How much sugar, butter, nuts and flour ingredients are needed to make all of three types of biscuits. Measurements of mass Conversion of measurements of mass The mass of an object is measured in metric units which include Large metric units of mass can be converted into small units. tonnes (t), kilograms (kg), hectograms (hg), dekagrams (dag), Similarly, small metric units of mass can be converted into large grams (g), decigrams (dg), centigrams (cg) and milligrams (mg). units. The conversion is done by considering the relationship between the metric units involved. The following pictures show the example of a weighing balance. © Convert 4 kg into grams. ? Solution Use the relationship between kilogram and grams (a) 1 kg = 1000g 4kg=4~x 1000g Relationships of metric units of mass = 4000 g The following table shows the relationships of metric units of Therefore, 4 kg = 4000 g: mass. (b) Convert 7,000 g into kilograms. | milligram | centigram decigtam gram | dekagram|hectogram | kilogram 1000g =1kg |(mg) (cg) (dg) (g) | (dag) (hg) (kg) 7 x 1000g =7 x 1kg 1 | | 7000 g=7kg 10 11 | Therefore, 7,000 g = 7 kg 100 10 1 | 1,000 — '100 10 1 | 10,000... 1,000 100 10 1 100,000 10,000 1,000 100 10 1 Convert the following measurements into kilograms. "4,000,000 100,000 10,000 1,000 100 10 1 _ (a) 2 tonnes (b) 6,000 g 1 tonne (t) = 1000 kilograms (kg) Solution (a) Use the relationship between tonnes and kilograms. From the table, the relationship between measurements can be established. For example, the following relationships can be 1 tonne =1000 kg easily established: 2 x tonne =2 x 1000 kg (a) 1 gram=1000 milligrams = (b) 1 centigram=10 milligrams =2 x 1000 kg (c) 1 gram = 100 centigrams (d) 1 kilogram = 1000 grams Therefore, 2 tonnes = 2000 kg. Word problems involving measurements of length Ashura walked a distance of 6928 m which is less than 8700 m. Thus, Kija walked a longer distance than Ashura. The length of a football ground is 100 metres. Convert this (b) The difference in the distances walked is; length into centimetres. 8700 m — 6928m =1772 m. Solution Therefore, the difference in distance walked is 1772 m. Convert 100 m into centimetre as follows: 1m=100cm 100 m= 100 cm x 100 | Exercise 5 - = 10000 cm. The length of the Standard Four classroom is 6 m and 75 cm. Therefore, the length of the football. ground is 10,000 cm. Convert the length of the classroom into centimetres. 2. The distance from Mtakuja market to Lake Tanganyika is 12 km. How many metres are equivalent to this distance? Kija walked a distance of 8 kilometres and 700 metres from 3. Bilali bought a piece of fabric of length 50 m while Kulwa his home to the open market. Ashura walked a distance of bought a piece of fabric of length 200 cm. Who bought a longer piece of fabric? Give reasons for your answer. 6,928 metres from school to her home. (a) Who walked a longer distance? 4. The distance from the school to the dispensary is 800 m. (b) Find. the difference in metres between the distances The distance from the school to the market is 1 km. Find the walked by Kija and Ashura. difference between the two distances. Solution 5. The distance from the Standard Four classroom to the (a) Kija walked 8 km and 700 m. Convert 8 km and 700 m into football ground is 7,000 cm. The distance from the Standard metres as follows. Four classroom to the Head teacher’s office is 70 m. Which distance between the two is longer? 1 km = 1000m 8 km = 8 x 1000m 6. Bahati walks 3 km and 500 m every morning, and 1 km and 500 m every evening. Doto walks 5 km and 100 m every = 8000m morning. Who walks a longer distance? Add 8000m and 700m. 7. Acertain road has a length of 3 kilometres and 500 metres. 8000 m + 700m =8700m. What is the length of the road in metres?  km om 3. Subtract kilometres: km m cm_ | 3. Subtract kilometres: 11 1200 11km — 4 km =7 km. Write 7 in the 9 1159 155 9 km — 4 km=5 km. Write 5 in the - 4 950 km column. -4 580 76 km column. 7 ~~ 250 5 579 79 Therefore, the answer is 7 km 250 m. Therefore, the answer is 5km 579 m 79 cm. Exercise 4 4 km m sm hs km m es km =m cm 10 160 55 105 200 27. 240 64 —4 580 76 - 5 105 — 14 860 95 Solution Steps 3 m cm 4. km m dm 1. Subtract centimetres: 12 30 125 120 8 km mcm 55cm — 76cm,it is not sufficient. 4 35 - 85 260 3 10 159 155 Take 1 m from 160 m and convert - 4 580..76 it to get 100 cm. Add centimetres; 5. dm «cm 6. dm cm mm 79 100cm + 55cm =155cm. 10 5 9 4 9 Now, subtract cm: 155cm- 76cm =79cm. Write 79 in - 3 7 -3 7 6 the cm column. Remember that 159 m remained in the m column 7 cm mm 8. dm mm km m cm 2. Subtract metres: 159 m — 580 m, itis 9 9 75 2 9 1159 155 not sufficient. Take 1km from 10 km -2 3 -4 5 -4 580 76 and convert it into 1000m. Add metres: 1000 m + 159 m =1159 m. 579 79 9. km dam cm Now, subtract metres: 1159 m — 580 m = 579 m. Write 17 6 61 579 in the m column. Remember that -—10 3 5 9 km remained in the km column.  Solution Steps i Si 1. Subtractcm: 45cm - 20cm = 25cm. 4 4 Write 25 cm in the cm column. 3 6 i -2 20 +7 5 9 25 a St 2. Subtract m: 4m —2m = 2m. Write 2 4. km hm 5. m cm mm 6. km dam * aS in the m column. m -2 20 5 6 4 25 4 8 9 7 2 25 +2 8 +6 80 8 +5 8 4 Therefore, the answer is 2m 25cm. 7. km om cm 8 km =m 9. dm cm mm 4 40 26 9 56 14 4 6 3 22 68 + 6 48 40 8 6 +5 71° 23 + 12 3 1 12 200 - 4 950 Solution Steps Subtraction.of measurements of length Subtraction can be performed when the measurements are of km m 1. Subtract metres: the same units. Mixed measurements can be subtracted after 12-200 200 m — 950 m, itis not sufficient. converting them using their relationships. —~ 4 950 Take 1 km from 12 km and convert it into 1000 m. 2. Add metres: m cm km =m 1000 m + 200 m =1200m. 4 45 11 1200 Now, subtract metres: -2 20 - 4 950 1200m-950m = 250m. Write 250 250 in the m column. Remember that 11 km remained in the km column.  \ GE Zell 1. Convert the following measurements into kilometres: km7 hm5+km4 hm8= (a) 9000 m (b) 15000m_ = (c)6000m_(d)9750m Solution Steps 2. Convert the following measurements into metres: km hm |. Add hm: 5hm + 8hm = 13hm, (a) 2000 cm (b)150cm = (c)325cm _—_ (d). 2025 cm 7 5 Convert 13 hm into 1 km and 3 hm. 3. Convert the following measurements into centimetres: 4A 8 Write 3 in the hm column. Take 1 km a to the km column. (a)40mm = (b) 100 mm_—(c) 245 mm _~(d) 550 mm Addition of measurements of length km hm | 2. Add km: 1 km + 7%kim + 4 km = 12 km. Measurements of the same unit can be added. Mixed 7 5 Write 12 in the km column. measurements are added after.converting them into a common +4 8 unit using the relationship between the given units. 12 3 Therefore, the answeris 12 km 3 hm. N\ aa 8km 3hm + 6km 5hm = Solution Steps = " 1. Add hm: 3 hm + 5 hm =8 hm. km hm dam Write 8 in the hm column. 7 4 9 +6 5 +6 6 3 8 km hm 2. Add km: 8km + 6km =14km. Solution 8 3 Write 14 in the km column. km hm dam +6 5 14 8 7 4 9 +6 6 3 Therefore, the answer is 14km 8hm. 14 1 2  Conversion of small units of length into large units Length measurements can be converted from small units to large Convert 7 m into decimetres. units. Use multiplication (+) method when converting small units into large units. Solution Use the relationship between metre and decimetre. 1m=10dm Convert 500 cm into metres. 7m=10x 7dm Solution =70dm Use the relationship between metre and centimetre Therefore, 7 m is equal to 70 dm. 1m=100cm _ 500cm x im OO en TOoem =5m _ Therefore, 500 cm is equal to.5 m. 1. Convert the following measurements: (a) 17 km into. metres (b) 7 km 500. m.into centimetres (c) 35 cm into millimetres Convert 4500 m into kilometres and metres. (d) 7 dam into metres Solution 2. A-road is 22 kilometres long. Convert this length to Use the relationship between kilometre and metre decimetres. m 4500 = m 4000 + m 500 _.3.~ Convert the following measurements: Convert 4000 m into kilometre: (a) A farm of length 268 metres into millimetres (6) A building with a height of 63 dam into metres 1km=1000m (c) A board with a length of 3 metres and 20 centimetres — 4000m x 1km 4000m —s000m = into millimetres = 4km (d) A tower with a height of 15 hectometres into metres. 500 m is less than 1 km. _ Therefore, 4500m = 4km 500m.