1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text_Reduced

Concept 10.2: Add and Subtract Money with Conversion 3) Add: a) ` 23.24 + ` 10.80 b) ` 31.20 + ` 19.16 c) ` 61.21 + ` 29.20 d) ` 11.10 + ` 12.90 e) ` 60.90 + ` 24.23 4) Subtract: a) ` 87.10 – ` 23.20 b) ` 20.12 – ` 10.13 c) ` 31.55 – ` 22.44 d) ` 99.99 – ` 22.22 e) ` 56.13 – ` 12.03 Concept 10.3: Multiply and Divide Money 5) Multiply: a) ` 23.14 × 2 b) ` 10.13 × 3 c) ` 99.99 × 1 d) ` 34.10 × 4 e) ` 54.29 × 5 6) Divide: a) ` 21 ÷ 7 b) ` 44 ÷ 2 c) ` 84 ÷ 4 d) ` 10.50 ÷ 5 e) ` 63.33 ÷ 3 Concept 10.4: Make Rate Charts and Bills 7) The rates of some vegetables and fruits per kg are given in the box. ` 10 ` 18 ` 15 ` 20 ` 7 ` 12 Raj buys a few items as given in the list. Make a bill for the items he bought. Item Quantity in kg Tomato 2 Carrot 3 Pumpkin 1 Cabbage 1 Money 145 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___151 / 1840

Measurement11CHAPTER 75 70 65Cm 60 55 50 45 40 35 30 25 20 15 10 5 0 20 I Will Learn Concepts 11.1: C1o.1n:veVresrioticneosfaSntadnDdiaagrdonUanlistsoof fTwLeon-gDtimh ensional Shapes 11.2: Conversion of Standard Units of Weight 11.3: Conversion of Standard Units of Volume JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___152 / 1804

Concept 11.1: Conversion of Standard Units of Length Think Neena went with her mother to a shop to buy a cloth. Her mother asked the shopkeeper to give two metres of the cloth. How do you think the shopkeeper should measure two metres of the cloth? To answer this question, we must know the concept of standard unit of length. Recall We know that people sometimes measure lengths of objects using their hands or feet. But the size of the body parts differ from person to person. So, the length of the same object also differs when measured by different people. Suppose a boy and a grown-up measure the same object. We see that the measures of the object are different. So, measures such as hand span, cubit, leg span and so on are called non-standard units. To express measurement in an exact way, standard units were developed. The measurement of objects remains the same anywhere in the world when these standard units are used. Measures of Length: Centimetre: It is a unit of length used to measure the length of pencil, the sides of a book and so on. We write centimetres as cm. Measurement 147 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___153 / 1804

Metres: It is the standard unit of length. It is used to measure length of a piece of cloth, a wall and so on. We write metres as m. Kilometre: It is a unit of length larger than metre. It is used to measure the distance between two places, length of a river and so on. We write it as km. By using our hand span, we can measure the lengths of the following objects. Fill in the blanks with the measurements obtained. a) Window of your class room - _____________. b) The benches on which you sit - _____________. c) The blackboard - _____________. d) Your math notebook - _____________. e) School bag - ____________. & Remembering & Understanding Measure the length of a blackboard with your hand span. Ask your friends to do the same and note the readings. Did everyone get the same measurement? What do you observe by this? We observe that the readings are different. So, we need a standard measurement. If all of us use the same standard instrument to measure length, there will be no dif- ference in the measurements. Instruments such as scale, tape and so on, are used to measure lengths throughout the world. These are known as standard instruments. A scale is used to measure length in centimetres and inches. A measuring tape is used to measure longer lengths in like metres and kilometres. 148 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___154 / 1804

Can we use a measuring tape to measure smaller lengths? Yes, for that we should know to convert the measurements. Conversion of length We can convert one unit of measurement into another using the relation between them. Larger units to smaller units Let us understand the conversion through a few examples. Example 1: Convert: a) 4 m into cm b) 8 m 6 cm into cm c) 5 km into m d) 6 km 4 m into m Solution: a) To convert metre into centimetre, multiply by 100. b) To convert kilometre into metre, multiply by 1000. c) To convert kilometre and metre into metre, convert kilometre to metre and add it to the metre. Solved Solve these 7 m = _______________ cm a) Conversion of m into cm 4 m = ___________ cm 1 m = 100 cm 4 m = 4 ×100 cm = 400 cm 4 m = 400 cm b) Conversion of m and cm into cm 4 m 5 cm = ___________ cm 8 m 6 cm = ____________ cm 1 m = 100 cm So, 8 m = 8 ×100 cm = 800 cm 8 m 6 cm = (800 + 6) cm = 806 cm Measurement 149 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___155 / 1804

Solved Solve these 7 km = ___________ m c) Conversion of km to m 5 km = __________ m 4 km 9 m = ___________ cm 1 km = 1000 m 5 km = 5 ×1000 m = 5000 m 5 km = 5000 m c) Conversion of km and m into m 6 km 4 m = ___________ m 1 km = 1000 m So, 6 km = 6 ×1000 m = 6000 m 6 km 4 m = (6000 + 4) m = 6004 m We can add or subtract lengths just as like we add or subtract numbers. Remember to write the units beside the sum or difference. Note: Introduce ‘0’ in the hundreds place, if the number in the metre of the kilometre have only 2 digits. Addition of lengths Example 2: Add: a) 25 m 16 cm and 32 m 30 cm b) 34 km 450 m and 125 km 235 m Solution: We can add the lengths as: Steps Solved Solved Solve these Step 1: Write m cm km m m cm the numbers 25 16 34 450 19 27 in columns as + 32 30 + 125 235 + 40 20 shown. 150 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___156 / 1804

Steps Solved Solved Solve these km m Step 2: Add the m cm km m 12 150 numbers under 25 16 34 450 the smaller unit + 32 30 + 125 235 + 14 340 and write the sum. 46 685 km m 10 100 Step 3: Add the m cm km m + 100 100 numbers under 25 16 34 450 the larger unit + 32 30 + 125 235 Solve these and write the 46 159 685 km m sum. 57 14 350 Subtraction of lengths − 12 150 Example 3: Subtract: a) 125 m 20 cm from 232 m 30 cm b) 234 km 15 m from 425 km 35 m Solution: We can subtract the lengths as: Steps Solved Solved Step 1: Write the m cm km m numbers in columns 232 30 425 035 as shown. − 125 20 − 234 015 Step 2: Subtract m cm km m m cm the numbers 232 30 425 035 26 42 under the − 125 20 − 234 015 − 13 21 smaller unit and write the 10 020 difference. m cm km m m cm Step 3: Subtract 2 12 3 12 the numbers 23 2 30 under the larger − 12 5 20 4 25 035 59 26 unit and write 10 7 10 − 2 34 015 − 39 14 the difference. \\ \\ \\ \\ 191 020 Measurement 151 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___157 / 1804

Application Let us solve some real-life examples where addition and subtraction of lengths is mostly used. Example 4: Reema rode her cycle for 9 km 6 m. How many metres did she ride? Solution: The distance travelled by Reema on her cycle = 9 km 6 m We know that 1 km = 1000 m So, 9 km = 9 ×1000 m = 9000 m 9 km 6 m = (9000 + 6) m = 9006 m Therefore, Reema rode for 9006 metres. Example 5: Sunny bought a rope of length 20 m 12 cm. Bunny bought another rope of length 12 m 20 cm. What is the total length of the rope they bought? Solution: The length of the rope bought by Sunny = 20 m 12 cm The length of the rope bought by Bunny = 12 m 20 cm The total length of the ropes = 20 m 12 cm + 12 m 20 cm Therefore, the total length of the rope bought by both of them = 32 m 32 cm Example 6: Raj’s house was at a distance of 36 km 119 m from his uncle’s house. Solution: He travelled by a car for 14 km 116 m from his uncle’s house. How much more distance has to be covered by Raj to reach his home? Distance between Raj’s house and his uncle’s house = 36 km 119 m Distance travelled by Raj to his house = 14 km 116 m Distance left to be covered km m 36 119 = 36 km 119 m – 14 km 116 m 14 116 Therefore, the distance yet to be covered to reach − 22 003 Raj’s home is 22 km 3 m. 152 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___158 / 1840

Higher Order Thinking Skills (H.O.T.S.) Let us now see some more examples where we use the concept of standard units of lengths. Example 7: Ramu’s height is 134 cm and Somu’s height is 1 m m cm Solution: 50 cm. Who is taller and by how many centimetres? 20 12 12 20 To compare heights of two persons, they must be in + 32 32 the same units. Height of Somu = 1 m 50 cm = 100 cm + 50 cm = 150 cm Height of Ramu = 134 cm The difference in their heights is (150 – 134) cm = 16 cm 150 cm > 134 cm Therefore, Somu is taller than Ramu by 16 cm. Example 8: The figure given below is a map. It shows the different ways to reach different places from the house. Post office Airport 3 km School House Market 3 km Railway Station Look at the map and answer these questions. a) How far is the post office from the house? b) What is the distance between the market and the railway station? c) Find the distance between the house and the airport through the post office? Measurement 153 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___159 / 1840

Solution: d) Which is closer to the house – post office or market? e) How far is the railway station from the school? From the map, we see that a) The post office is 3 km from the house. b) The distance between the market and the railway station is 3 km. c) Through the post office, the distance between the house and the airport is 3 km + 6 km = 9 km d) Post office is closer to the house. e) The railway station is 10 km from the school. Concept 11.2: Conversion of Standard Units of Weight Think Neena went to the market with her father. They bought several things like vegetables, sweets and fruits. The shopkeeper measured the vegetables with a machine. He used some units to tell the weight. Do you know which units he used? To know the answer, we have to learn the concept of standard unit of weight. Recall The weight of an object is the measure of its heaviness. Different objects have different weights. We use standard units to measure the weights of objects around us. The standard unit of weight is kilogram. We write kilogram as ‘kg’. Another unit of weight is gram. We write gram as ‘g’. The smallest unit of weight is milligram. We write milligram as ‘mg’. Milligram (mg) is the unit used for weighing medicines, tablets and so on. 154 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___160 / 1840

Gram (g) is used for weighing objects such as pencils, books, and spices. Kilogram (kg) is used for weighing heavier objects such as rice, wheat, and flour. & Remembering & Understanding Sometimes, to measure the weight of an object, we need the smaller unit instead of the larger unit. For this, we need to convert the units for appropriate measurement. Let us see how we can convert weights. Conversion of weights We can convert one unit of measurement into another using the relation between them. Larger units to smaller units Let us understand the conversion through a few examples. Measurement 155 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___161 / 1804

Example 9: Convert into grams: 4 kg Solution: To convert kilogram into gram, multiply by 1000. Solved Solved this 4 kg to grams 6 kg to grams 1 kg = 1000 g So, 4 kg = 4 × 1000 g = 4000 g Example 10: Convert into grams: 3 kg 150 g Solution: To convert kilogram and gram into gram, convert kilogram to gram and add it to the gram. Solved Solved this 3 kg 150 g to grams 4 kg 20 g to grams 1 kg = 1000 g So, 3 kg = 3 × 1000 g = 3000 g 3 kg 150 g = 3000 g + 150 g = 3150 g We add or subtract weights just as we add or subtract numbers. Remember to write the unit beside the sum or difference. Introduce ‘0’ in the hundreds place if the number in the milligram of gram and gram of kilogram has only 2 digits Addition of weights Example 11: Add: a) 15 g 150 mg and 23 g 285 mg b) 17 kg 706 g and 108 kg 189 g Solution: We can add the weights as: Steps Solved Solved Solve these Step 1: Write g mg kg g kg g the numbers in 15 150 17 706 11 230 the columns as + 23 285 + 108 189 + 8 760 shown. 156 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___162 / 1840

Steps Solved Solved Solve these g mg Step 2: Add the g mg kg g 26 190 numbers under 1 1 the smaller unit 15 150 + 23 260 and write the + 23 285 17 706 sum. + 108 189 g mg 435 33 333 895 + 22 333 Step 3: Add the g mg kg g Solve these numbers under 1 11 kg g the larger unit 15 150 17 706 505 600 and write the + 23 285 sum. 435 + 108 189 − 200 400 38 125 895 Subtraction of weights Example 12: Subtract: a) 153 g 100 mg from 262 g 300 mg b) 234 kg 150 g from 355 kg 305 g Solution: We can subtract the weights as: Steps Solved Solved Step 1: Write g mg kg g the numbers in 262 300 355 305 columns as shown. − 153 100 − 234 150 Step 2: Subtract g mg kg g g mg the numbers 2 10 under the smaller 262 300 15 260 unit and write the − 153 100 3 5 5 \\3 \\0 5 − 15 260 difference. − 234 150 200 g mg Step 3: Subtract 15 5 the numbers g mg 23 555 under the larger 5 12 kg g − 16 454 unit and write the 2 6\\ \\2 3 0 0 2 10 difference. − 153 100 109 200 3 5 5 \\3 \\0 5 − 234 150 121 155 Measurement 157 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___163 / 1840

Application Look at some real-life examples where addition and subtraction of weights is used. Example 13: Rahul had a bag full of vegetables which weighed 17 kg 241 g. His friend had another bag of vegetables weighing 21 kg 243 g. What is the total weight of the vegetables in both the bags? Solution: Weight of the vegetables in Rahul’s bag = 17 kg 241 g Weight of the vegetables in friend’s bag = 21 kg 243 g kg g The total weight of the vegetables in both the 17 241 bags = 17 kg 241 g + 21 kg 243 g = 38 kg 484 g + 21 243 Therefore, the weight of vegetables in Rahul’s and his 38 484 friend’s bag is 38 kg 484 g. Example 14: Reena got a box of pins which weighed 43 g 132 mg. She took out 11 g 100 mg of pins. What is the weight of the pins left in the box? Solution: The weight of pins in the box = 43 g 132 mg g mg The weight of pins taken out from the box = 11 g 100 mg 43 132 The weight of the remaining pins in the box = − 11 100 43 g 132 mg – 11 g 100 mg = 32 g 032 mg 32 032 Therefore, the weight of the remaining pins is 32 g 32 mg Higher Order Thinking Skills (H.O.T.S.) Let us now see how we use standard units of weight in real-life situations. Example 15: Kiran weighs 13 kg and Venu weighs 11 kg 750 g. Who weighs more and by how many grams? Solution: To compare the weights, they must be in the same units. Weight of Venu = 11 kg 750 g = 11 × 1000 g + 750 g (As 1 kg = 1000 g) = 11000 g + 750 g = 11750 g 158 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___164 / 1840

Weight of Kiran = 13 kg = 13 × 1000 g = 13000 g = 13000 g > 11750 g Therefore, Kiran weighs more than Venu. The difference in their weights is (13000 – 11750) g = 1250 g. Example 16: Suresh bought apples, grapes and watermelon. The total weight of the fruits in his bag is 3 kg 750 g. The weight of apples is 1 kg 100 g and grapes is 1 kg 150 g. What is the weight of watermelon? Solution: Suresh had 3 kinds of fruits: apples, grapes and watermelon in his bag. kg g Weight of apples = 1 kg 100 g 1 100 Weight of grapes = 1 kg 150 g +1 150 Total weight of apples and grapes 2 250 = 1 kg 100 g + 1 kg 150 g Therefore, the weight of apples and grapes together is 2 kg 250 g. Weight of watermelon = weight of the bag − total weight of apples and grapes Weight of the bag = 3 kg 750 g kg g Weight of apples and grapes together = 2 kg 250 g 3 750 Weight of watermelon = 3 kg 750 g – 2 kg 250 g Therefore, the weight of watermelon is 1 kg 500 g. −2 250 1 500 Concept 11.3: Conversion of Standard Units of Volume Think Neena’s 10 cousins visited her during their summer vacation. Neena bought two big bottles of cold drink. If each takes a glassful, can she serve equally to all? To answer this question, we have to learn the concept of the measurement of capacity. Measurement 159 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___165 / 1840

Recall Bottles and glasses come in different sizes. We cannot specify the quantity of cold drink served in bottles and glasses as they are non-standard units. So, we need a standard unit of measuring capacity of liquids. Standard units of capacity are millilitres, litres and kilolitres. Commonly used containers for measuring the quantity of liquids are shown in the figure. The quantity of liquid (water, oil, milk and so on) that a container can hold is called its capacity or volume. The standard unit of capacity or volume is litre, denoted by ‘ℓ’. The unit smaller than a litre that is used for measuring capacity is called millilitre. We write it as ‘mℓ’. & Remembering & Understanding To find the measure of the quantity of the smaller units, we need to convert the larger unit to smaller unit. Conversion of units of capacity We can convert one unit of measurement into another using the relation between them. Let us understand the conversion through a few examples. Larger units to smaller units To convert litres into millilitres, multiply by 1000. Example 17: Convert into millilitres: 3 ℓ Solution: Multiply the litres by 1000 to convert it to millilitre. Solved Solve this 3 ℓ to mililitres 7 ℓ to mililitres 1 ℓ = 1000 mℓ 3 ℓ = 3 × 1000 mℓ = 3000 mℓ 160 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___166 / 1840

Example 18: Convert into millilitres: 2ℓ 269 mℓ Solution: To convert litres and millilitres into millilitres, convert litres to millilitres and add it to the millilitres. Solved Solve this 3 ℓ 750 mℓ to millilitre 2ℓ 269 mℓ to millilitre 1 ℓ = 1000 mℓ So, 2 ℓ = 2 × 1000 mℓ = 2000 mℓ 2 ℓ 269 mℓ = 2000 mℓ + 269 mℓ = 2269 mℓ We add or subtract volumes just as we add or subtract numbers. Remember to write the unit beside the sum or difference. Introduce ‘0’ in the hundreds place if the millilitre in litre and litre in kilolitre if there are only two digits. Addition of volumes Example 19: Add: 13 ℓ 450 mℓ and 32 ℓ 300 mℓ Solution: We can add the volume as: Steps Solved Solve these Step 1: Write ℓ mℓ ℓ mℓ the numbers in 13 450 21 200 columns as shown. + 32 300 + 11 303 Step 2: Add the ℓ mℓ ℓ mℓ numbers under the 13 450 24 129 smaller unit and + 32 300 + 31 110 write the sum. 750 ℓ ℓ mℓ Step 3: Add the 13 mℓ 52 000 numbers under + 32 450 + 41 000 the larger unit and 45 300 write the sum. 750 Measurement 161 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___167 / 1804

Subtraction of volumes Example 20: Subtract: 351 ℓ 200 mℓ from 864 ℓ 350mℓ Solution: We subtract the volume as: Steps Solved Solve these Step 1: Write the ℓ mℓ ℓ mℓ numbers in columns 864 350 316 186 as shown. − 351 200 − 116 205 Step 2: Subtract the ℓ mℓ ℓ mℓ numbers under the 864 350 119 209 smaller unit and write − 351 200 − 11 101 the difference. 150 Step 3: Subtract the ℓ mℓ ℓ mℓ numbers under the 119 209 larger unit and write 864 350 − 11 101 the difference. − 351 200 513 150 Application Let us solve some real-life examples where conversion of units, addition and subtraction of volumes are used. Example 21: Seema has a 2 ℓ packet of milk. How many mℓ of milk does she have? Solution: Quantity of milk that Seema has = 2 ℓ As 1 ℓ = 1000 mℓ, 2 ℓ = 2 × 1000 = 2000 m ℓ. Therefore, Seema has 2000 mℓ of milk. Example 22: The capacity of a tank is 20 litres. The volume of water in the tank is 13 litres. How much more water is needed to fill the tank? 162 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___168 / 1840

Solution: The capacity of the tank = 20 litres ℓ mℓ Volume of water in the tank = 13 litres 1 10 Quantity of water needed to fill the tank \\2 0\\ = 20 litres – 13 litres = 7 litres −1 3 0 7 Therefore, the quantity of water needed to fill the tank is 7 litres. Higher Order Thinking Skills (H.O.T.S.) Let us see the use of standard units of volumes in a few real-life situations. Example 23: Chandu, the milkman has only 5 ℓ and 3 ℓ measures. How will he sell 4 ℓ of milk to Gita? (Hint: Find the difference between 5 ℓ and 3 ℓ) Solution: Chandu first pours milk in 5ℓ measure. He then transfers some of it into the 3 ℓ measure. Then the quantity of milk left in the 5ℓ measure is 2 ℓ. This 2 ℓ milk can be transferred into Gita’s vessel. He repeats the same procedure once more. Thus, he sells 4ℓ of milk to Gita. Example 24: A container has some juice. A glass has a capacity of 200 mℓ. How many glasses of juice must be poured to have 2 ℓ of juice? Solution: Capacity of the glass = 200 mℓ Quantity of juice needed = 2 ℓ = 2 × 1000 mℓ = 2000 mℓ 2000 = 200 × 10 Therefore, 10 glasses of juice must be poured to make 2 ℓ. Measurement 163 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___169 / 1804

Drill Time 11.1: Conversion of Standard Units of Length 1) Convert into centimetres. a) 3 m b) 9 m c) 2 m 45 cm d) 5 m 20 cm e) 8 m 36 cm 2) Convert into metres. a) 4 km b) 15 km c) 5 km 555 m d) 6 km 112 m e) 1 km 100 m 3) Solve the following. a) 24 m 13 cm + 13 m 45 cm b) 31 m 00 cm + 18 m 59 cm c) 10 km 100 m + 20 km 200 m d) 88 km 100 m − 10 km 800 m e) 26 m 14 cm – 20 m 10 cm 4) Word Problem a) Roopa’s house and the places close to it are shown on the map. Study the map and answer these questions. a) The shortest route from Roopa’s house to the market is via __________ and is __________ km. b) The shortest route from Roopa’s house to the airport is _________ km. c) What is the shortest route from post office to the market? d) Roopa went to post office from school. What is the distance she travelled? 164 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___170 / 1840

11.2: Conversion of Standard Units of Weight 5) Convert into grams. a) 14 kg b) 29 kg c) 14 kg 300 g d) 75 kg 226 g e) 10 kg 112 g 6) Solve the following. a) 28 kg 421 g + 30 kg 232 g b) 42 kg 876 g + 31 kg 111 g c) 44 kg 444 g – 22 kg 222 g d) 43 g 230 mg - 11 g 100 mg 7) Word Problem a) Maya bought these vegetables. Brinjal – 2 kg 250 g; Onion – 1 kg 750 g; Potato – 1 kg 250 g Find the total weight of vegetables in her bag. Measurement 165 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___171 / 1840

11.3: Conversion of Standard Units of Volume 8) Convert into millilitres. a) 13 ℓ b) 28 ℓ c) 13 ℓ 400 mℓ d) 64 ℓ 206 mℓ e) 14 ℓ 142 mℓ 9) Solve the following. a) 28 ℓ 421 mℓ + 40 ℓ 262 mℓ b) 41 ℓ 836 mℓ + 41 ℓ 113 mℓ c) 30 ℓ 320 mℓ + 20 ℓ 300 mℓ d) 33 ℓ 530 mℓ - 11 ℓ 300 mℓ e) 66 ℓ 666 mℓ – 44 ℓ 444 mℓ 10) Word Problem a) A arthi has a jug with some buttermilk. She uses glasses which can hold 150 mℓ. How many glasses must she fill so that she has 3 ℓ of buttermilk? 166 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___172 / 1804

DataHandling12CHAPTER I Will Learn Concepts 12.1: R1e.c1:orVdedrtaicteasuasnindgDtiaalglyomnaalrskos f Two-Dimensional Shapes JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___173 / 1840

Concept 12.1: Record Data Using Tally Marks Think Neena made a table of the things that her mother bought for her. From the table she could tell how many of each thing her mother has bought. Do you know how? To answer this, we must know to arrange data in the form of a table. Recall We know to answer the questions based on the data in a given table. Let us revise the concept by studying the following table. The number of students of a class who like different types of chocolate is given in the table. Name of the No. of students chocolate Jelly 3 6 5 Star 5 4 Éclairs Melody a) How many students are present in the class? [ ] [ ] (A) 13 (B) 18 (C) 15 (D) 20 [ ] (D) 4 b) Ho w many students like Éclairs? (D) Melody (A) 3 (B) 6 (C) 5 c) Which type of chocolate is liked by four students? (A) Jelly (B) 5 Star (C) Éclairs 168 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___174 / 1840

d) How many students like jelly? [ ] [ ] (A) 3 (B) 4 (C) 6 (D) 5 e) Which chocolate is liked by most of the students? (A) Jelly (B) 5 Star (C) Eclairs (D) Melody & Remembering & Understanding Let us now learn to make a table when data is given. The data given can be arranged in the form of a table. We first identify different items in the data and list them out in the first column of the table. In the second column, the number of items is denoted by drawing a vertical line (⎮). This vertical line is called the tally mark. In the third column, we write the count of these tally marks. Let us see a few examples to understand the concept better. Example 1: Seema bought the following fruits: banana, apple, watermelon, mango, mango, apple, watermelon, apple, banana, banana, apple, mango, watermelon, mango, banana, mango, mango. How many of each fruit did Seema buy? Represent the data in the form of a table using tally marks. Solution: Fruit Tally marks Number Example 2: Apple |||| 4 Banana |||| 4 Watermelon ||| 3 Mango ||||| 6 The months in which the birthdays some of children fall are as given. Heena – January, Sheena – March, Yash – March, Harsh – January, Hemal – February, Jinal – August, Jihaan – December, Asmita – January, Chetana – August Use tally marks to represent this information in a table. Data Handling 169 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___175 / 1804

Solution: Birthday month Tally marks Number of children January ||| 3 February | 1 March || 2 August || 2 | 1 December Application Let us see some real-life examples where we represent data using tally marks. Example 3: The different types of ice-cream in Raj’s shop are as follows: Cones: 14 Small cups: 9 Medium cups: 6 Large cups: 11 Tubs: 5 Represent this data in a table using tally marks. From the table, find the type of ice cream that is: a) maximum in number. b) less in number than medium cups. c) more in number than small cups but less in number than cones . Solution: We can represent data in a table using tally marks as: Ice cream Tally marks Number Cones |||| |||| |||| 14 Small cups |||| |||| 9 Medium cups |||| | 6 Large cups |||| |||| | 11 Tubs |||| 5 So, a) Cones b) Tubs c) Large cups Example 4: Nandu asked each boy and girl of his class as to how they come to school. He noted their answers as shown below: 170 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___176 / 1840

Heena – Bus, Raju – On foot, Pooja – Auto, Reena – On foot, Sheela – Bus, Rohan – On foot, Rahul – Bicycle, Ajay – On foot, Neha – Auto, Hema – Bus, Arun – Bicycle, Komal – On foot, Anil – Bus, Anita – Auto, Soham – Bicycle Represent this data in a table using tally marks. Solution: Tally marks Number of children |||| 5 On foot 4 Bus |||| 3 Auto ||| 3 ||| Bicycle Higher Order Thinking Skills (H.O.T.S.) Example 5: The different sizes of T-shirts in a shop are as follows: Small, Large, XXXL, Small, Small, 34, XXXL, Small, XXXL, Large, 34, XXXL, Medium, 34, XXXL, Large, Small, Large, 34, Medium, XXXL, Small, Large, 34, 34, XXXL, Small, XXXL, Medium, 34, Small, XXXL, Small, XXXL, 34, Small, XXXL, 34, Large, Small, XXXL, 34, Small, Small, Medium, XXXL, Large, XXXL, Large, XXXL, 34 Represent this data in a table using tally marks. From the table, find the size of the T-shirt that is: a) which size is more if we add the medium and the large sizes together. b) less in number than the large size shirts. c) more in number than medium size shirts but less in number than the ‘34’ size shirts. Solution: Size of T-Shirt Tally marks Number Small |||| |||| ||| 13 Medium |||| 4 Large |||| |||| 8 34 |||| |||| | 11 XXXL |||| |||| |||| 15 Data Handling 171 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___177 / 1840

a) XXXL b) Medium c) Large Example 6: The number of two-wheelers, three-wheelers and four-wheelers are as given: Two-wheelers: 24 Three-wheelers: 10 Four-wheelers: 19 Represent this data in a table using tally marks. Solution: Vehicle Tally Marks Two-wheelers |||| |||| |||| |||| |||| Three-wheelers |||| |||| Four-wheelers |||| |||| |||| |||| Drill Time Concept 12.1: Record Data Using Tally Marks 1) Solve the following. a) I nschool there are seven plastic chairs, twelve wooden chairs and three iron chairs. Represent this data using tally marks. Find the total number of chairs. b) T here are five bowls, ten plates, one pot, seven cups, ten glasses, two saucers and eleven spoons. Represent this data in a table using tally marks. c) T he number of children present for a sports day are as given below. Boys: Rohan, Tushar, Sanket, Ankit, Siddharth, Harsh Girls: Piya, Kshitija, Reema, Prachi R epresent the data in a table using tally marks. How many boys and how many girls were there in the party on the sports day? d) Ami noted down the color of school bags of children in her class. She made a list as below: Purple: Krishna, Sanika, Harshada, Suvarna, Anu, Shreya Pink: Yash, Jigar, Vijay, Virat Black: Bhavna, Rashmi, Jay, Sagar, Sonu, Tina, Mona, Shefali White: Payal, Sakshi Represent the data in a table using tally marks. 172 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___178 / 1840

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