Application Look at some real-life examples where we use addition and subtraction of money. Example 8: Arun had ` 45.50 with him. He gave ` 23.50 to Amar. `p How much money is left with Arun? 4 5. 5 0 − 2 3. 5 0 Solution: Amount Arun had = ` 45.50 2 2. 0 0 Amount Arun gave to Amar = ` 23.50 Difference in the amounts = ` 45.50 – ` 23.50 = ` 22 Therefore, Arun has ` 22 left with him. Example 9: Ramu has ` 12.75 with him. His friend has ` 28.50 with him. What is the amount both of them have? Solution: Amount Ramu has = ` 12.75 `p Amount Ramu’s friend has = ` 28.50 11 1 2. 7 5 To find the total amount we have to add both the + 2 8. 5 0 amounts. 4 1. 2 5 So, the total amount with Ramu and his friend is ` 41.25. Higher Order Thinking Skills (H.O.T.S.) In some situations, we may need to carry out both addition and subtraction to find the answer. In such cases, we need to identify which operation is to be carried out first. Let us see a few examples. Example 10: Add ` 20 and ` 10.50. Subtract the sum from ` 40. Solution: First add ` 20 and ` 10.50. `p `p ` 20 + ` 10.50 = ` 30.50 2 0. 0 0 4 0. 0 0 + 1 0. 5 0 − 3 0. 5 0 Now, let us find the difference 3 0. 5 0 0 9. 5 0 between ` 30.40 and ` 50. Therefore, ` 40 – ` 30.50 = ` 9.50 Money 47
Concept 10.3: Multiply and Divide Money Think Farida's father gave her ` 150 on three occasions. Farida wants to share the total amount equally with her brother. How should she find the total amount? How much will Farida and her brother get? Recall While multiplying, we begin from ones place and move to the tens and hundreds places. Sometimes, we may need to regroup the products. We begin division from the largest place and move to the ones place of the number. Let us answer these to revise the concepts of multiplication and division. a) 32 × 4 = _____ b) 11 × 6 = _____ c) 20 ÷ 2 = _____ b) 48 ÷ 3 = _____ e) 10 × 6 = _____ f) 24 ÷ 8 = _____ & Remembering and Understanding Multiplication and division of money is similar to that of numbers. To multiply money, first multiply the numbers under paise (as we start multiplying from the rightmost digit), and place the point. Then multiply the number under rupees. To divide money, we divide the numbers under rupees (as we start dividing from the leftmost digit) and place the point in the quotient. Then, divide the number under paise. Now, let us understand multiplying and dividing money through a few examples. Example 11: Multiply ` 72 by 8. ` 1 Solution: To find the total amount, multiply the number under rupees as 72 actual multiplication of a 2-digit number by a 1-digit number. ×8 576 Therefore, ` 72 × 8 = ` 576 48
Example 12: Divide ` 35 by 7. 5 Solution: Divide the amount just as you would divide a 2-digit number )7 35 by a 1-digit number. So, ` 35 ÷ 7 = ` 5 − 35 00 Application We apply multiplication and division of money in many real-life situations. Let us see some examples. Example 13: The cost of a dozen bananas is ` 48. ` a) What is the cost of three dozen bananas? 2 b) What is the cost of one banana? 48 S olution: One dozen = 12 ×3 144 a) Cost of one dozen bananas = ` 48 Cost of three dozen bananas = ` 48 × 3 = ` 144 4 b) Cost of one dozen (12) bananas = ` 48 Cost of one banana = ` 48 ÷ 12 = ` 4 )12 48 − 48 00 (Recall that 10 × 4 = 40. Then, 11 × 4 = 44 and 12 × 4 = 48). Higher Order Thinking Skills (H.O.T.S.) In some situations, we have to carry out more than one operation on money. Consider the following examples. Example 14: Nidhi buys 4 bunches of flowers each costing ` 54. She buys 6 candy bars for her brothers at the cost of ` 5 each. If she has ` 8 left with her after paying the amount, how much did she have in the beginning? Solution: Cost of a bunch of flowers = ` 54 Cost of 4 bunches = ` 54 × 4 = ` 216 Cost of each candy bar = ` 5 Cost of 6 candy bars = ` 5 × 6 = ` 30 Money 49
Total cost of the things she bought = ` 216 + ` 30 = ` 246 Amount she is left with = ` 8 Therefore, amount she had in the beginning = ` 246 + ` 8 = ` 254 Concept 10.4: Rate Charts and Bills Think Farida went to a mall with her parents. She buys a pair of jeans, 2 shirts, a story book and a ball. How much should she pay? She was given a bill for what she has bought. Can you prepare a bill similar to the one given to her? Recall Recall that we make lists of items when we go shopping. The lists could be of provisions, stationery and items like vegetables or fruits. We can compare the list of items and the items we bought. We can compare their rates and add them to get the total amount to be paid. Let us answer these to revise addition and multiplication of money. a) ` 12 × 2 = __________ b) ` 20 × 3 = __________ c) ` 25 × 4 = __________ d) ` 12 + ` 20 = __________ e) ` 30 + ` 40 = __________ Trfa) `in21M+ `y10B=ra__i_n_______ & Remembering and Understanding Making bills A bill is a list of items that we have bought from a shop. A bill tells us the cost of each item and the total money to be paid to the shopkeeper. To make a bill of items, we write the rate of the object and the quantity in the bill. We then find the product of the rate and the quantity. We add the products to find the total bill amount. Addition of amounts is similar to the addition of numbers with two or more digits. Let us understand how to make bills through a few examples. 50
Example 15: L ook at the rates of the items from a stationery shop in the box below. Geometry Set Sharpener ` 5 ` 140 Colour pencils Notebooks ` 140 ` 40 Pencils ` 3 Pens ` 10 Water colours ` 100 Scissors ` 25 Sunil buys a few items as given in the list. Make a bill for the items he bought. Item Pencil Water colour Sharpener Pen Notebook Quantity 2 14 4 2 Solution: Follow the steps to make the bill. Step 1: Step 2: Write the items and their quantities in the bill. Step 3: Then write the cost per item. Step 4: Find the total cost of each item by multiplying the number of items by their rates. Find the total bill amount by adding the amount of each item. Bill S.No Item Quantity Rate per item Amount 1 Pencil 2 ` 3.00 `p 6 00 2 Water colour 1 ` 100.00 100 00 3 Sharpener 4 ` 5.00 20 00 4 Pen 4 ` 10.00 40 00 5 Notebook 2 ` 40.00 80 00 Total 246 00 Money 51
Making rate charts A rate chart is a chart in which the rate of the different items are written. A rate chart makes it easier for us to see and compare the prices of the items. Example 16: Anil and his friends are playing with play money. Anil runs a supermarket. Some items in his supermarket are given below, along with their rates. ` 40 per kg ` 147 ` 50 ` 34 ` 240 per kg ` 149.50 ` 44 per litre ` 48 per kg ` 80 per kg ` 150 per kg ` 50 ` 20 per dozen He makes a rate chart to display the price of each item. How will the rate chart look? Solution: 1. Draw a table. 2. Complete the table with each item and its rate. Item Rate (in `) Item Rate (in `) 1 kg sugar 40 1 litre milk 44 Tomato Ketchup 147 1 kg wheat 48 Chocolate bar 50 1 kg oranges 80 Soap bar 34 1 kg apples 150 1 kg tea 240 1 kg pineapple 50 Honey 149.50 1 dozen bananas 20 52
Application Let us learn how to make rate charts and bills and use them in our daily life with an activity. Go to a vegetable store. Suppose you see the rate chart of all vegetables with their rates per kg. Buy some vegetables and make the bill. Rate Chart Item Bill Vegetables Rate per kg (in `) Rate per kg ` Paise Brinjal 30.00 1 kg brinjal 30.00 30 00 Cabbage 24.00 2 kg potato 40.00 80 00 Potato 40.00 2 kg tomato 20.00 40 00 Tomato 20.00 1 kg onion 22.00 22 00 Onion 22.00 Total 172 00 The bill for the items you bought would be as shown. Write the rates and their amounts carefully, by considering the quantity. Find the total bill by adding total cost of each vegetable. Here, the total bill is ` 172.00. Example 17: Ashish went to 'Seven Seas' restaurant. The rate chart of the items available there is as given. Burger Vegetable Pizza 1 pack of sandwich finger chips Item Rate 105.00 25.00 200.00 40.00 (in `) Coke Cupcake Grilled sandwich 1 packet of Item Potato wafers Rate 20.00 50.00 125.00 70.00 (in `) What can he buy at this restaurant, if he has to spend ` 250? Money 53
(Write 3 different options and make a bill for one of the options.) Solution: To write three different options for Ashish to choose, see that the sum of the rates does not exceed ` 250. The three options could be: a) 2 burgers and 1 pack of finger chips b) 2 cupcakes c) 1 burger, 1 cupcake, 1 packet of potato wafers Let us now make a bill for 1st option. Find the cost and write the total. Seven Seas Restaurant Bill Item Rate per item ` p 210 00 2 burgers ` 105.00 40 00 1 pack of finger chips ` 40.00 Total 250 00 Higher Order Thinking Skills (H.O.T.S.) Seeing the rate chart in a shop, we can calculate mentally the amount for the items we want to buy. Let us now see an example. Example 18: Sneha went to an ice cream 1000 ml tub of ice cream Rate in ` shop and saw the rate chart Butter Scotch 150.00 given. Sneha took 2 Butter Vanilla 120.00 Scotch, 2 Mango and 1 Vanilla ice cream tubs. What Strawberry 130.00 is the total bill? Make the bill. Mango 140.00 If she gave ` 1000, how much did she get as change? Solution: Write the items, number of each item and their rates. Multiply them to find cost of each flavour of ice cream. Find the total by adding all the amounts. Ice cream shop Item Quantity Rate per tub ` paise Butter Scotch 300 00 2 ` 150.00 280 00 Mango 120 00 Vanilla 2 ` 140.00 7000 00 1 ` 120.00 Total 54
Amount Sneha gave = ` 1000 Total bill amount = ` 700 The amount she received as change = ` 1000 – ` 700 = ` 300 Drill Time Concept 10.1: Convert Rupees to Paise 1) Convert rupees to paise. a) ` 34 b) ` 12 c) ` 80 d) ` 29 e) ` 10 2) Convert paise to rupees. a) 320 paise b) 140 paise c) 450 paise d) 298 paise e) 100 paise 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) Solve the following: c) ` 21 ÷ 7 d) ` 34 × 4 e) ` 84 ÷ 4 a) ` 23 × 2 b) ` 10 × 3 Concept 10.4: Rate Charts and Bills 6) The rates of some vegetables and fruits per kg are given in the box. ` 18 Item Quantity ` 10 in kg 2 Tomato 3 ` 15 ` 20 Carrot Pumpkin 1 `7 ` 12 Cabbage 1 Raj buys a few items as given in the list. Make a bill for the items he bought. Money 55
Chapter Measurements 11 Let Us Learn About • estimating and measuring length and distance. • conversion, addition and subtraction of length. • weighing objects using simple balance. • conversion of units of capacity. • comparing capacities using different containers. Concept 11.1: Conversion of Standard Units of Length Think Farida went with her mother to a shop to buy a piece of cloth for a dress. 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? 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. 56
Hand span Cubit Foot Pace 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 classroom - _____________. b) The benches on which you sit - _____________. c) The blackboard - _____________. d) Your math notebook - _____________. e) School bag - ____________. To express measurement in an exact way, standard units were developed. The measurement of object 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. Metre: 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 the metre. It is used to measure the distance between two places, length of a river and so on. We write it as km. & Remembering and 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 difference in the measurements. Measurements 57
Instruments such as a scale, a tape and so on, are used to measure lengths throughout the world. These are known as standard instruments. A scale is used to measure the length in centimetres and inches. A measuring tape is used to measure longer lengths in like metres and kilometres. 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. Relation between units of length 1 m = 100 cm 1 km = 1000 m Let us understand the conversion of larger units to smaller 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 a) Conversion of m into cm: 7 m = _______________ cm 4 m = ___________ cm 1 m = 100 cm 4 m = 4 ×100 cm = 400 cm 4 m = 400 cm 58
Solved Solve these b) Conversion of m and cm into cm: 8 m 6 cm = ____________ cm 4 m 5 cm = ___________ cm 1 m = 100 cm So, 8 m = 8 ×100 cm = 800 cm 8 m 6 cm = (800 + 6) cm = 806 cm c) Conversion of km to m: 5 km = __________ m 7 km = ___________ m 1 km = 1000 m 5 km = 5 ×1000 m = 5000 m 5 km = 5000 m d) Conversion of km and m into m: 6 km 4 m = ___________ m 4 km 9 m = ___________ cm 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 has 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 Measurements 59
Solution: Write the numbers in columns, one below the other. Steps Solved Solved Solve these Step 1: Add the + m cm km m km m numbers under 25 16 34 450 12 150 the smaller unit 32 30 + 125 235 + 14 340 and write the sum. 46 685 Step 2: Add the m cm km m km m 16 34 450 10 100 numbers under 25 30 + 125 235 + 100 100 46 159 685 the larger unit and + 3 2 write the sum. 57 Subtraction of lengths Example 3: Subtract: a) 125 m 20 cm from 232 m 30 cm b) 234 km 15 m from 425 km 35 m Solution: Write the numbers in columns, the smaller number below the larger number. Steps Solved Solved Solve these Step 1: 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 2: Subtract 2 12 3 12 the numbers 23 2 30 4 25 035 58 26 under the larger − 12 5 20 − 2 34 015 − 39 14 unit and write the 10 7 10 191 020 difference. \\ \\ \\ \\ 60
Application Let us solve some real-life examples with addition and subtraction of lengths. Example 4: 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 m cm The length of the rope bought by Bunny = 12 m 20 cm 20 12 The total length of the ropes = 20 m 12 cm + 12 m 20 cm + 12 20 Therefore, the total length of the rope bought by both of 32 32 them = 32 m 32 cm Example 5: Raj’s house was at a distance of 36 km 119 m from his uncle’s house. 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 house? km m Solution: Distance between Raj’s house and his uncle’s house 36 119 − 14 116 = 36 km 119 m Distance travelled by Raj to his house = 14 km 116 m 22 003 Distance left to be covered = 36 km 119 m – 14 km 116 m Therefore, the distance to be covered to reach Raj’s house is 22 km 3 m. 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 6: The figure given is a map. It shows the different ways to reach different places from the house. 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. d) Is the post office or the market closer to the house? e) How far is the railway station from the school? Measurements 61
Post Office Airport 2 km 4 km 6 km 8 km Market School 3 km 3 km Railway Station House 10 km Solution: 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 Farida 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? 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. 62
The standard unit of weight is kilogram. We write kilogram as ‘kg’. Another unit of weight is gram. We write gram as ‘g’. The unit of weight smaller than the gram is milligram. We write milligram as ‘mg’. Milligram (mg) is the unit used for weighing medicines, tablets and so on. 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 and 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 larger units of weights into smaller units using the relation between them. Relation between units of weight 1 g = 1000 mg 1 kg = 1000 g Measurements 63
Let us understand the conversion through a few examples. Example 7: Convert 4 kg into grams. Solution: To convert kilogram into gram, multiply by 1000. Solved Solve this 4 kg to grams 6 kg to grams 1 kg = 1000 g So, 4 kg = 4 × 1000 g = 4000 g Example 8: Convert 3 kg 150 g into grams. Solution: To convert kilogram and gram into gram, convert kilogram to gram and add it to the gram. Solved Solve 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. Note: Introduce ‘0’ in the hundreds place if the milligram of the gram or the gram of the kilogram has only 2 digits. Addition of weights Example 9: Add: a) 15 g 150 mg and 23 g 285 mg b) 17 kg 706 g and 108 kg 189 g Solution: Write the numbers in the columns, one below the other. 64
Steps Solved Solved Solve these g mg Step 1: Add the g mg kg g numbers under the 1 1 26 190 smaller unit and 15 150 + 23 260 write the sum. + 23 285 17 706 435 + 108 189 895 Step 2: Add the g mg kg g g mg numbers under the 1 11 larger unit and write 15 150 17 706 33 333 the sum. + 23 285 + 22 333 435 + 108 189 38 125 895 Subtraction of weights Example 10: Subtract: a) 153 g 100 mg from 262 g 300 mg b) 234 kg 150 g from 355 kg 305 g Solution: Write the numbers in columns, the smaller number below the larger number. Steps Solved Solved Solve these Step 1: Subtract the g mg kg g g mg numbers under the 2 10 smaller unit and 262 300 355 3\\ \\0 5 15 260 write the difference. − 153 100 − 234 150 − 15 260 15 5 200 Step 2: Subtract g mg kg g g mg the numbers 5 12 2 10 under the larger 2 \\6 \\2 3 0 0 355 \\3 \\0 5 23 555 unit and write the − 153 100 − 234 150 − 16 454 difference. 109 200 155 121 Measurements 65
Application Look at some real-life examples where addition and subtraction of weights is used. Example 11: 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? kg g Solution: Weight of the vegetables in Rahul’s bag = 17 kg 241 g 17 241 Weight of the vegetables in friend’s bag = 21 kg 243 g + 21 243 The total weight of the vegetables in both the 38 484 bags = 17 kg 241 g + 21 kg 243 g = 38 kg 484 g Therefore, the total weight of vegetables in Rahul’s and his friend’s bag is 38 kg 484 g. Example 12: 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 Therefore, the weight of the remaining pins is 32 g 32 mg 32 032 Higher Order Thinking Skills (H.O.T.S.) Let us now see how we use standard units of weight in real-life situations. Example 13: Suresh bought apples, grapes and a 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 the watermelon? Solution: Suresh had 3 kinds of fruits: apples, grapes and a watermelon in his bag. Weight of apples = 1 kg 100 g kg g Weight of grapes = 1 kg 150 g 1 100 +1 150 2 250 66
Total weight of apples and grapes = 1 kg 100 g + 1 kg 150 g Therefore, the weight of apples and grapes together is 2 kg 250 g. Weight of watermelon = w eight 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 − 2 250 Therefore, the weight of watermelon is 1 kg 500 g. 1 500 Concept 11.3: Conversion of Standard Units of Volume Think Farida’s 10 cousins visited her during their summer vacation. Farida bought two big bottles of cold drink. If each takes a glassful, can she serve equally to all? 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 standard unit for measuring the quantity of liquids. Commonly used containers for measuring the quantity of liquids are shown. The quantity of liquid (water, oil, milk and so on) that a container can hold is called its capacity or volume. Standard units of capacity are millilitres, litres and kilolitres. 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’. Measurements 67
& Remembering and 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. Relation between units of capacity 1 litre = 1000 millilitres 1 kilolitre = 1000 litres Let us understand the conversion of capacity from larger units to smaller units through a few examples. To convert litres into millilitres, multiply by 1000. Example 14: Convert 2ℓ 269 mℓ into millilitres. 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. Note: 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 15: Add: 13 ℓ 450 mℓ and 32 ℓ 300 mℓ Solution: Write the numbers in columns. 68
Steps Solved Solve these Step 1: Add the ℓ mℓ ℓ mℓ numbers under the 13 450 24 129 smaller unit and write + 32 300 + 31 110 the sum. 750 Step 2: Add the ℓ mℓ ℓ mℓ numbers under the 13 450 52 000 larger unit and write + 32 300 + 41 000 the sum. 45 750 Subtraction of volumes Example 16: Subtract: 351 ℓ 200 mℓ from 864 ℓ 350mℓ Solution: Write the numbers in columns, the smaller number below the larger number. Steps Solved Solve these Step 1: Subtract the ℓ mℓ ℓ mℓ numbers under the 864 350 119 209 smaller unit and write the − 351 200 − 11 101 difference. 150 Step 2: Subtract the ℓ mℓ ℓ mℓ numbers under the 864 350 126 410 larger unit and write the − 351 200 − 21 200 difference. 513 150 Application Let us solve some real-life examples where conversion of units, addition and subtraction of volumes are used. Example 17: Seema has a 2 ℓ packet of milk. Express the quantity of milk in millilitres. 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. Measurements 69
Example 18: 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? Solution: The capacity of the tank = 20 litres ℓ 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 Therefore, 7 more litres of water is needed to fill the tank. 07 Higher Order Thinking Skills (H.O.T.S.) Let us see the use of standard units of volumes in a real-life situations. Example 19: A container has capacity of 2 ℓ. A glass has a capacity of 200 mℓ. How many glasses of juice must be poured to fill up the container? 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. Drill Time Concept 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 70
4) Word Problem a) Roopa’s house and the places close to it are shown on the map. 2 km 2 km Hospital Playground 4 km 2 km 1 km 250 m Market Post Office 5 km 500 m Roopa’s house School 2 km 450 m 4 km 6 km 3 km 300 m Airport Study the map and answer these questions. a) T he 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? Concept 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 Measurements 71
7) Word Problem a) Mary 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. Concept 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) Aarthi 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? 72
Chapter Data Handling 12 Let Us Learn About • understanding handling data. • making a table when data is given. • recording data using tally marks and pictorial representation. Concept 12.1: Record Data Using Tally Marks Think Farida 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 had bought for her. Do you know how? Recall We know to answer questions based on the data in a given table. Let us revise the concept by studying the following table. The number of students in a class who like different types of chocolate is given in the table. 73
Name of the chocolate Number of students Strawberry 3 Cream 6 Caramel 5 Nuts 4 a) How many students are present in the class? [] [] (A) 13 (B) 18 (C) 15 (D) 20 [] [] b) How many students like Caramel? (A) 3 (B) 6 (C) 5 (D) 4 c) Which type of chocolate is liked by four students? (A) Strawberry (B) Cream (C) Caramel (D) Nuts d) How many students like strawberry? (A) 3 (B) 4 (C) 6 (D) 5 & Remembering and Understanding Let us now learn to make a table when data is given. We can arrange the data given 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, every item of one type is denoted by drawing a vertical line (⎮). This vertical line is called tally mark. To represent 5 items we draw 4 vertical lines and cross them with the fifth line. ( ) 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. 74
Solution: Fruit Tally marks Number Apple |||| 4 Banana |||| 4 Watermelon ||| 3 Mango 6 \\||||| Application Let us see a real-life example where we represent data using tally marks. Example 2: 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 the number of medium cups. c) m ore in number than the number of 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 Data Handling 75
Higher Order Thinking Skills (H.O.T.S.) Example 3: 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) In school 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) There 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) The number of children present for a sports day is as given below. Boys: Rohan, Tushar, Sanket, Ankit, Siddharth, Harsh Girls: Piya, Kshitija, Reema, Prachi Represent the data in a table using tally marks. How many boys and how many girls were present on the sports day? d) A mi noted down the colour 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, Pooja Black: Bhavna, Rashmi, Jay, Sagar, Sonu, Tina, Mona, Shefali White: Payal, Sakshi Represent the data in a table using tally marks. 76
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