Maths Munchies Egyptians have a different way to represent fractions. 213 To represent 1 as numerator, they use a mouth picture which literally means ‘part’. So, the fraction ‘one-fifth’ will be shown as given in the image. On the other hand, fractions were only written in words in Ancient Rome. 1 was called unica 6 was called semis 12 12 1 1 was called scripulum 24 was called semunica 144 Connect the Dots Science Fun Around 7 out of 10 parts of air is nitrogen. Oxygen is at the second position. 2 out of 10 parts of air is oxygen. English Fun Think of at least two words that rhyme with each ‘numerator’ and ‘denominator’. Drill Time Concept 9.1: Fraction as a Part of a Whole 1) Find the numerator and the denominator in each of these fractions. 2 b) 1 2 a) 5 7 c) 3 45 d) 9 e) 7 Fractions 47 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 51 12/17/2018 4:12:39 PM
Drill Time 2) Identify the fractions of the shaded parts. a) b) c) d) e) Concept 9.2: Fraction of a Collection 3) Find fraction of coloured parts. a) b) c) d) e) 48 12/17/2018 4:12:39 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 52
Drill Time 4) Find 1 and 1 of the following collection. 2 4 5) Word Problems a) A circular disc is divided into 12 equal parts. Venu shaded 1 of the 4 pdiinsck and 1 of the disc green. How many parts of the disc are 3 shaded? How many parts are not shaded? and 1 of them are b) John has 24 notebooks. 1 of them are unruled 6 2 four-ruled. How many books are (a) unruled and (b) four-ruled? A Note to Parent Fractions are present all around us. The easiest way to make a child relate to fractions is through food items. Cut fruits such as apples and oranges in different equal parts and use it to help your child understand fractions. Fractions 49 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 53 12/17/2018 4:12:39 PM
Chapter Money 10 I Will Learn About • converting rupees to paise and vice-versa. • adding and subtracting money. • multiplying and dividing money. • making rate charts and bills. Concept 10.1: Convert Rupees to Paise I Think Farida has ` 38 in her piggy bank. She wants to know how many paise she has. Do you know? 10.1 I Recall We have learnt to identify different coins and currency notes. We have also learnt that 100 paise make a rupee. Let us learn more about money. 1 rupee = 100 paise 100 p = 1 rupee Let us revise the concept about money. a) Identify the value of the given coin. [ ] (A) ` 1 (B) ` 2 (C) ` 5 (D) ` 10 50 12/17/2018 4:12:39 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 54
b) The ` 500 note among the following is: [] (A) (B) (C) (D) c) The combination that has the greatest value is: [] (A) (B) (C) (D) 10.1 I Remember and Understand Let us understand the conversion of rupees to paise through an activity. Activity: The students must use their play money (having all play notes and coins). As the teacher writes the rupees on the board, each student picks the exact number of paise in it. There can be many combinations for the same amount of rupees. For example, 1 rupee is 100 paise. So, the students may take two 50 paise coins. Money 51 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 55 12/17/2018 4:12:39 PM
Let us understand the conversion through some examples. Example 1: Convert the given rupees into paise: a) ` 2 b) ` 5 c) ` 9 Solution: We know that 1 rupee = 100 paise a) ` 2 = 2 × 100 paise = 200 paise b) ` 5 = 5 × 100 paise = 500 paise Converting paise c) ` 9 = 9 × 100 paise = 900 paise into rupees is the Similarly, we can convert paise into rupees. reverse process of Example 2: Convert 360 paise to rupees. converting rupees Solution: We can convert paise to rupees as: into paise. Steps Solved Solve this 380 paise Step 1: Write the given 360 paise paise as hundreds of paise. = 300 paise + 60 paise Step 2: Rearrange 300 300 paise paise as a product of 100 = (3 × 100) paise + 60 paise paise. ` 3 + 60 paise Step 3: Write in rupees. = 3 rupees 60 paise Train My Brain Convert as given. a) 550 paise to rupees b) 25 rupees to paise c) 110 paise to rupees 10.1 I Apply Let us see some real-life examples involving the conversion of rupees into paise and paise to rupees. Example 3: Anil has ` 10 with him. How many paise does he have? Solution: 1 rupee = 100 paise 52 12/17/2018 4:12:39 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 56
So, 10 rupees = 10 × 100 paise = 1000 paise Therefore, Anil has 1000 paise with him. Example 4: Raj has 670 paise. How many rupees does he have? Solution: Amount with Raj = 670 paise = 600 paise + 70 paise = (6 × 100) paise + 70 paise = ` 6 + 70 paise = 6 rupees 70 paise Therefore, Raj has 6 rupees 70 paise. 10.1 I Explore (H.O.T.S.) Observe these examples where conversion of rupees to paise and that of paise to rupees are mostly useful. Example 5: Vani has ` 4, Gita has ` 5 and Ravi has 470 paise. Who has the least amount of money? Solution: Amount Vani has = ` 4 Amount Gita has = ` 5 Amount Ravi has = 470 paise To compare money, all the amounts must be in the same unit. So, let us first convert the amounts from rupees to paise. ` 4 = (4 × 100) = 400 paise ` 5 = (5 × 100) = 500 paise Now, arranging the money in ascending order, we get 400 < 470 < 500. Therefore, Vani has the least amount of money. Example 6: Ram has 1 rupee 10 paise, Shyam has 1 rupee 40 paise and Rishi has 1 rupee 20 paise. Arrange the amount in ascending order. Who has the most money? Solution: Amount Ram has = 1 rupee 10 paise Amount Shyam has = 1 rupee 40 paise Money 53 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 57 12/17/2018 4:12:39 PM
Amount Rishi has = 1 rupee 20 paise To compare the money, all of them must be in the same unit. So, let us convert the amounts from rupees to paise. 1 rupees 10 paise = (1 × 100) + 10 = 110 paise 1 rupees 40 paise = (1 × 100) + 40 = 140 paise 1 rupees 20 paise = (1 × 100) + 20 = 120 paise Arranging the amounts in ascending order we get, 110 < 120 < 140. Therefore, Shyam has more money than Ram and Rishi. Concept 10.2: Add and Subtract Money with Conversion I Think Farida’s father bought a toy car for ` 56 and a toy bus for ` 43. How much did he spend altogether? How much change does he get if he gives ` 100 to the shopkeeper? 10.2 I Recall Recall that two or more numbers are added by writing them one below the other. This method of addition is called the column method. We know that rupees and paise are separated using a dot or a point. In the column method, we write money in such a way that the dots or points are placed exactly one below the other. The rupees are placed under rupees and the paise under paise. Let us recall a few concepts about money through these questions. a) 50 paise + 50 paise = ________________ b) ` 50 – ` 10 = _______________ c) ` 20 + ` 5 + 50 paise = ______________ d) ` 20 + ` 10 = _______________ e) ` 50 – ` 20 = _______________ 54 12/17/2018 4:12:39 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 58
10.2 I Remember and Understand While adding and subtracting money, we write numbers one below Paise is always the other and add or subtract as needed. written in two Let us understand this through some examples. digits after the Example 7: Add: ` 14.65 and ` 23.80 point. Solution: We can add two amounts as: Steps Solved Solve these `p Step 1: Write the given numbers `p with the points exactly one below 1 4. 6 5 4 1. 5 0 the other, as shown. + 2 3. 8 0 + 4 5. 7 5 Step 2: First add the paise. `p `p Regroup the sum if needed. Write 1 the sum under paise. Place the 1 4. 6 5 3 8. 4 5 dot just below the dot. + 2 3. 8 0 + 3 5. 6 0 Step 3: Add the rupees. Add . 45 `p the carry forward (if any) from the previous step. Write the sum `p 2 3. 6 5 under rupees. 1 + 1 4. 5 2 1 4. 6 5 + 2 3. 8 0 3 8. 4 5 Step 4: Write the sum of the given ` 14.65 + ` 23. 80 amounts. = ` 38.45 Example 8: Write in columns and subtract ` 56.50 from ` 73.50. Solution: We can subtract the amounts as: Money 55 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 59 12/17/2018 4:12:39 PM
Steps Solved Solve these Step 1: Write the given numbers with the ` p `p dots exactly one below the other, as 7 3. 50 8 0. 7 5 shown. − 5 6. 50 − 4 1. 5 0 Step 2: First subtract the paise. Regroup `p `p if needed. Write the difference under 7 3. 5 0 6 0. 7 5 paise. Place the dot just below the dot. − 5 6. 5 0 − 3 2. 5 0 Step 3: Subtract the rupees. Write the difference under rupees. 00 Step 4: Write the difference of the given `p amounts. 6 13 7 3. 5 0 − 5 6. 5 0 1 7. 0 0 ` 73. 50 – ` 56. 50 = ` 17.00 Train My Brain Solve the following: b) ` 32.35 + ` 65.65 c) ` 70.75 – ` 62.45 a) ` 28.65 + ` 62.35 10.2 I Apply Look at some real-life examples where we use addition and subtraction of money. Example 9: 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. 56 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 60 12/17/2018 4:12:39 PM
Example 10: 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. 75 To find the total amount we have to add both the + 2 8. 50 amounts. 4 1. 25 So, the total amount with Ramu and his friend is ` 41.25. 10.2 I Explore (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 11: 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 Example 12: Surya went to a water park with his parents. The ticket for each ride is: Roller coaster: ` 35, River fall: ` 32, Water ride: ` 20 Surya went on two rides. He gave ` 60 and got a change of ` 5. Which two rides did he go on? Solution: Surya gave ` 60. The change he got is ` 5. The money spent for two rides = ` 60 – ` 5 = ` 55 So, we must add and check which two tickets cost ` 55. ` 35 + ` 32 = ` 67 which is not ` 55. ` 32 + ` 20 = ` 52 which is not ` 55. ` 35 + ` 20 = ` 55 Therefore, the two rides that Surya went on are roller coaster and water ride. Money 57 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 61 12/17/2018 4:12:39 PM
Concept 10.3: Multiply and Divide Money I 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? 10.3 I 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 = _____ 10.3 I Remember and Understand Multiplication and division of money is similar to that of numbers. To multiply money, first multiply the numbers under paise, In multiplication, start and place the point. Then multiply the number under multiplying from the rupees. To divide money, we divide the numbers under rightmost digit. rupees and place the point in the quotient. Then, divide In division, start dividing the number under paise. from the leftmost digit. Now, let us understand multiplying and dividing money through a few examples. Example 13: 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 58 12/17/2018 4:12:40 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 62
Example 14: 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 Train My Brain 00 Solve the following: a) ` 28 × 5 b) ` 70 ÷ 2 c) ` 44 × 5 10.3 I Apply We apply multiplication and division of money in many real-life situations. Let us see some examples. Example 15: 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 three dozen bananas = ` 48 × 3 = ` 144 4 b) one dozen (12) bananas = ` 48Train My Brain 12 48 − 48 )Cost of of Cost Cost of one banana = ` 48 ÷ 12 = ` 4 00 (Recall that 10 × 4 = 40. Then, 11 × 4 = 44 and 12 × 4 = 48). Example 16: Rahul went to buy a few chocolates. If a chocolate costs ` 20, how much would 4 such chocolates cost? ` Solution: Cost of one chocolate = ` 20 20 Cost of 4 chocolates = ` 20 × 4 = ` 80 ×4 80 10.3 I Explore (H.O.T.S.) In some situations, we have to carry out more than one operation on money. Consider the following examples. Money 59 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 63 12/17/2018 4:12:40 PM
Example 17: 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 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 Example 18: Bhanu bought some items for ` 362. She has some ` 100 notes. How many notes should she give the shopkeeper? Solution: Cost of the items = ` 362 = ` 300 + ` 62 = (` 100 x 3) + ` 62 As ` 362 has to be paid, Bhanu has to give 3 + 1 = 4 notes of ` 100. Concept 10.4: Rate Charts and Bills I 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? 10.4 I 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 = __________ f) ` 21 + ` 10 = __________ 60 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 64 12/17/2018 4:12:40 PM
10.4 I Remember and Understand Making bills Addition of A bill is a list of items that we have bought from a shop. A bill amounts is similar tells us the cost of each item and the total money to be paid to to the addition of the shopkeeper. numbers with two or more digits. 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. Let us understand how to make bills through a few examples. Example 19: 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 Scissors ` 25 Water colours ` 100 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: Write the items and their quantities in the bill. Step 2: Then write the cost per item. Step 3: Find the total cost of each item by multiplying the number of items by their rates. Money 61 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 65 12/17/2018 4:12:40 PM
Step 4: Find the total bill amount by adding the amount of each item. S.No Item Bill Rate per item Amount 1 Pencil Quantity ` 3.00 `p 2 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 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 20: 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? 62 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 66 12/17/2018 4:12:40 PM
Solution: 1. Draw a table. 2. Complete the table with each item and its rate. Item Rate (in `) Item Rate (in `) 44 1 kg sugar 40 1 litre milk 48 80 Tomato Ketchup 147 1 kg wheat 150 50 Chocolate bar 50 1 kg oranges 20 Soap bar 34 1 kg apples 1 kg tea 240 1 kg pineapple Honey 149.50 1 dozen bananas Train My Brain Answer the following questions. a) If you buy 4 items from a shop, how will you decide the amount to be paid? b) Suppose you need to buy 10 items from the shop, how will you remember the names? What will you do? How will the shopkeeper prepare a bill of the items? c) Make a bill for the following items. Cake - ` 100, candle - ` 25, 10 birthday caps - ` 5 each, 10 small gifts - ` 15 each. 10.4 I Apply 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. Money 63 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 67 12/17/2018 4:12:40 PM
Rate Chart Item Bill ` Paise Vegetables Rate per kg (in `) 1 kg brinjal Rate per kg 30 00 2 kg potato 80 00 Brinjal 30.00 2 kg tomato 30.00 40 00 1 kg onion 40.00 22 00 Cabbage 24.00 20.00 172 00 22.00 Potato 40.00 Total Tomato 20.00 Onion 22.00 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 21: 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 1 packet of Cupcake Grilled sandwich Potato wafers Item Rate 20.00 50.00 125.00 70.00 (in `) 12/17/2018 4:12:40 PM 64 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 68
What can he buy at this restaurant, if he has to spend ` 250? (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 00 250 00 1 pack of finger chips ` 40.00 Total 10.4 I Explore (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 22: Sneha went to an ice cream shop and saw the rate chart given. Sneha took 2 Butter Scotch, 2 Mango, 1 Chocolate and 1 Vanilla ice cream tubs. What is the total bill ? Make the bill. If she gave ` 1000, how much did she get as change? 1000 ml tub of ice cream Rate in ` Solution: Write the items, number of Butter Scotch 150.00 each item and their rates. Vanilla 120.00 Multiply them to find cost of 130.00 each flavour of ice cream. Strawberry Find the total by adding all Mango 140.00 the amounts. Chocolate 160.00 Money 65 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 69 12/17/2018 4:12:40 PM
Ice cream shop Item Quantity Rate per tub ` paise Butter Scotch 300 00 2 ` 150.00 Mango 2 ` 140.00 280 00 Chocolate 1 ` 160.00 160 00 Vanilla 1 ` 120.00 120 00 Total 860 00 Amount Sneha gave = ` 1000 Total bill amount = ` 860 The amount she received as change = ` 1000 – ` 860 = ` 140 Maths Munchies Punch marked coins were the first ever coins documented between 213 7th - 6th century BC and 1st century AD. Most of the coins were made of silver. Connect the Dots Social Studies Fun Different countries have different types of money. Like we have Rupees and Paise, Americans have Dollars and Cents 1 rupee = 100 paise and 1 dollar = 100 cents. 66 12/17/2018 4:12:40 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 70
English Fun Here is a poem about Indian rupee. Very odd are the things A rupee coin can make, A pleasure to give and take. Toss it up for head or tail, Buy a stamp for your mail, Offer it to god and pray, It can buy you toys of clay, Use it for a call you make, Or to check your body weight 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: b) ` 31.20 + ` 19.16 c) ` 61.21 + ` 29.20 a) ` 23.24 + ` 10.80 e) ` 60.90 + ` 24.23 d) ` 11.10 + ` 12.90 4) Subtract: b) ` 20.12 – ` 10.13 c) ` 31.55 – ` 22.44 a) ` 87.10 – ` 23.20 e) ` 56.13 – ` 12.03 d) ` 99.99 – ` 22.22 Money 67 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 71 12/17/2018 4:12:40 PM
Drill Time Concept 10.3: Multiply and Divide Money 5) Solve the following: b) ` 10 × 3 c) ` 21 ÷ 7 a) ` 23 × 2 d) ` 34 × 4 e) ` 84 ÷ 4 Concept 10.4: Rate Charts and Bills 6) The rates of some vegetables and fruits per kg are given in the box. ` 18 ` 10 ` 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 A Note to Parent Take your child shopping and show them what a bill looks like. Make them calculate the total using addition, subtraction and multiplication. 68 12/17/2018 4:12:40 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 72
Chapter Measurements 11 I Will 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 I 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? 11.1 I 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. NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 73 69 12/17/2018 4:12:40 PM
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. 11.1 I Remember and Understand 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. 70 12/17/2018 4:12:40 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 74
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 Relation between We can convert one unit of measurement into another using the units of length relation between them. 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: 4 m = ___________ cm 7 m = _______________ cm 1 m = 100 cm 4 m = 4 ×100 cm = 400 cm 4 m = 400 cm Measurements 71 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 75 12/17/2018 4:12:40 PM
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 Solution: Write the numbers in columns, one below the other. 72 12/17/2018 4:12:40 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 76
Steps Solved Solved Solve these km m Step 1: Add the m cm km m numbers under the 25 16 3 4 4 5 0 1 2 1 5 0 smaller unit and + 32 30 + 1 4 3 4 0 write the sum. 46 + 125 235 685 km m Step 2: Add the m cm 1 0 1 0 0 16 km m + 100 100 numbers under 25 30 34 450 46 + 125 235 the larger unit and + 3 2 159 685 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 m cm difference. km m 58 26 Step 2: Subtract m cm 3 12 − 39 14 the numbers 2 12 4 25 035 under the larger 2 3 2 3 0 − 2 34 015 unit and write the − 12 5 20 191 020 difference. 10 7 10 \\ \\ \\ \\ Measurements 73 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 77 12/17/2018 4:12:40 PM
Train My Brain b) Convert 8 km into m d) 42 m 30 cm – 30 m 20 cm Solve the following: a) Convert 5 m 7 cm into cm c) 10 km 20 m + 20 km 10 m 11.1 I Apply Let us solve some real-life examples with addition and subtraction of lengths. 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 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 6: 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 = 36 km 119 m − 1 4 1 1 6 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. 74 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 78 12/17/2018 4:12:41 PM
11.1 I Explore (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 50 cm. Who is taller and by how many centimetres? Solution: To compare heights of two persons, the heights must be in the same units. Height of Somu = 1 m 50 cm = 100 cm + 50 cm = 150 cm Height of Ramu = 134 cm So, Somu is taller as 150 cm > 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 6 km 4 km 2 km School 3 km 8 km House Market 10 km 3 km Railway Station Measurements 75 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 79 12/17/2018 4:12:41 PM
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? Solution: 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 I 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? 11.2 I 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. 76 12/17/2018 4:12:41 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 80
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. 11.2 I Remember and Understand Sometimes, to measure the weight of an object, we need the Relation between smaller unit instead of the larger unit. For this, we need to convert units of weight the units for appropriate measurement. Let us see how we can convert weights. 1 g = 1000 mg 1 kg = 1000 g Conversion of weights We can convert larger units of weights into smaller units using the relation between them. Measurements 77 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 81 12/17/2018 4:12:41 PM
Let us understand the conversion through a few examples. Example 9: 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 10: 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 Solved this 3 kg 150 g to grams 1 kg = 1000 g So, 3 kg = 3 × 1000 g = 3000 g 4 kg 20 g to grams 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 11: 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. 78 12/17/2018 4:12:41 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 82
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 1 7 7 0 6 435 + 108 189 895 Step 2: Add the g mg kg g g mg numbers under the 1 1 1 larger unit and write 15 150 17 706 3 3 3 3 3 the sum. + 23 285 + 22 333 435 + 108 189 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: 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 3 5 5 \\3 0\\ 5 15 260 write the difference. − 153 100 − 2 3 4 150 − 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 23 555 unit and write the − 1 5 3 1 0 0 3 5 5 \\3 0\\ 5 − 16 454 difference. 1 0 9 2 0 0 − 2 3 4 1 5 0 1 2 1 1 5 5 Measurements 79 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 83 12/17/2018 4:12:41 PM
Train My Brain Solve the following: a) Convert 5 kg into g. b) Convert 10 kg 250 g into g. c) Add 124 kg and 200 kg. d) Subtract 120 g 50 mg from 325 g 70 mg. 11.2 I Apply 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? 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 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 Therefore, the weight of the remaining pins is 32 g 32 mg 32 032 80 12/17/2018 4:12:41 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 84
11.2 I Explore (H.O.T.S.) Let us now see how we use standard units of weight in real-life situations. Example 15: Kiran weighs 12785 g 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 Weight of Kiran = 12785 g As 12785 g > 11750 g, Kiran weighs more than Venu. The difference in their weights is (12785 – 11750) g = 1250 g. Example 16: 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 Total weight of apples and grapes = 1 kg 100 g + 1 kg 150 g +1 150 2 250 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 Measurements 81 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 85 12/17/2018 4:12:41 PM
Concept 11.3: Conversion of Standard Units of Volume I 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? 11.3 I 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 in the figure. 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’. 82 12/17/2018 4:12:41 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 86
11.3 I Remember and Understand 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 Relation between units of capacity We can convert one unit of measurement into another using the relation between them. 1 litre = 1000 millilitres Let us understand the conversion of capacity from larger 1 kilolitre = 1000 litres units to smaller units through a few examples. To convert litres into millilitres, multiply by 1000. Example 17: Convert 3 ℓ into millilitres. Solution: Multiply the litres by 1000 to convert it to millilitre. Solved Solve this 3 ℓ to millilitres 7 ℓ to millilitres 1 ℓ = 1000 mℓ 3 ℓ = 3 × 1000 mℓ = 3000 mℓ Example 18: 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. Measurements 83 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 87 12/17/2018 4:12:41 PM
Addition of volumes Example 19: Add: 13 ℓ 450 mℓ and 32 ℓ 300 mℓ Solution: Write the numbers in columns. 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 20: 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 84 12/17/2018 4:12:41 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 88
Train My Brain Convert the following: a) 8 ℓ into mℓ b) 34 ℓ 420 mℓ into mℓ c) 15 ℓ into mℓ 11.3 I Apply 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. 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. 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? Solution: The capacity of the tank = 20 litres 1 ℓ Volume of water in the tank = 13 litres \\2 10 Quantity of water needed to fill the tank −1 0\\ = 20 litres – 13 litres = 7 litres 0 3 Therefore, 7 more litres of water is needed to fill the tank. 7 11.3 I Explore (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. Measurements 85 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 89 12/17/2018 4:12:41 PM
Example 24: 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. Maths Munchies 213 The blood in our body also has a unit of measurement called ‘pint’ or ‘unit’. An adult body contains 8 to 10 pints of blood. 1 pint is equal to 473 mℓ. Therefore, our body has 3784 mℓ to 4730 mℓ of blood. Connect the Dots Science Fun Dwarf Willow is one of the smallest woody plants in the world. It grows to only 1 to 6 cm in height. It has round, shiny green leaves 1 to 2 cm long and broad Social Studies Fun India measures about 3,200 kilometres from north to south. The length from the west to the east is about 2,900 kilometres. 86 12/17/2018 4:12:41 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 90
Drill Time Concept 11.1: Conversion of Standard Units of Length 1) 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? Measurements 87 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 91 12/17/2018 4:12:41 PM
Drill Time 2) Convert into centimetres. c) 2 m 45 cm a) 3 m b) 9 m d) 5 m 20 cm e) 8 m 36 cm c) 5 km 555 m 3) Convert into metres. a) 4 km b) 15 km b) 31 m 00 cm + 18 m 59 cm d) 6 km 112 m e) 1 km 100 m d) 88 km 100 m − 10 km 800 m 4) Solve the following: a) 24 m 13 cm + 13 m 45 cm c) 10 km 100 m + 20 km 200 m e) 26 m 14 cm – 20 m 10 cm 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 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 88 12/17/2018 4:12:41 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 92
Drill Time 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? A Note to Parent Ask your child to weigh different things present at home such as a pencil, flower vase or utensils. This will help them to form a clear understanding of lighter and heavier with respect to the usage of mg, g and kg. Measurements 89 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 93 12/17/2018 4:12:42 PM
Chapter Data Handling 12 I Will 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 I 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? 12.1 I 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. 90 12/17/2018 4:12:42 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 94
Name of the chocolate No. 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 12.1 I Remember and Understand Let us now learn to make a table when data is given. To represent 5 items we draw 4 vertical We can arrange the data given in the form of a table. We first lines and cross them identify different items in the data and list them out in the first with the fifth line. ( ) 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. 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. Data Handling 91 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 95 12/17/2018 4:12:42 PM
Solution: Fruit Tally marks Number Apple |||| 4 Banana |||| 4 Watermelon ||| 3 Mango \\||||| 6 Example 2: Given below are some children and the months in which they celebrate their birthdays. 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. Solution: Birthday month Tally marks Number of children January ||| 3 February | 1 March || 2 August || 2 | 1 December Train My Brain The colours of different frocks owned by Rashi are: yellow, pink, blue, green, yellow, red, pink, blue, blue, red, yellow, red, blue, pink, red, yellow. Represent this data in the form of a table using tally marks. Colours Tally marks Number 12.1 I Apply Let us see some real-life examples where we represent data using tally marks. 92 12/17/2018 4:12:42 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 96
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 the number of medium cups. c) more 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 Example 4: Nandu asked his classmates how they came to school. He noted their answers as shown below: 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 ||| Data Handling 93 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 97 12/17/2018 4:12:42 PM
12.1 I Explore (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) w hich size is 3 more than the number we get if we add the medium and the large sizes together. b) less in number than the large size t-shirts. c) m ore in number than medium size t-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 |||\\|||\\|| | 15 XXXL ||\\|| |||\\| |||\\| 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. 94 12/17/2018 4:12:42 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 98
Solution: Vehicle Tally Marks Two-wheelers |||| |||| |||| |||| |||| Three-wheelers Four-wheelers |||| |||| |||| |||| |||| |||| Maths Munchies 213 Tally is also the name of software used to maintain accounts in large companies. It is based on the same method that we use to make tables of the available items and their numbers. Connect the Dots Science Fun Data handling or recording data is useful while carrying out science experiments. Observing and studying the recorded data may lead to new discoveries and studies. Social Studies Fun The population of a country is calculated every 10 years. This activity is called Census. A census is carried out using data handling. Teams of people go to every house and manually write the number of people in the house, their names, ages and genders. This data is then arranged in tables and the final population of the city or a country is calculated. Data Handling 95 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 99 12/17/2018 4:12:42 PM
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) Ami 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. A Note to Parent To help children understand data handling, ask them to make a chart of their stationery or clothes they have. Introduce the value of maintaining a stock of their things and knowing what is missing using tally marks. 96 12/17/2018 4:12:42 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 100
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