2110032-Passport-G4-FoundationMax-Maths-FY

Connect the Dots Social Studies Fun The Earth takes 23 hours, 56 minutes and 4.09 seconds to complete a rotation. But, to make it easy to calculate time, we take this as 24 hours. English Fun A word contains ten letters, out of which three are vowels. Write the fraction of the number of consonants. Express this in decimal form. A Note to Parent Give your child a shopping bill and make him or her write the decimal numbers in it. Then ask him or her to write them as fractions and in words. Such an exercise will give them a good practice of decimals. Decimals 145 Merged File_PPS_Maths_G4_TB_Part 1.indb 145 2/1/2017 3:12:14 PM

Drill Time Concept 10.1: Conversion between Fractions and Decimals 1) Convert the following into fractions: a) 2.56 b) 14.02 c) 105.89 d) 52.60 e) 8.01 2) Convert the following into decimals: 6 2 6 23 6 6 73 6 834 45 a) b) c) d) e) 1000 10 100 10 10 10 10 10 10 100 3) Write the following decimals in words: a) 73.5 b) 413.45 c) 0.73 d) 13.45 e) 1.87 4) Word problem The measures of some objects are given in the table. Height of a flag pole 9.50 m Side of a dining table 1.20 m Distance between the 325.75 km two cities Height of a plant 127.80 cm Write these lengths in words. 146 Merged File_PPS_Maths_G4_TB_Part 1.indb 146 2/1/2017 3:12:15 PM

Mo Moneyney I Will Learn Concepts 11.1: Conversion between Rupees and Paise 11.2: Add and Subtract Money with Conversion 11.3 Multiply and Divide Money Merged File_PPS_Maths_G4_TB_Part 1.indb 147 2/1/2017 3:12:16 PM

Concept 11.1: Conversion between Rupees and Paise I Think Surbhi had some play money in the form of notes and coins. While playing, her friend gave her ` 10. Surbhi has to give paise for the amount her friend gave her. How many paise should Surbhi give her friend? To answer this, we must know the conversion of money. 11.1 I Recall We have already learnt to identify currency and coins, conversion of rupees to paise and also that 1 ` = 100 p. Let us answer these to revise the concept of conversion of money. a) ` 62 = __________ paise b) 500 paise = ` __________ c) ` 28 = __________ paise d) 900 paise = ` __________ e) ` 76 = __________ paise f) 200 paise = ` __________ 11.1 I Remember and Understand We already know that to change rupees into paise we multiply the rupees by 100. For example, as ` 1 = 100 paise, ` 3 = 3 × 100 paise = 300 paise To convert paise to rupee just add a decimal point To convert an amount in ‘rupees’ and ‘paise’ into two digits from the right. ‘paise’ we multiply the rupees by 100 and add the product to the number of paise. 148 Merged File_PPS_Maths_G4_TB_Part 1.indb 148 2/1/2017 3:12:19 PM

Let us see a few examples involving conversion between rupee and paise. Example 1: Convert ` 132.28 into paise. Solution: ` 132.28 = ` 132 + 28 p = ` 132 × 100 p + 28 p = 13200 p + 28 p = 13228 p Note: Easy way to convert rupees into paise is to remove the symbol and the dot (.) between rupees and paise and write the number together. So, ` 132.28 = 13228 p. An amount of more than 100 paise, can be expressed in rupees and paise. To convert paise into rupees and paise, divide the number by 100. Write the quotient as rupees and remainder as paise. Example 2: Convert 24365 paise into rupees and paise. Solution: 24365 p = 24300 p + 65 p = ` 243 + 65 p = ` 243.65 Note: Easy way to convert ‘paise’ into ‘rupees’ and paise is to just put a dot (.) after two digits (ones and tens places) from the right and express it as `. TTh Th H T O So, 24365 = ` 243.65 2 4 3 6 5 Solve these a) Convert ` 477.95 to b) Convert ` 892.95 into c) Convert 44390 paise paise. paise. into rupees. Money 149 Merged File_PPS_Maths_G4_TB_Part 1.indb 149 2/1/2017 3:12:19 PM

Train My Brain Solve the following: a) Convert 67923 paise into rupees. b) Convert ` 890.03 into paise. c) Convert 2234 paise into rupees. 11.1 I Apply Now let us solve some examples involving the conversion of money. Example 3: Sheeba has ` 223.57. How many paise does she have in all? Solution: Amount with Sheeba = ` 223.57 We know that, ` 1 = 100 paise. ` 223.57 = ` 223 + 57 p = 223 × 100 p + 57 p= (22300 + 57) p = 22357 p Hence, Sheeba has 22357 paise. Example 4: Anish has 2435 p and Beena has ` 23.75. Who has more money? Solution: Amount with Anish = 2435 p Amount with Beena = ` 23.75 To compare the money they have, both the amounts must be in the same units. So, we convert rupees to paise. ` 23.75 = ` 23 × 100 p + 75 p (Since ` 1 = 100 p.) = (2300 + 75) p = 2375 p Clearly, 2435 > 2375. Therefore, Anish has more money. Example 5: Ram has ` 374.50 and Chandu has ` 365.75 in their kiddy banks. Who has less amount and by how much? Solution: Amount with Ram = ` 374.50 Amount with Chandu = ` 365.75 150 Merged File_PPS_Maths_G4_TB_Part 1.indb 150 2/1/2017 3:12:19 PM

Comparing the rupee part of the amounts, we get 365 < 374. So, ` 365.75 < ` 374.50. Therefore, Chandu has less money. The difference in their amounts = ` 374.50 - ` 365.75 = ` 8.75 Therefore, Chandu has ` 8.75 less than Ram. 11.1 I Explore (H.O.T.S.) Let us see some more examples of conversion of money. Example 6: Complete the following by writing the number of different coins that can be used to pay ` 10 using different coins. 50 paise coins 1 - rupee coins ` 10 2 - rupee coins 2 - rupee coins and 1 - rupee coins 5 - rupee coins Solution: 20 50 paise coins 10 1 - rupee coins ` 10 5 2 - rupee coins 3 2 - rupee coins and 1 - rupee coins 4 2 5 - rupee coins Money 151 Merged File_PPS_Maths_G4_TB_Part 1.indb 151 2/1/2017 3:12:20 PM

Example 7: Write two different ways in which you can pay ` 50. Solution: Combination 1: ` 50 = ` 20 + ` 20 + ` 10 Combination 2 : ` 50 = ` 10 + ` 10 + ` 10 + ` 10 + ` 10 Concept 11.2: Add and Subtract Money with Conversion I Think Surbhi went shopping with her elder sister. She bought some groceries for ` 110.50, vegetables for ` 105.50 and stationery for ` 40. They had ` 300. Do you know how much money was left with them after shopping? To know the answer, we have to learn addition and subtraction of money. 11.2 I Recall Recollect that we can add or subtract money just as we add or subtract numbers. 1) To find the total amount, we write one amount below the other. We see to it that the decimal points are exactly one below the other. We then add the amounts just as we add numbers. 2) To find the difference amount, we write the smaller amount below the bigger one. We see to it that the decimal points are exactly one below the other. We then subtract the smaller amount from the bigger one. Answer the following to revise the concept of addition and subtraction of money. a) ` 22.10 – ` 11.10 = ___________ b) ` 15.30 + ` 31.45 = ___________ c) ` 82.45 – ` 42.30 = __________ d) ` 15.30 – ` 5.20 = __________ e) ` 32 + ` 7.20 = ___________ 152 Merged File_PPS_Maths_G4_TB_Part 1.indb 152 2/1/2017 3:12:23 PM

11.2 I Remember and Understand To add or subtract a given amount of money, we follow these steps: Step 1: Express the given amounts in figures as decimal numbers. Money can be added or Step 2: Arrange the given amounts in a subtracted easily using the column. column method. The rupees Place the decimal points exactly and paise should be written below one another. with the decimal points are Step 3: Add or subtract the amounts as exactly one below the other. usual. Step 4: In the sum or difference so obtained, put the decimal point exactly below the other decimal points. Let us see some examples. Example 8: Add: a) ` 547.38 + ` 130.83 b) ` 239.74 + ` 355.54 Solution: a) ` p b) ` p 1 1 1 1 5 4 7 . 3 8 2 3 9 . 7 4 + 1 3 0 . 8 3 + 3 5 5 . 5 4 ` 6 7 8 . 2 1 ` 5 9 5 . 2 8 Example 9: Subtract: a) ` 53354 − ` 24765 b) ` 866.95 − ` 492.58 Solution: a) ` p b) ` p 12 12 14 4 2 2 4 14 7 16 8 15 ` 5 3 ⁄ 3 ⁄ 5 4 ⁄ 8 6 6 . 9 5 − ` 2 4 7 6 5 − 4 9 2 . 5 8 ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ` 2 8 5 8 9 ` 3 7 4 . 3 7 Money 153 Merged File_PPS_Maths_G4_TB_Part 1.indb 153 2/1/2017 3:12:25 PM

Train My Brain Solve the following: a) ` 323.47 + ` 135.55 b) ` 656.85 + ` 750.50 c) ` 500.00 – ` 393.67 11.2 I Apply Let us now see a few real-life situations where addition and subtraction of money are used. Example 10: Anita saved ` 213.60, ` 105.30 and ` 305.45 in three months from her pocket money. How much did she save in all? Solution: Amount saved in 1 month = ` 213.60 st Amount saved in 2 nd month = + ` 105.30 Amount saved in 3 rd month = + ` 305.45 Therefore, the total amount saved in 3 months = ` 624.35 Example 11: Mrs. Gupta had ` 5000 with her. She spent ` 3520.50 for buying different food items. How much money is left with her? Solution: Amount with Mrs. Gupta = ` 5000.00 Amount spent on food items = – ` 3520.50 Therefore, the amount left with Mrs. Gupta = ` 1479.50 11.2 I Explore (H.O.T.S.) Let us see some more real-life examples involving addition and subtraction of money. Example 12: Tanya had ` 525 and her sister Tanvi had ` 330. They bought a gift for their brother’s birthday which cost ` 495.75. How much amount is left with Tanya and Tanvi so that they can continue their shopping? 154 Merged File_PPS_Maths_G4_TB_Part 1.indb 154 2/1/2017 3:12:26 PM

Solution: Amount Tanya had = ` 525 Amount Tanvi had = ` 330 Total amount = ` 525 + ` 330 = ` 855 ` p Total amount = 855 . 00 The amount spent for gift = – 495 . 75 359 . 25 Therefore, amount left with Tanya and Tanvi = ` 359.25 Example 13: The cost of three items are ` 125, ` 150 and ` 175. Suresh has only notes of ` 100. If he buys the three items, how many notes must he give the shopkeeper? Does he get any change? If yes, how much change does he get? Solution: Total cost of the three items = ` 125 + ` 150 + ` 175 = ` 450 The denomination of money Suresh has = ` 100 The nearest hundred, greater than the cost of the three items is ` 500. So, the number of notes that Suresh has to give the shopkeeper is 5. ` 450 < ` 500. So, Suresh gets change from the shopkeeper. The change he gets = ` 500 − ` 450 = ` 50 Concept 11.3: Multiply and Divide Money I Think Surbhi knows the cost of one dairy milk chocolate and the cost of five biscuit packets. She could quickly find the cost of 10 dairy milk chocolates and 1 biscuit packet. Can you do such quick calculations? To do that, we have to learn multiplication and division of money. Money 155 Merged File_PPS_Maths_G4_TB_Part 1.indb 155 2/1/2017 3:12:27 PM

11.3 I Recall Remember that we use multiplication to find cost of many items from the cost of one. Similarly, we divide to find the cost of one item from the cost of many. Multiplying or dividing an amount by a number is similar to the usual multiplication and division of numbers. Answer the following to revise the multiplication and division of numbers. a) 2356 × 10 = __________ b) 72 × 3 = ____________ c) 200 ÷ 4 = ___________ d) 549 ÷ 3 = ___________ e) 621 × 2 = _________ 11.3 I Remember and Understand Let us understand how to multiply or divide the given amounts of money. Multiplying money Train My Brain When 1 or more items are of To multiply an amount of money by a number, we follow these steps. the same price, multiply the amount by the number of Step 1: Write the amount in figures without items to get the total amount. the decimal point. To find out the price of one Step 2: Multiply it by the given number, as item, divide the total amount we multiply any two numbers. by the number of items. Step 3: In the product, place the decimal point after the second digit from the right. 156 Merged File_PPS_Maths_G4_TB_Part 1.indb 156 2/1/2017 3:12:28 PM

Example 14: Multiply: a) ` 14105 by 7 b) ` 312. 97 by 34 c) ` 506. 75 by 125 Solution: a) 2 3 b) 2 2 c) 1 1 1 ` 1 4 1 0 5 1 3 2 3 3 2 × 7 ` 3 1 2 . 9 7 ` 5 0 6 . 7 5 ` 9 8 7 3 5 × 3 4 × 1 2 5 1 1 1 1 1 1 1 2 5 1 . 8 8 2 5 3 3 . 7 5 + 9 3 8 9 . 1 0 + 1 0 1 3 5 . 0 0 ` 1 0 6 4 0 . 9 8 + 5 0 6 7 5 . 0 0 ` 6 3 3 4 3 . 7 5 Dividing money To divide an amount of money by a number, we follow these steps. Step 1: Write rupees as the dividend and the number as the divisor. Step 2: Carry out the division just as we divide any two numbers. Step 3: Place the decimal point in the quotient, immediately after dividing the rupees, that is, digits before the decimal point in the dividend. Example 15: Divide: a) ` 23415 by 7 b) ` 481.65 by 13 c) ` 543.40 by 110 Solution: a) 3345 b) 37 05. c) 494. 7 23415 13 481 65 110 543 40. . ) ) ) − 2 1↓ − 3 9↓ − 440↓ 24 91 1034 − 21 − 91 − 990 31 06 440 − 28 − 00 − 440 35 65 000 − 35 − 65 00 00 Money 157 Merged File_PPS_Maths_G4_TB_Part 1.indb 157 2/1/2017 3:12:32 PM

Train My Brain Solve the following: a) `123.67 × 768 b) ` 86.34 × 11 c) ` 334.12 ÷ 14 11.3 I Apply Let us solve some real-life examples involving multiplication and division of money. Example 16: A textbook of class 4 costs ` 75.20. What ` p is the cost of 35 such textbooks? 1 2 1 Solution: Cost of one textbook = ` 75. 20 7 5 . 2 0 × 3 5 Cost of 35 such textbooks = ` 75. 20 × 35 1 1 Therefore, the cost of 35 textbooks is + 2 3 7 6 0 0 5 2 6 0 0 ` 2632. ` 2 6 3 2 . 0 0 Example 17: 19 cakes cost ` 332. 50. What is the cost of 1 cake? 17 50. . ) Solution: Cost of 19 cakes = ` 332. 50 19 332 50 − 19↓ Cost of 1 cake = ` 332. 50 ÷ 19 142 Therefore, the cost of 1 cake is ` 17. 50. − 133 95 − 95 00 11.3 I Explore (H.O.T.S.) Let us see some more examples involving multiplication and division of money. Example 18: Multiply the sum of ` 2682 and ` 2296 by 10 . Solution: The sum of ` 2682 and ` 2296 is ` 2682 + ` 2296. 158 Merged File_PPS_Maths_G4_TB_Part 1.indb 158 2/1/2017 3:12:34 PM

1 ` 2 6 8 2 4 9 7 8 + ` 2 2 9 6 × 1 0 ` 4 9 7 8 ` 4 9 7 8 0 Therefore, the sum multiplied by 10 = 4978 × 10 = ` 49780. Example 19: A bag has one bundle of ` 50 notes and one bundle of ` 20 notes. It also has two bundles of ` 10 notes and one bundle of ` 5 notes. What is the total amount of money in the bag? [Note: Each bundle consists of 100 notes.] Solution: Amount in the bundle of ` 50 = 100 × ` 50 (1 bundle) = ` 5000 Amount in the bundle of ` 20 = ` 20 × 100 (1 bundle) = ` 2000 Amount in two bundles of ` 10 = ` 10 × 200 (2 bundles) = ` 2000 Amount in the bundle of ` 5 = ` 5 × 100 (1 bundle) = ` 500 Total money = ` 5000 + ` 2000 + ` 2000 + ` 500 = ` 9500 Therefore, the total amount of money in the bag is ` 9500. Maths Munchies To convert Rupee to Paise, add two zeros at the end of the number and 2 3 1 shift the decimal point two places to the right. Connect the Dots English Fun Apart from Hindi and English, which language appears on the front side of a currency note? Fifteen other languages appear on the reverse side of an Indian rupee note. List the names of the other languages. Money 159 Merged File_PPS_Maths_G4_TB_Part 1.indb 159 2/1/2017 3:12:35 PM

Social Studies Fun The earliest metal coins came from China. Try to find out different coins with their values and their shapes. A Note to Parent Show your child different currency notes like `10, `20, `100, and so on. Also show them some shopping bills to make them understand how addition and subtraction of money are useful in our day-to-day life. Drill Time Concept 11.1: Conversion between Rupees and Paise 1) Convert the following to paise. a) ` 632.18 b) ` 952.74 c) ` 231.48 d) ` 537.58 e) ` 724.80 2) Convert paise to rupees. a) 52865 b) 64287 c) 13495 d) 34567 e) 78654 3) Word problems a) Raju has ` 892.64. How many paise does he have in all? b) Anil has 56700 paise. How much money does he have in all? Express your answer in rupees. Concept 11.2: Add and Subtract Money with Conversion 4) Add: a) ` 875.62 + ` 964.98 b) ` 3467.45 + ` 2356. 50 c) 25382 p + 65237 p d) ` 456.23 + ` 123.75 e) ` 279.50 + ` 642.90 160 Merged File_PPS_Maths_G4_TB_Part 1.indb 160 2/1/2017 3:12:36 PM

Drill Time 5) Subtract: a) ` 132.75 – ` 112.90 b) 85732 p – 23784 p c) ` 578.14 – ` 345.89 d) ` 456.72 – ` 234.34 e) ` 784.50 – ` 234.25 6) Word problems a) Rekha has ` 451.20 and Chetan has ` 495.35 in their piggy banks. Who has more amount and by how much? b) Saurabh spent ` 213.60, ` 105.30 and ` 305.45 in three months. How much did he spend in all? c) Rama had ` 7000 with her. She spent ` 4576.50 for buying household items and food. How much money is left with her? Concept 11.3: Multiply and Divide Money 7) Multiply: a) ` 152.45 × 5 b) 27510 p × 2 c) ` 315.50 × 10 d) ` 113.50 × 15 e) ` 115.50 × 35 8) Divide: a) ` 126.12 ÷ 3 b) 22347 p ÷ 9 c) ` 111.44 ÷ 7 d) ` 121.77 ÷ 7 e) ` 824.40 ÷ 8 9) Word problems a) A packet of chips costs ` 24.40. How much will 5 such packets cost? b) A football costs ` 159.99. What is the cost of 26 such footballs? c) 35 soaps cost ` 946.75. What is the cost of 1 soap? Money 161 Merged File_PPS_Maths_G4_TB_Part 1.indb 161 2/1/2017 3:12:36 PM

M Measurementeasurement I Will Learn Concept 12.1: Multiply and Divide Lengths, Weights and Capacities Merged File_PPS_Maths_G4_TB_Part 1.indb 162 2/1/2017 3:12:37 PM

Concept 12.1: Multiply and Divide Lengths, Weights and Capacities I Think Surbhi had some guests visiting her place. Surbhi’s mother asked her to pour juice from three bottles, each of 1.5 litres, into 15 glasses. What was the total quantity of juice and how much juice was poured in each glass? To answer this question, we must learn to multiply and divide measures. 12.1 I Recall Let us revise the basic concepts of measurements, their units and the different operations involving measurements. Length: kilometre, centimetre, millimetre Weight: kilogram, gram, milligram Capacity: litre, millilitre Solve the following problems based on addition and subtraction of lengths, weights and capacities. a) 560 m 65 cm – 230 m 55 cm = ___________ b) 250 g + 2 kg 500 g = ___________ c) 5 ℓ 250 mℓ + 4 ℓ 250 mℓ = ___________ d) 240 m 22 cm – 220 m 20 cm = ___________ e) 745 km 45 m – 434 km 15 m = ___________ Measurement 163 Merged File_PPS_Maths_G4_TB_Part 1.indb 163 2/1/2017 3:12:39 PM

12.1 I Remember and Understand Let us understand the relation between the different units of length, weight and capacity in detail. Relation between units of length, weight and capacity Larger unit – Smaller unit Smaller unit – Larger unit Length 1 1 km = 1000 m 1 mm = cm 10 1 m = 100 cm 1 1 cm = m 100 1 cm = 10 mm 1 1 cm = 1000 m Weight 1 g = 1000 mg 1 1 mg = 1000 g 1 1 kg = 1000 g 1 g = 1000 kg Capacity 1 litre = 1000 mℓ 1 mℓ = 1 ℓ 1000 1 1 kilolitre = 1000 litres 1 ℓ = 1000 kℓ Conversion of smaller units to larger units Let us understand conversions through a few examples. To convert measures from a Example 1: Convert the following: larger unit to a smaller unit, we multiply. a) 5000 m to km To convert measures from a b) 8000 g to kg smaller unit to a larger unit, we c) 2000 mℓ to ℓ divide. 164 Merged File_PPS_Maths_G4_TB_Part 1.indb 164 2/1/2017 3:12:40 PM

Solution: Solved Solve these a) Conversion of m into km 5000 m = _____________ km 9000 m = ________________ km 1000 m = 1 km So, 5000 m = 5000 ÷ 1000 km = 5 km 5000 m = 5 km b) Conversion of g into kg 8000 g = _____________ kg 4000 g = ______________ kg 1000 g = 1 kg So, 8000 g = 8000 g ÷ 1000 g = 8 kg c) Conversion of mℓ into ℓ 2000 mℓ = _____________ ℓ 3000 mℓ = ______________ ℓ 1000 mℓ = 1 ℓ So, 2000 mℓ = 2000 mℓ ÷ 1000 ℓ = 2 ℓ Multiply and divide length, weight and capacity Interestingly, multiplication and division of lengths, weights and capacities are similar to that of usual numbers. Let us see a few examples. Example 2: Multiply: a) 65 kg 345 g × 28 b) 18 km 361 m × 19 c) 7 ℓ 260 mℓ × 37 Measurement 165 Merged File_PPS_Maths_G4_TB_Part 1.indb 165 2/1/2017 3:12:40 PM

Solution: a) 65 kg 345 g × 28 b) 18 km 361 m × 19 c) 7  260 m× 37 kg g km m ℓ mℓ 1 1 1 4 2 3 4 7 3 5 1 4 6 5 3 4 5 1 8 3 6 1 7 2 6 0 × 2 8 × 1 9 × 3 7 1 1 1 5 2 2 7 6 0 1 6 5 2 4 9 5 0 8 2 0 + 1 3 0 6 9 0 0 + 1 8 3 6 1 0 + 2 1 7 8 0 0 1 8 2 9 6 6 0 3 4 8 8 5 9 2 6 8 6 2 0 Example 3: Divide: a) 15 kg 183 g ÷ 21 b) 3 km 84 m ÷ 12 c) 5 ℓ 882 mℓ ÷ 17 a) 15 kg 183 g ÷ 21 b) 3 km 84 m ÷ 12 c) 5 ℓ 882 mℓ ÷ 17 15 kg 183 g 3 km 84 m 5 ℓ 882 mℓ = 15 × 1000 g + 183 g = 3 × 1000 m + 84 m = 5 × 1000 mℓ + 882 mℓ = 15183 g = 3084 m = 5882 mℓ 723 257 346 21 ) 15183 12 ) 3084 17 5882 ) − 147 − 24 − 51 0 48 0 68 − 042 − 060 0 78 0063 0084 − 068 − 0063 − 0084 0102 0000 0 0000 0 − 0102 0 15 kg183 g ÷ 21 = 723 g 3 km 84 m ÷ 12 = 257 m 5 ℓ 882 mℓ ÷ 17 = 346 mℓ Train My Brain Solve the following: a) 52 kg 240 g × 15 b) 3 ℓ 150 mℓ × 24 c) 3 km 15 m ÷ 15 166 Merged File_PPS_Maths_G4_TB_Part 1.indb 166 2/1/2017 3:12:42 PM

12.1 I Apply Let us solve a few examples based on multiplication and division of length, weight and capacity. Example 4: The distance between two post offices A and B is 58 km 360 m. What is the total distance travelled in four round trips from A to B? Solution: The distance between two post offices A and B is 58 km 360 m. Four round trips = 4 times from A to B and 4 times from B to A = 8 times the distance between A and B Therefore, the total distance travelled for four round trips = 58 km 360 m × 8 = 466 km 880 m Example 5: Mrs Rani has 2 kg of coffee powder. She wants to put it into smaller packets of 25 g each. How many packets will she need? Solution: Weight of coffee powder Mrs Rani has = 2 kg 1 kg = 1000 g 2 kg = 2 × 1000 g = 2000 g Weight of small packet = 25 g Therefore, the number of packets she needs = 2000 g ÷ 25 g = 80 Example 6: Rahul has a can of 6112 mℓ juice. If he pours it equally in 16 glasses, what is the quantity of juice in each glass? Solution: Quantity of juice in full can = 6112 mℓ Number of glasses into which the juice is poured = 16 Quantity of juice in each glass = 6112 mℓ ÷ 16 = 382 mℓ Measurement 167 Merged File_PPS_Maths_G4_TB_Part 1.indb 167 2/1/2017 3:12:43 PM

12.1 I Explore (H.O.T.S.) Sometimes we have to use more than one mathematical operation to measure things. Consider these examples. Example 7: 185 kg sugar costing ` 444 is put in paper bags. Each bag can hold 5 kg of sugar. Find the number of bags needed to pack all the sugar. Also, find the cost of each bag. Solution: Weight of sugar = 185 kg Weight of sugar in the paper bag = 5 kg Number of paper bags needed = 185 kg ÷ 5 kg = 37 Therefore, 37 paper bags of 5 kg sugar each can be made. Cost of 37 bags of sugar = ` 444 Cost of each bag = ` 444 ÷ 37 = ` 12 Therefore, 185 kg sugar is made into 37 bags costing ` 12 each. Example 8: A container can hold 13 ℓ 625 mℓ of milk in it. What is the capacity of 15 such containers? Give your answer in mℓ. Solution: Capacity of one container = 13 ℓ 625 mℓ Capacity of 15 such containers = 13 ℓ 625 mℓ × 15 = 204 ℓ 375 mℓ 1 litre = 1000 mℓ 204 ℓ = 204 × 1000 mℓ = 204000 mℓ 204 ℓ 375 mℓ = 204000 mℓ+ 375 mℓ = 204375 mℓ Therefore, the capacity of 15 cans is 204375 mℓ. Example 9: The distance between two places is 4520 km. Ratan travelled a fourth of the distance by bus paying ` 12 per km. As the bus failed, he hired a car and travelled three-fourths of the distance by paying ` 20 per km. What amount did he spend on travelling? Solution: Total distance = 4520 km 168 Merged File_PPS_Maths_G4_TB_Part 1.indb 168 2/1/2017 3:12:43 PM

1 1 of the distance = × 4520 km = 1130 km 4 4 Distance travelled by bus = 1130 km Ratan travelled 1130 km by bus. Cost of ticket per km = ` 12 Cost of ticket for 1130 km = 1130 × ` 12 = ` 13560 3 Fraction of distance travelled by car = 4 3 Actual distance travelled by car = × 4520 km 4 = 3 × 1130 km = 3390 km Cost of travelling by car per km = ` 20 Cost of travelling 3390 km = 3390 × ` 20 = ` 67800 Total amount spent by Ratan on travelling = ` 13560 + ` 67800 = ` 81360 Maths Munchies The metric system is an internationally accepted decimal system of 2 3 1 measurement. It consists of a basic set of units of measurement, now known as base units. Connect the Dots Social Studies Fun Did you know that every country uses a different group of standard measurement? For example, In India, distance is measured in kilometres and weight is measured in kilograms. However, in the United States of America, miles is used to measure distance and pound to measure weight. Measurement 169 Merged File_PPS_Maths_G4_TB_Part 1.indb 169 2/1/2017 3:12:44 PM

Science Fun A light year is the distance travelled by light in a year. It is used to measure the distances between the Earth and far away stars and galaxies. A Note to Parent Show your child various measurements written on various packaged goods. For example, milk packet, ice-cream packet, wheat flour packet, and so on for him or her to be able to visualise different measurements used in the household. Drill Time Concept 12.1: Multiply and Divide Lengths, Weights and Capacities 1) Convert: a) 2000 cm to m b) 5000 g to kg c) 5000 m to km d) 8000 mℓ to ℓ 2) Multiply: a) 85 kg 145 g ×10 b) 5 ℓ 225 mℓ × 65 c) 7 m 450 cm × 25 d) 5 km 150 cm × 12 3) Divide: a) 34 kg 450 g by 6 b) 50 ℓ 225 mℓ by 5 c) 17 m 85 cm by 9 d) 42 kg 420 g by 7 170 Merged File_PPS_Maths_G4_TB_Part 1.indb 170 2/1/2017 3:12:45 PM

D Data Handlingata Handling I Will Learn Concept 13.1: Bar Graphs Merged File_PPS_Maths_G4_TB_Part 1.indb 171 2/1/2017 3:12:47 PM

Concept 13.1: Bar Graphs I Think Surbhi attended a fruit festival conducted for a week in her school. She was asked to give a report on the sale of different fruits per day in the form of a graph. Till then Surbhi only knew how to represent the data as a pictograph. She wanted to find an easier and simpler way of representation. How do you think Surbhi would have given the report? To know this, we have to learn the concept of bar graphs. 13.1 I Recall Recall these points: • The information collected for a specific purpose is called data. • The information given as numbers is called numerical data. • The information shown in the form of pictures is called a pictograph. We have already learnt about pictographs. Let us recall them through the following. The favourite game of Class 4 boys is given. Read the pictograph and answer the questions. Key: 1 = 6 students Favourite game of Class 4 boys Volley ball Cricket 172 Merged File_PPS_Maths_G4_TB_Part 1.indb 172 2/1/2017 3:12:49 PM

Favourite game of Class 4 boys Basketball Kabaddi Football a) Which is the most favourite game of Class 4 boys? [ ] b) Which is the least favourite game of Class 4 boys? [ ] c) How many students like to play basketball? [ ] d) How many students like to play football? [ ] e) How many students like to play kabaddi? [ ] 13.1 I Remember and Understand While drawing pictographs, we choose a relevant picture to represent the given data. If the data is large, it is tedious and time consuming to draw a pictograph. An easier way of representing data is the bar graph. It uses rectangular bars of the same width. The bars in a bar graph Bar graphs are drawn on a graph paper. A suitable can be drawn either title is given for the bar graph. horizontally or vertically. Bar graphs are useful in Let us understand how to read and interpret bar comparing data. graphs. Example 1: Marks scored by Kamala in a monthly test are represented using a bar graph as given. Understand the graph and answer the questions that follow. Data Handling 173 Merged File_PPS_Maths_G4_TB_Part 1.indb 173 2/1/2017 3:12:50 PM

Kamala’s performance in a monthly test Scale on X – axis: 1 cm = 1 subject on Y – axis: 1 cm = 5 marks a) What is the title of the graph? b) In which subject did Kamala perform well? c) In which subject does Kamala need to improve? d) What are Kamala’s total marks? Solution: a) The title of the graph is “Kamala’s performance in a monthly test”. b) Kamala performed well in Mathematics, as the height of the bar representing Mathematics is the maximum. 174 Merged File_PPS_Maths_G4_TB_Part 1.indb 174 2/1/2017 3:12:51 PM

c) The height of the bar representing Social Studies is the minimum. So, Kamala needs to improve in Social Studies. d) Kamala’s total marks are 35 + 47 + 42 + 28 + 32 + 40 = 224 Example 2: Information about a primary school is represented in the form of a bar graph as shown. Observe the graph carefully and answer the questions that follow. Primary School Strength Scale: On X – axis: 1 cm = 1 class On Y – axis: 1 cm = 5 students a) What is the total strength of all the 5 classes? b) Which class has the least strength? Data Handling 175 Merged File_PPS_Maths_G4_TB_Part 1.indb 175 2/1/2017 3:12:51 PM

c) Which class has the greatest strength? d) What is the title of the graph? Solution: a) Total strength is 42 + 36 + 38 + 43 + 45 = 204 b) Class 2 c) Class 5 d) Primary School Strength Train My Brain Fill in the blanks. a) A bar graph is used to represent ___________________. b) _________________ bars are used in a bar graph. c) Bar graphs are drawn on __________. 13.1 I Apply We have learnt how to read and interpret bar graphs. Now, let us learn to draw a bar graph. Steps to draw a bar graph: Step 1: Draw one horizontal line and another vertical line, called the axes. They meet at a point called origin. Step 2: Take a suitable scale such as 1 cm = 5 units. Step 3: On the X-axis, show the items of the data and on the Y-axis show their values. Step 4: Draw bars of equal width on the X-axis. The heights of the rectangles represent the values of the data which are given on the Y- axis. Step 5: Give a relevant title to the bar graph. 176 Merged File_PPS_Maths_G4_TB_Part 1.indb 176 2/1/2017 3:12:52 PM

Let us understand this through an example. Example 3: The following pictograph shows the number of scooters manufactured by a factory in a week. Complete the pictograph. Then draw a bar graph for the same data. Weekday Scooters manufactred in a week Number of scooters Monday Tuesday Wednesday Thursday Friday Saturday Total Key: 1 = 5 scooters Solution: Let us follow these steps to draw a bar graph. Step 1: Count the number of pictures in the pictograph. Complete the table by writing the product of the number of pictures and the number of scooters as per the key. Step 2: Take a graph paper and draw the X and Y axes meeting each other at one corner as shown. Data Handling 177 Merged File_PPS_Maths_G4_TB_Part 1.indb 177 2/1/2017 3:12:53 PM

Step 3: Choose a suitable scale. Since the maximum number of scooters is 30 and the minimum is 10, we can take the scale as 1 cm = 5 scooters. Mark weekdays on the X-axis as 1 cm = 1 weekday. Mark the number of scooters manufactured on the Y-axis from 0 to 35. Take 1 cm = 5 scooters as shown. 178 Merged File_PPS_Maths_G4_TB_Part 1.indb 178 2/1/2017 3:12:54 PM

Step 4: On the X – axis, mark the points 30, 15, 20,25, 20 and 10 against the Y-axis as shown. Step 5: Draw vertical rectangular bars from these points for each weekday on the X-axis and label the graph with a title. Data Handling 179 Merged File_PPS_Maths_G4_TB_Part 1.indb 179 2/1/2017 3:12:55 PM

The same graph can also be drawn using horizontal bars by interchanging the X and Y axes. Train My Brain Example 4: The number of roses sold during a month in Roopa’s shop is given in the table. Week Number of roses sold 1 week 148 st 2 nd week 165 3 week 130 rd 4 week 172 th Represent the data in a bar graph. Solution: Scale: 180 Merged File_PPS_Maths_G4_TB_Part 1.indb 180 2/1/2017 3:12:58 PM

On X-axis: 1 cm = 1 week On Y-axis: 1 cm = 20 roses 13.1 I Explore (H.O.T.S.) Consider a few real-life examples where we represent data using a bar graph. Example 5: In 2010, the heights of Ramu, Somu, Radha and Swetha were noted as 130 cm, 125 cm, 115 cm and 120 cm respectively. After two years, their heights were again noted as 140 cm, 132 cm, 124 cm and 128 cm respectively. Draw a bar graph to represent the data and answer the questions that follow. a) Who was the tallest among the friends in 2010? b) Who was the shortest among them during 2012? c) How much taller was Ramu than Somu in 2010? d) Whose height has increased the maximum in 2 years? Data Handling 181 Merged File_PPS_Maths_G4_TB_Part 1.indb 181 2/1/2017 3:13:00 PM

e) Arrange the heights of the friends in 2010 in the ascending order and their heights in 2012 in the descending order. Solution: Name Height in 2010 Height in 2012 Ramu 130 cm 140 cm Somu 125 cm 132 cm Radha 115 cm 124 cm Swetha 120 cm 128 cm Scale: On X-axis: 2 cm = 1 student On Y -axis: 1 cm = 20 cm Solution: a) As the bar for Ramu’s height in 2010 is the highest, Ramu is the tallest among the friends in 2010. b) Radha is the shortest among them during 2012. (Shortest bar for 2012). 182 Merged File_PPS_Maths_G4_TB_Part 1.indb 182 2/1/2017 3:13:02 PM

c) Ramu is 5 cm (130 – 125) taller than Somu. d) Increase in height: Ramu: (140 – 130) cm = 10 cm Somu: (132 – 125) cm = 7 cm Radha: (124 – 115) cm = 9 cm Swetha: (128 – 120) cm = 8 cm 7 cm < 8 cm < 9 cm < 10 cm Thus, Ramu’s height increased the maximum from 2010 to 2012. e) Heights of four friends in 2010: 130 cm, 125 cm, 115 cm, 120 cm Ascending order: 115 cm, 120 cm, 125 cm, 130 cm Heights of four friends in 2012: 140 cm, 132 cm, 124 cm, 128 cm Descending order: 140 cm, 132 cm, 128 cm, 124 cm Example 6: The weights of the friends in example 5 are noted in 2010 and 2012 as given. Draw a bar graph and answer the questions that follow. Name Weight in 2010 Weight in 2012 Ramu 30 kg 34 kg Somu 34 kg 32 kg Radha 28 kg 31 kg Swetha 29 kg 31 kg a) Who weighed the most in 2010 and 2012? b) Whose weight has decreased in 2012 than in 2010? c) Name the two friends who were of equal weight in 2012. d) Whose weight in 2010 is the same as that of another in 2012? e) Write the weights of the friends in 2010 in the descending order and their weights in 2012 in the ascending order. Data Handling 183 Merged File_PPS_Maths_G4_TB_Part 1.indb 183 2/1/2017 3:13:02 PM

Solution: Scale: On X – axis: 2 cm = 1 student On Y – axis: 1 cm = 5 kg a) Somu was the heaviest in 2010 and Ramu was the heaviest in 2012. b) Somu’s weight decreased from 2010 to 2012. c) Radha and Swetha are of equal weight in 2012. d) Somu’s weight in 2010 is equal to Ramu’s weight in 2012. e) Weights in 2010: 30 kg, 34 kg, 28 kg, 29 kg Descending order: 34 kg, 30 kg, 29 kg, 28 kg Weights in 2012: 34 kg, 32 kg, 31 kg and 31 kg Ascending order: 31 kg, 31 kg, 32 kg, 34 kg 184 Merged File_PPS_Maths_G4_TB_Part 1.indb 184 2/1/2017 3:13:03 PM

Maths Munchies Data handling is used to organise data properly. Here is the simplest use of 2 3 1 data handling. Make a list of your marks in each subject, in each test on a sheet of paper. Add them for each test and know your report card even before your teacher gives you one. Compare the marks with those obtained in the previous test. This helps you to identify the areas you need to concentrate more and prepare well for the forthcoming exams. Connect the Dots Social Studies Fun The population of different states can be compared using a bar graph. English Fun Make a list of your favourite authors. Count the number of books that you know of each author. Using this data, draw a bar graph. (Some names of authors for reference: J K Rowling, Ruskin Bond, C S Lewis, Charles Dickens, R K Narayan and so on.) Data Handling 185 Merged File_PPS_Maths_G4_TB_Part 1.indb 185 2/1/2017 3:13:05 PM

A Note to Parent From newspapers or magazines, find out the bar graphs and explain what they are about. Explain the terms mentioned in the bar graph first to give the background and then form basic questions from the same. You may choose articles of common interest like cars, bikes, movies, travel, hobbies and so on. Drill Time Concept 13.1: Bar Graph 1) The marks of a student in different subjects are given in the table. Draw a bar graph. Subject Marks scored Maths 65 Science 72 English 55 Social Studies 82 Hindi 93 2) The table shows the marks secured by Rajeev in SA1 and SA2. Subject Marks in SA1 Marks in SA2 First language 65 68 Second language 72 63 English 78 80 Mathematics 60 85 Science 88 80 Social studies 54 65 186 Merged File_PPS_Maths_G4_TB_Part 1.indb 186 2/1/2017 3:13:06 PM

Drill Time Compare his performance in the two SAs by drawing a bar graph and answer the questions that follow. a) Find Rajeev’s total marks in SA1 and SA2 separately. b) In which SA has he performed well with respect to Mathematics? c) In which subject(s) had he improved from SA1 to SA2? d) In which of SA1 and SA2, had Rajeev not performed well? 3) The approximate monthly attendance of Grade4 is given in the following table. Draw a bar graph and answer the questions that follow. Month Attendance June 35 July 45 August 52 September 41 October 31 November 55 a) In which month is the average attendance the maximum? b) In which month is the average attendance the minimum? c) In which month is the average attendance less than 45? Data Handling 187 Merged File_PPS_Maths_G4_TB_Part 1.indb 187 2/1/2017 3:13:06 PM

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