Concept 11.2: Add and Subtract Money with Conversion I Think Jasleen 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? 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 in amounts, 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 = ___________ 11.2 I Remember and Understand To add or subtract a given amount of money, we follow the steps given below. Step 1: Express the given amounts in figures as decimal numbers. Step 2: Arrange the given amounts in a column. In column method, the rupees and paise should be written Place the decimal points exactly below one with the decimal points Step 3: another. exactly one below the other. Add or subtract the amounts as usual. Money 47
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 11 5 4 7.38 2 3 9.7 4 + 1 3 0.83 + 3 5 5.5 4 ` 6 7 8.21 ` 5 9 5.2 8 Example 9: Subtract: a) ` 53354 − ` 24765 b) ` 866.95 − ` 492.58 p Solution: b) ` a) ` 12 12 14 7⁄ 1⁄6 8⁄ 1⁄5 8 6 6.9 5 4⁄ 2⁄ 2⁄ 4⁄ 1⁄4 − 4 9 2.5 8 53354 −24765 ` 3 7 4.3 7 ` 2 8 5 8 9 Train My Brain Solve the following: b) ` 656.85 + ` 750.50 c) ` 500.00 – ` 393.67 a) ` 323.47 + ` 135.55 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 the 1st month = ` 213.60 Amount saved in the 2nd month = + ` 105.30 Amount saved in the 3rd month = + ` 305.45 Therefore, the total amount saved in 3 months = ` 624.35 48
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 solve a few more real-life examples involving addition and subtraction of money. Example 12: Tanya had ` 525 and her friend Arpan had ` 330. They bought a gift for their brother’s birthday costing ` 495.75. How much amount is left with Tanya and Arpan so that they can continue their shopping? Solution: Amount Tanya had = ` 525 Amount Arpan had = ` 330 Total amount = ` 525 + ` 330 = ` 855 `p Total amount = 855 . 00 – 495 . 75 The amount spent for the gift = 359 . 25 Therefore, ` 359.25 is left with Tanya and Arpan. 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 Money 49
Concept 11.3: Multiply and Divide Money I Think Jasleen 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? 11.3 I Recall Remember that we use multiplication to find cost of many items from the cost of one. Similarly, we use division 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 When 1 or more items are of the To multiply an amount of money by a number, we same price, multiply the amount follow these steps. by the number of items to get the total amount. Step 1: Write the amount in figures without the decimal point. To find out the price of one item, divide the total amount by the number of items. 50
Step 2: Multiply it by the given number, as we multiply any two numbers. Step 3: In the product, place the decimal point ( if the amount is a decimal number) after the second digit from the right. 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) 11 1 13 2 `14105 33 2 ` 312 . 97 ×7 × 34 ` 506 . 75 `98735 1 11 × 125 1251 . 88 111 + 9389 . 10 ` 10640 . 98 2533 . 75 + 10135 . 00 + 50675 . 00 ` 63343 . 75 Dividing money To divide an amount by a number, we follow these steps. Step 1: Write the amount 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) 4.94 )7 23415 )13 481.65 )110 543.40 − 21↓ − 39↓ − 440↓ 24 91 1034 − 21 − 91 − 990 31 06 440 − 28 − 00 − 440 35 65 000 − 35 − 65 00 00 Money 51
Train My Brain Solve the following: b) ` 86.34 × 11 c) ` 334.12 ÷ 14 a) `123.67 × 768 11.3 I Apply Let us solve a few real-life examples involving multiplication and division of money. Example 16: A textbook of class 4 costs ` 75.20. What is the ` p cost of 35 such textbooks? Solution: 1 20 Cost of one textbook = ` 75. 20 21 35 75 Cost of 35 such textbooks = ` 75. 20 × 35 . 00 × . 00 Therefore, the cost of 35 textbooks is ` 2632. 1 1 00 3 76 + 2 2 56 `2 6 32 Example 17: 19 cakes cost ` 332.50. What is the cost of 1 cake? Solution: Cost of 19 cakes = ` 332.50 17.50 Cost of 1 cake = ` 332.50 ÷ 19 Therefore, the cost of 1 cake is ` 17. 50. )19 332.50 Train My Bra−1i9n↓ 142 − 133 95 − 95 00 11.3 I Explore (H.O.T.S.) Let us see a few more examples involving multiplication and division of money. Example 18: Multiply the sum of ` 2682 and ` 2296 by 10. 52
Solution: The sum of ` 2682 and ` 2296 is ` 2682 + ` 2296. ` ` 1 8 497 0 2682 ×1 0 +2296 `4 9 7 8 4978 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 213 To convert rupee to paise, add two zeros at the end of the number and 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 53
Social Studies Fun The earliest metal coins came from China. Try to find out different coins with their values and their shapes. Drill Time Concept 11.1: Conversion of 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) Rehmat has ` 892.64. How many paise does he have in all? b) Andrews 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 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) Rosy has ` 451.20 and Chetan has ` 495.35 in their piggy banks. Who has more amount and by how much? b) Shane spent ` 213.60, ` 105.30 and ` 305.45 in three months. How much did he spend in all? 54
Drill Time 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? 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. Money 55
Chapter Measurements 12 I Will Learn About • relation between units of length, weight and capacity. • converting smaller units to larger units. • multiplying and dividing length, weight and capacity. Concept 12.1: Multiply and Divide Lengths, Weights and Capacities I Think Jasleen had some guests visiting her place. Jasleen’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? 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. 56
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 = ___________ 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 km = 1000 m 1 1 m = 1000 km 1 m = 100 cm 1 1 cm = 100 m 1 cm = 10 mm Weight 1 Capacity 1 mm = 10 cm 1 g = 1000 mg 1 kg = 1000 g 1 1 litre = 1000 mℓ 1 mg = 1000 g 1 1 g = 1000 kg 1 1 mℓ = 1000 ℓ 1 kilolitre = 1000 litres 1 1 ℓ = 1000 kℓ Measurements 57
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, a) 5000 m to km we multiply. b) 8000 g to kg c) 2000 mℓ to ℓ To convert measures from a Solution: smaller unit to a larger unit, we divide. Solved Solve these a) Conversion of m into km 9000 m = ________________ km 5000 m = _____________ km 4000 g = ______________ kg 1000 m = 1 km 3000 mℓ = ______________ ℓ So, 5000 m = 5000 ÷ 1000 m = 5 km 5000 m = 5 km b) Conversion of g into kg 8000 g = _____________ kg 1000 g = 1 kg So, 8000 g = 8000 ÷ 1000 g = 8 kg c) Conversion of mℓ into ℓ 2000 mℓ = _____________ ℓ 1000 mℓ = 1 ℓ So, 2000 mℓ = 2000 ÷ 1000 mℓ = 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: Solve: a) 65 kg 345 g × 28 58
b) 18 km 361 m × 19 c) 7 ℓ 260 mℓ × 37 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 73 5 1 42 34 18 361 65 345 × 14 × 1 19 7 260 28 165 1 183 249 × 37 522 348 610 +1 3 0 6 859 1 1829 760 50 820 900 660 + + 217 800 268 620 Example 3: Solve: 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 346 723 257 )17 5882 )21 15183 )12 3084 − 51 − 147 − 24 078 048 068 − 068 − 042 − 060 0102 0063 0084 − 0102 − 0063 − 0084 0 0000 0000 5 ℓ 882 mℓ ÷ 17 = 346 mℓ 15 kg183 g ÷ 21 = 723 g 3 km 84 m ÷ 12 = 257 m Measurements 59
Train My Brain Solve the following: b) 3 ℓ 150 mℓ × 24 c) 3 km 15 m ÷ 15 a) 52 kg 240 g × 15 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 between A and 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 in 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 one 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 Therefore, each glass contains 382 ml of juice. 60
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 packed 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 can be packed into 37 bags costing ` 12 each. Example 8: A container can hold 13 ℓ 625 mℓ of milk. 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 1 of the distance = 1 × 4520 km = 1130 km 4 4 Distance travelled by bus = 1130 km Measurements 61
Ratan travelled 1130 km by bus. Cost of ticket per km = ` 12 213 Cost of ticket for 1130 km = 1130 × ` 12 = ` 13560 Fraction of distance travelled by car = 3 4 Actual distance travelled by car = 3 × 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 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 measurements? 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. 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 distant stars and galaxies. 62
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) 11 m 50 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 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 them to be able to visualise different measurements used in the household. Measurements 63
Chapter Data Handling 13 I Will Learn About • reading and interpreting bar graphs. • drawing bar graphs based on the given data. Concept 13.1: Bar Graphs I Think Jasleen 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 Jasleen 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 Jasleen would have given the report? 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. 64
Let us recall the pictographs through the following example. The favourite sports of Class 4 students are given. Read the pictograph and answer the questions. Key: 1 = 6 students Favourite Sports of Class 4 Students Volleyball Cricket Basketball Kabaddi Football a) The most favourite sports of Class 4 students is _____________. b) The least favourite sports of Class 4 students is _____________. c) The number of students who like to play basketball is___________. d) The number of students who like to play football is _____________. e) The number of students who like to play kabaddi is _____________. 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. Data Handling 65
An easier way of representing data is the bar graph. It uses The bars in a bar graph rectangular bars of the same width. can be a drawn either horizontally or vertically. Bar graphs are drawn on a graph paper. A suitable title is given for the bar graph. Let us understand how to read and interpret bar graphs. Example 1: The 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. Scale: X-axis: 1 cm = 1 subject; Y-axis: 1 cm = 5 marks Kamala’s Performance in a Monthly Test Marks English Maths Science Social Music Hindi Studies Subjects a) What is the title of the graph? b) In which subject did Kamala perform the best? c) In which subject does Kamala need to improve? 66
d) What are Kamala’s total marks? Solution: a) The title of the graph is “Kamala’s Performance in a Monthly Test”. b) The height of the bar representing Maths is maximum. It means that, Kamala performed the best in Maths. 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. Scale: X-axis: 1 cm = 1 class; Y-axis: 1 cm = 5 students Strength of Primary School l oohcS Class strength Class a) What is the total strength of all the 5 classes? Data Handling 67
b) Which class has the least strength? 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) Strength of a Primary School 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 the 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. Let us understand this through an example. Example 3: The following pictograph shows the number of scooters manufactured by a factory in a week. 68
Complete the pictograph. Then draw a bar graph for the same data. Key: 1 = 5 scooters Weekday Scooters manufactured in a week Number of scooters Monday Tuesday Wednesday Thursday Friday Saturday Solution: Total Step 1: Let us follow these steps to draw a bar graph. Step 2: 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 per key. Take a graph paper and draw the X and Y axes meeting each other at one corner as shown. Data Handling 69
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. Number of scooters manufactured Mon Tues Wed Thurs Fri Sat Weekdays 70
Step 4: On the X-axis, mark 30, 15, 20, 25, 20 and 10 against the Y-axis as shown. We Y - axis can plot these points two points apart. Number of scooters manufactured X - axis Monday Tuesday Wednesday Thursday Friday Saturday Weekdays Step 5: Draw vertical rectangular bars from these points for each weekday on the X-axis. Give a suitable title to the graph. Scale: X-axis: 1 cm = 1 day; Y-axis: 1 cm = 5 scooters Weekly Manufacturing of Scooters Number of scooters manufactured Monday Tuesday Wednesday Thursday Friday Saturday 71 Weekdays Data Handling
We can draw the same graph using horizontal bars by interchanging the values on X and Y axes. Weekly Manufacturing of Scooters Weekdays Number of scooters manufactured Example 4: The number of roses sold during a month in Roopa’s shop is given in the table Week Number of roses sold 1st week 148 2nd week 165 3rd week 130 4th week 172 Represent the data in a bar graph. 72
Solution: Scale: X-axis: 1 cm = 1 week;Y-axis: 1 cm = 20 roses Roses sold Weeks 13.1 Train My Brain 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 73
e) A rrange the children’s heights in 2010 in ascending order and their heights in Solution: 2012 in descending order. 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 Comparison of Heights Height (in cm) Names of children 74
a) A s the bar for Ramu’s height in 2010 is the highest, Ramu is the tallest among the children. b) Radha is the shortest among them in 2012. (Shortest bar in 2012). c) Ramu is 5 cm (130 – 125) taller than Somu. d) Increase in the heights of the children in the two years: Ramu: (140 – 130) cm = 10 cm S omu: (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 Therefore, Ramu’s height increased the maximum in 2 years. e) Heights of the children in 2010: 130 cm, 125 cm, 115 cm, 120 cm Ascending order: 115 cm, 120 cm, 125 cm, 130 cm Heights of the children 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 four children are noted in 2014 and 2016 as given. Draw a bar graph and answer the questions that follow. Name Weight in 2014 Weight in 2016 Ram 30 kg 34 kg Shyam 34 kg 32 kg Reema 28 kg 31 kg Seema 29 kg 31 kg a) Who weighed the most in 2014 and 2016? b) Whose weight has decreased in 2016 from 2014? c) Name the two children who were of the same weight in 2016. d) Whose weight in 2014 is the same as that of another child in 2016? Data Handling 75
e) W rite the weights of the children in 2014 in descending order and their Solution: weights in 2016 in ascending order. Scale: O n X-axis: 2 cm = 1 student; Y-axis: 1 cm = 5 kg Comparison of Weights Comparison of Weights Weights (in kg) Ram Shyam Reema Seema Names of children a) Shyam was the heaviest in 2014 and Ram was the heaviest in 2016. b) Shyam’s weight decreased in 2016 from 2014. c) Reema and Seema are of the same weight in 2016. d) Shyam’s weight in 2014 is equal to Ram’s weight in 2016. e) Weights in 2014: 30 kg, 34 kg, 28 kg, 29 kg Descending order: 34 kg, 30 kg, 29 kg, 28 kg Weights in 2016: 34 kg, 32 kg, 31 kg and 31 kg Ascending order: 31 kg, 31 kg, 32 kg, 34 kg 76
Maths Munchies Data handling is used to organise data properly. Here is the simplest use of data 213 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 77
Drill Time Concept 13.1: Bar Graphs 1) The score of students in an essay writing competition are given in the table. Draw a bar graph. Subject Marks scored Piyush 65 Suman 72 Vaishnavi 82 Pooja 93 2) The table shows the marks secured by Rajeev in Test 1 and Test 2. Subject Marks in Test 1 Marks in Test 2 Hindi 65 68 78 80 English 60 85 Mathematics 88 80 54 65 Science Social Studies C ompare his performance in the two tests by drawing a bar graph and answer the questions that follow. a) Find Rajeev’s total marks in Test 1 and Test 2 separately. b) In which of the two tests did he perform well with respect to Mathematics? c) In which subject(s) has he improved from Test 1 to Test 2? d) In which of the two tests has Rajeev got less marks? 3) The approximate monthly attendance of Grade 4 is shown in the pictograph given. Draw a bar graph and answer the questions that follow. 78
Drill Time Attendance Month June July August September October November Key: 1 = 10 students Data Handling 79
Drill Time a) In which month is the attendance maximum? b) In which month is the attendance minimum? c) In which months is the attendance less than 45? 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. 80
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