Hazelwood G3 Maths TB P2_Nameslip.pdf 1 8/4/2023 1:20:28 PM Name: _________________________________________ Section: ________________ Roll No.: ______________ School: ________________________________________ MATHEMATICS TEXTBOOK Part - 2
PREFACE The latest National Curriculum Framework (NCF), furthering 1 the vision of the National Education Policy (NEP) 2020, provides a comprehensive framework for the holistic 5 2 development of students. It places a strong emphasis on 4 foundational literacy and numeracy and a competency-based and learner-centred approach to ensure a well-rounded education that prepares students for the challenges of the 21st century. ClassKlap by Eupheus partners with schools and supports them through the steps of planning, teaching, learning, 3 personal revision and assessment to equip students with the desired knowledge and skills relevant to the 21st century. The present series has been carefully crafted to provide a solid foundation for students keeping in mind the principles outlined in the NCF. The books promote active learning and skill development and strive to ensure inclusiveness in terms of gender and diversity in representation, catering to the heterogeneous Indian classroom. The books have been split into two parts for lighter bag weight. The larger aim of Mathematics teaching is to develop the abilities of a student to think and reason mathematically, pursue assumptions to their logical conclusions and handle abstraction. To this end, the Mathematics textbooks and workbooks offer the following features: Skill-based lessons are structured as per Bloom’s Revised Taxonomy (Remember-Understand-Apply-Analyse-Evaluate-Create) Inquiry-based lessons are structured based on a Socratic approach using a question-answer format, aiming at discovery-based learning as per NCF guidelines Student engagement through simple, age-appropriate language Increasing rigour in sub-questions for every question in order to scaffold learning for students Word problems based on real-life scenarios help students relate Mathematics to their everyday experiences Mental Maths practice to inculcate level-appropriate mental calculation skills Stepwise breakdown of solutions to provide an easier premise for learning problem-solving skills Fostering interdisciplinary learning by connecting themes and concepts across subjects The Mathematics textbooks, workbooks and teacher companion books aim to enhance logical reasoning, problem-solving and critical thinking skills that are at the heart of Mathematics teaching and learning. It is our sincere hope that this series will enable students to deepen their understanding and appreciation of Mathematics. Hazelwood_G3_Maths_TB_Part 2.indb 2 06-08-2023 00:00:51
ENGLISH COURSEBOOK FEATURESTEXTBOOK FEATURES Art-Integrated Learning Let Us Learn About Lesson plans provided for Indicates the learning outcomes to be covered in the lesson art-integrated learning Recall SKILL-BASED LESSONS Revises the pre-requisite knowledge needed for the concept covered Think previously Introduces the concept and arouses Remembering and curiosity about it among students Understanding Application Explains the fundamental aspects of the concept in detail, in an age-appropriate Connects the concept to real-life situations and engaging manner by enabling students to apply what has been learned through practice questions Drill Time Higher Order Thinking Additional practice questions at the Skills (H.O.T.S.) end of every concept Encourages students to extend the Connect the Dots concept to advanced scenarios using higher-order thinking skills A multidisciplinary section to connect the lesson theme with other subjects INQUIRY-BASED LESSONS Reflection Time! Concepts organised using a Thought-provoking questions to question-answer approach to foster encourage reflection on the concept and a mindset of inquiry and reasoning on how it is related to the student's life, experiences and the world around Hazelwood_G3_Maths_TB_Part 2.indb 3 06-08-2023 00:00:54
Contents 3Class 7 Time 1 3 7.1 Read a Calendar Art-Integrated Learning Inquiry-Based 11 7.2 Read Time Correct to the Hour Skill-Based 21 29 8 Division 35 8.1 Divide 2-digit and 3-digit Numbers by 1-digit Numbers Skill-Based 39 42 9 Fractions 44 9.1 Fraction as a Part of a Whole 48 Art-Integrated Learning Skill-Based 55 61 9.2 Fraction of a Collection Skill-Based 66 10 Money 10.1 Convert Rupees to Paise Skill-Based 10.2 Add and Subtract Money with Conversion Inquiry-Based 10.3 Multiply and Divide Money Inquiry-Based 10.4 Rate Charts and Bills Inquiry-Based 11 Measurements 11.1 Conversion of Standard Units of Length Skill-Based 11.2 Conversion of Standard Units of Weight Skill-Based 11.3 Conversion of Standard Units of Volume Skill-Based 12 Data Handling 12.1 Record Data Using Tally Marks Art-Integrated Learning Skill-Based Hazelwood_G3_Maths_TB_Part 2.indb 4 06-08-2023 00:01:00
Chapter Time 7 Let Us Learn About • identifying a day and a date on a calendar. • reading the time correctly to the hour. 7.1: Read a Calendar The calendar that we use is called We have learnt there are 7 days in a week and 12 months in a the Gregorian year. Can you recall them? calendar. Do you know that we can see the days of the week and the months of the year in a calendar? But what is a calendar and how do we read one? A calendar lists the days and months of a year. We can find the day of a given date on a calendar. We can also find dates that fall on a particular day of a month. You can see the number of days in January by looking at the given calendar. Look at the number of times weekdays and weekends appear in the month. For example, notice that there are five Sundays, five Mondays and five Tuesdays in January, but the rest of the days of the week only appear four times in January. Hazelwood_G3_Maths_TB_Part 2.indb 1 1 06-08-2023 00:01:03
Calendars also help you find specific days and dates in a month. By looking at the calendar, you can see that the Republic Day falls on the 26th of January and that it is on the fourth and last Thursday of the month. In fact, you can find all national holidays and festivals, such as Independence Day, Diwali, Eid, Children’s day, Christmas and so on, by simply turning the pages of your calendar. You can even find the day that your birthday falls on. You can also check when your summer vacation begins and ends. Look at this year’s calendar and answer the following questions. • When is/was your parents’ birthday? • On which day is/was your birthday this year? • On what date and day is/was your best friend’s birthday? Reflection Time! 1) We use the calendar on a daily basis for different reasons. Can you think of any two reasons? 2) Use the calendar to answer the question: Rupali is a clerk in a bank. She has holidays on Sundays and on the first and the third Saturdays of the month. She also has holidays on New Year’s Day and Republic Day. How many holidays does she have in the month of January this year? 2 06-08-2023 00:01:03 Hazelwood_G3_Maths_TB_Part 2.indb 2
Drill Time 7.1: Read a Calendar 1) Observe the calendar and answer the following questions. a) H ow many weekends and weekdays are JANUARY there in the month shown in the calendar? SUN MON TUES WED THU FRI SAT (Consider Saturday and Sunday as 1234 weekend days.) 5 6 7 8 9 10 11 b) W rite the day and date two days before 12 13 14 15 16 17 18 the fourth Saturday of January. 19 20 21 22 23 24 25 26 27 28 29 30 31 c) On which day does the month end? 2) Word Problems a) R aju bought a new dress on 1st SEPTEMBER September. He bought another new SUN MON TUES WED THU FRI SAT dress 10 days after the first day of the 1 2 34567 same month. On which date did he buy 8 9 10 11 12 13 14 the other dress? 15 16 17 18 19 20 21 b) Shane’s birthday was on 2nd September. 22 23 24 25 26 27 28 What is the date if he celebrated it on 29 30 the same day of the third week. c) A rif solved problems from one chapter of his book on 9th September. He solved problems from the next chapter 5 days later. On which day did he solve problems from the next chapter? Concept 7.2: Read Time Correct to the Hour Think Farida’s teacher taught her to read time. She now knows the units of time. Farida reads time when her father moves the hands of a clock to different numbers. Can you also read time from a clock? Time 3 Hazelwood_G3_Maths_TB_Part 2.indb 3 06-08-2023 00:01:04
Recall We learnt that the long hand on the clock shows minutes and the short hand shows hours. In some clocks, we see another hand, thinner than the hour and the minute hands. This is the seconds hand. Let us recall reading time from a clock. a) 7 o’clock is _______________ hours more than 4 o’clock. b) The _______________ hand takes one hour to go around the clock. c) The _______________ hand is the shortest hand on the clock. d) T he time is _______________ when both the hour hand and the minute hand are on 12. e) 2 hours before 10 o’clock is _______________. & Remembering and Understanding We see numbers 1 to 12 on the clock. These numbers are for counting hours. There are 60 parts or small lines between these numbers. They stand for minutes. The minute hand takes 1 hour to go around the clock face once. 1 hour is equal to 60 minutes. The minute hand takes 5 minutes to go from one number to the next number on the clock face. We multiply the number to which the minute hand points by 5 to get the minutes. For example, the minute hand in the clock is at 6. So, it denotes 6 × 5 = 30 minutes past the hour (here, after 3). Therefore, the time is read as 3:30. The hour hand takes one hour to move from one number to the other. Let us now read the time shown by these clocks. 4 06-08-2023 00:01:05 Hazelwood_G3_Maths_TB_Part 2.indb 4
Fig. (a) Fig. (b) Fig. (c) Fig. (d) In figure (a), the minute hand is at 9. The hour hand is in between 5 and 6 . The number of minutes is 9 × 5 = 45. Thus, the time shown is 5:45. In figure (b), the minute hand is at 6. The number of minutes is 6 × 5 = 30. The hour hand is between 7 and 8. Therefore, the time shown is 7:30. In figure (c), the minute hand is at 3. The number of minutes is 3 × 5 = 15. The hour hand has just passed 9. Therefore, the time shown is 9:15. In figure (d), the minute hand is at 4. So, the number of minutes is 4 × 5 = 20. The hour hand has just passed 2. Therefore, the time shown is 2:20. Example 1: On which number is the minute hand if the time is as given? a) 35 minutes b) 15 minutes c) 40 minutes d) 30 minutes Solution: To find minutes when the minute hand is at a number, we multiply by 5. So, to get the number from the given minutes, we must divide it by 5. a) 35 ÷ 5 = 7. So, the minute hand is at 7. b) 15 ÷ 5 = 3. So, the minute hand is at 3. c) 40 ÷ 5 = 8. So, the minute hand is at 8. d) 30 ÷ 5 = 6. So, the minute hand is at 6. Quarter past, half past and quarter to the hour We know that, ‘quarter’ means 1 . 4 In Fig (a), the minute hand of the clock has travelled a quarter of an hour. So, we call it quarter past the hour. Fig. (a) Time 5 Hazelwood_G3_Maths_TB_Part 2.indb 5 06-08-2023 00:01:10
The time shown is 2:15 or 15 minutes past 2 or quarter past 2. ‘Half’ means 1 2 In Fig. (b), the minute hand has travelled half the clock after an hour. So, we call it half past the hour. The time shown is 2:30 or 30 minutes past 2 or half past 2. Fig. (b) Fig. (c) In Fig. (c), the minute hand has to travel a quarter of the clock before it completes one hour. We call it quarter to the hour. The time shown is 7:45 or 45 minutes past 7 or quarter to 8. Example 2: Read the time in each of the given clocks and write it in two different ways. Solved Solve these Fig. (a) Fig. (b) Fig. (c) Fig. (d) The hour hand is The hour hand is The hour hand is The hour hand is between 3 and 4. between _____ and between _____ and between _____ and _____. The minutes _____. The minutes _____. The minutes The minutes are are after ____hours. are after ____hours. are after ____hours. after 3 hours. The The minute hand The minute hand The minute hand minute hand is at is at _____. So, is at _____. So, is at _____. So, 6. So, the time is 30 the time is _____ the time is _____ the time is _____ minutes after 3. We minutes after _____. minutes after _____. minutes after _____. write it as 3:30 or We write it as _____ We write it as _____ We write it as _____ half past 3. or _____. or _____. or _____. Application We have learnt how to read the time. Now let us draw hands on the clocks when the time is given. 6 06-08-2023 00:01:16 Hazelwood_G3_Maths_TB_Part 2.indb 6
Example 3: Draw the hands of a clock to show the given time. a) 1:15 b) 6:15 c) 7:30 d) 9:45 Solution: To draw the hands of a clock, first note the minutes. If the minutes are between 1 and 30, draw the hour hand between the given hour and the next. But care should be taken to draw it closer to the given hour. If the minutes are between 30 and 60, draw the hour hand closer to the next hour. Then, draw the minute hand on the number that shows the given minutes. a) b) c) d) Example 4: Draw the hands of a clock to show the given time. a) Quarter to 7 b) Half past 4 Solution: a) b) Higher Order Thinking Skills (H.O.T.S.) We have learnt to read and show time, exact to minutes and hours. Let us now learn to find the length of time between two given times. Time 7 Hazelwood_G3_Maths_TB_Part 2.indb 7 06-08-2023 00:01:19
Example 5: The clocks given show the start time and the end time of the Maths class. How long was the class? Solution: The start time is 10:00 and the end time is 10:45. The difference in the given times = 10:45 – 10:00 = 45 minutes Therefore, the length of the Maths class was 45 minutes. Example 6: Sanjay spends an hour between 4:30 and 5:30 doing different activities. The start time for each activity is as shown. playing drinking milk homework TV on TV off Read the clocks and answer the following questions. a) When did Sanjay begin drinking milk? b) For how long did he play? c) For how long did he watch TV? d) When did he switch off the TV? Solution: From the given figures, a) Sanjay began drinking milk at 4:45. b) S anjay began playing at 4:30 and ended at 4:45. So, he played for a quarter hour (15 minutes) as 4:45 – 4:30 = 15 minutes. c) The time for which he watched TV was 5:30 – 5:20 = 10 minutes. d) Sanjay switched off the TV at 5:30. The time between two given times is called the length of time. It is also called time duration or time interval. It is given by the difference of end time and start time. 8 Hazelwood_G3_Maths_TB_Part 2.indb 8 06-08-2023 00:01:23
Drill Time Concept 7.2: Read Time Correct to the Hour 1) Draw the hands of the clock to show the given time. a) Half past 2 b) 4:15 c) Quarter to 12 d) 4:25 e) 6:20 f) Quarter past 5 2) What is the time shown on each of these clocks? a) b) c) d) 3) Word problems a) On which number is the minute hand if the time is as given? A) 25 minutes B) 45 minutes C) 20 minutes D) 50 minutes b) The start time of Ram’s activities are shown in these figures. wake up brush have bath Hazelwood_G3_Maths_TB_Part 2.indb 9 Time 9 06-08-2023 00:01:30
Wear uniform study breakfast From the figures, answer the following questions. A) When did Ram wake up? B) How much time did Ram spend to wear his school uniform? C) When did Ram start studying? D) At what time did Ram have his breakfast? Connect the Dots Science Fun Have you noticed that you start feeling hungry between 12 noon to 2 o’clock? Why don’t you feel hungry before that? Train My Brain It is because our body gets used to a sequence of events. This sequence of events is called our ‘body cycle’. Another example of the body cycle is that if you sleep daily by 10:00 p.m. then you will feel sleepy at that time even when you are not in your bed. 10 06-08-2023 00:01:33 Hazelwood_G3_Maths_TB_Part 2.indb 10
Chapter Division 8 Let Us Learn About • dividing 2-digit and 3-digit numbers by 1-digit numbers. • checking the correctness of division. Concept 8.1: Divide 2-digit and 3-digit Numbers by 1-digit Numbers Think Farida has 732 stickers. She wants to distribute them equally among her 3 friends. How will she distribute them? Recall In the previous grade, we have learnt that division is related to multiplication. For every division fact, we can write two multiplication facts. For example, the two multiplication facts of 35 ÷ 7 = 5 are: a) 7 × 5 = 35 and b) 5 × 7 = 35. Let us answer these to recall the concept of division. a) The number which divides a given number is called _________________. b) The answer we get when we divide a number by another is called ______________________. 11 Hazelwood_G3_Maths_TB_Part 2.indb 11 06-08-2023 00:01:35
c) The division facts for the multiplication fact 2 × 4 = 8 are ________________ and __________________. & Remembering and Understanding We can make equal shares or groups and divide with the help of vertical arrangement. A number divided by the same number is always 1. Let us see some examples. D ividing a 2-digit number by a 1-digit number (1-digit quotient) Example 1: Solve: 45 ÷ 5 Solution: Follow these steps to divide a 2-digit number by a 1-digit number. Steps Solved Solve these Step 1: Write the dividend and 5)45 Dividend = _____ Divisor = ______ )divisor as shown: Divisor Dividend Quotient = ____ Remainder = _____ Step 2: Find the multiplication fact 45 = 5 × 9 8) 56 which has the dividend and divisor. - Step 3: Write the other factor as the 9 quotient. Write the product of the factors below the dividend. 5)45 − 45 Step 4: Subtract the product 9 4) 36 Dividend = _____ from the dividend and write the Divisor = ______ difference below the product. 5)45 - Quotient = ____ This difference is called the Remainder = _____ remainder. − 45 00 45 = Dividend 5 = Divisor 9 = Quotient 0 = Remainder Note: If the remainder is zero, the divisor is said to divide the dividend exactly. Checking for correctness of division: The multiplication fact of the division is used to check its correctness. 12 06-08-2023 00:02:55 Hazelwood_G3_Maths_TB_Part 2.indb 12
Step 1: Compare the remainder and divisor. The remainder must always be less than the divisor. Step 2: Check if (Quotient × Divisor) + Remainder = Dividend Let us now check if our division in example 1 is correct or not. Step 1: Remainder < Divisor 0 < 5 (True) Step 2: Quotient × Divisor 9×5 Step 3: (Quotient × Divisor) + Remainder = Dividend 45 + 0 = 45 = Dividend Note: The division is incorrect if: a) Remainder > or = divisor b) (Quotient × Divisor) + Remainder ≠ Dividend 2-digit quotient In the examples we have seen so far, the quotients are 1-digit numbers. In some divisions, the quotients may be 2-digit numbers. Let us see some examples. Example 2: Solve: 57 ÷ 3 Solution: Follow these steps to divide a 2-digit number by a 1-digit number. Steps Solved Solve these Step 1: Check if the tens digit of the 5>3 5) 60 dividend is greater than the divisor. 1 − Step 2: Divide the tens and write the quotient. 3)57 − Write the product of quotient and divisor, −3 below the tens digit of the dividend. Step 3: Subtract and write the difference 1 Dividend = _____ Step 4: Check if difference < divisor is true. Divisor = ______ 3)57 Quotient = ____ Remainder = ___ −3 2 2 < 3 (True) Division 13 Hazelwood_G3_Maths_TB_Part 2.indb 13 06-08-2023 00:03:12
Steps Solved Solve these 1 Step 5: Bring down the ones digit of the dividend and write it beside the remainder. 3)57 − 3↓ 27 Step 6: Find the largest number in the 3 × 8 = 24 1 3) 42 multiplication table of the divisor that can be subtracted from the 2-digit number in )3 × 9 = 27 3 57 − the previous step. 3 × 10 = 30 − 24 < 27 < 30. − 3↓ So, 27 is the 27 required number. Step 7: Write the factor of required number, 19 Dividend = _____ other than the divisor, as the quotient. Write Divisor = ______ the product of the divisor and the quotient 3)57 Quotient = ____ below the 2-digit number. Subtract and Remainder = ___ write the difference. − 3↓ 27 − 27 00 Step 8: Check if remainder < divisor is true. 0 < 3 (True) Stop the division. (If this is false, the division is incorrect.) Quotient = 19 Step 9: Write the quotient and the Remainder = 0 remainder. Step 10: Check if (Divisor × Quotient) + 3 × 19 + 0 = 57 Remainder = Dividend is true. 57 + 0 = 57 57 = 57 (True) (If this is false, the division is incorrect.) Divide 3-digit numbers by 1-digit numbers (2-digit quotient) Dividing a 3-digit number by a 1-digit number is similar to dividing a 2-digit number by a 1-digit number. Let us understand this through a few examples. Example 3: Solve: a) 265 ÷ 5 Solution: Follow these steps to divide a 3-digit number by a 1-digit number. 14 06-08-2023 00:03:35 Hazelwood_G3_Maths_TB_Part 2.indb 14
Steps Solved Solve these Step 1: Check if the hundreds digit of 4) 244 the dividend is greater than the divisor. 5)265 − If it is not, consider the tens digit too. 2 is not greater than 5. So, consider 26. Step 2: Find the largest number that 5 − can be subtracted from the 2-digit number of the dividend. Write the 5)265 Dividend = _____ quotient. Divisor = ______ − 25 Quotient = ____ Remainder = ___ Write the product of the quotient and 5 × 4 = 20 the divisor below the dividend. 5 × 5 = 25 9) 378 5 × 6 = 30 Step 3: Subtract and write the − difference. 25 < 26 − 5 5)265 − 25 1 Step 4: Check if difference < divisor 1 < 5 (True) is true. (If it is false, the division is incorrect.) Step 5: Bring down the ones digit 5 of the dividend. Write it beside the remainder. 5)265 Step 6: Find the largest number in the − 25↓ multiplication table of the divisor that 15 can be subtracted from the 2-digit number in the previous step. 5 5)265 − 25↓ 15 5 × 2 = 10 5 × 3 = 15 5 × 4 = 20 15 is the required number. Division 15 Hazelwood_G3_Maths_TB_Part 2.indb 15 06-08-2023 00:04:26
Steps Solved Solve these Step 7: Write the factor of required 53 number, other than the divisor, as Dividend = _____ quotient. Write the product of divisor 5)265 Divisor = ______ and quotient below the 2-digit Quotient = ____ number. Then, subtract them. − 25↓ Remainder = ___ 15 Step 8: Check if remainder < divisor is true. Stop the division. (If this is false, − 15 the division is incorrect.) 00 0 < 5 (True) Step 9: Write the quotient and Quotient = 53 remainder. Remainder = 0 Step 10: Check if (Divisor × Quotient) + 5 × 53 + 0 = 265 Remainder = Dividend is true. (If this is 265 + 0 = 265 false, the division is incorrect.) 265 = 265 (True) 3-digit quotient Example 4: Solve: 784 by 7 Solution: Follow these steps to divide a 3-digit number by a 1-digit number. Steps Solved Solve these Step 1: Check if the hundreds digit of the dividend is greater than or equal to the 7)784 8) 984 divisor. 7=7 − Step 2: Divide the hundreds and write the quotient in the hundreds place. 1 − Write the product of the quotient and the 7)784 − divisor under the hundreds place of the dividend. −7 16 06-08-2023 00:05:01 Hazelwood_G3_Maths_TB_Part 2.indb 16
Steps Solved Solve these Step 3: Subtract and write the difference. Dividend = _____ 1 Divisor = ______ Quotient = ____ 7)784 Remainder = ___ −7 5) 965 0 − Step 4: Check if difference < divisor is true. 0 < 7 (True) − Step 5: Bring down the next digit of the 1 − dividend. Check if it is greater than or equal to the divisor. 7)7 84 Dividend = _____ Divisor = ______ − 7↓ Quotient = ____ 08 Remainder = ___ 8>7 Step 6: Find the largest number in the 11 multiplication table of the divisor that can be subtracted from the 2-digit number in 7)784 the previous step. − 7↓ Write the factor other than the divisor as 08 quotient. −7 Write the product of the quotient and the divisor below it. 7×1=7<8 The required number is 7. Step 7: Subtract and write the difference. 11 Bring down the next digit (ones digit) of the dividend. 7)784 Check if the dividend is greater than or − 7↓ equal to the divisor. 08 −7 14 14 > 7 Division 17 Hazelwood_G3_Maths_TB_Part 2.indb 17 06-08-2023 00:05:54
Steps Solved Solve these Step 8: Find the largest number in the multiplication table of the divisor that can 112 2) 246 be subtracted from the 2-digit number in the previous step. 7)784 − Write the factor other than the divisor as − the quotient. − 7↓ − Write the product of the quotient and the 08 divisor below it. Dividend = _____ −7 Divisor = ______ Step 9: Subtract and write the difference. 14 Quotient = ____ Check if it is less than the divisor. Stop the Remainder = ___ division. − 14 Step 10: Write the quotient and the 7 × 2 = 14 remainder. The required Step 11: Check if (Divisor × Quotient) + number is 14. Remainder = Dividend is true. (If it is false, the division is incorrect.) 112 7)784 − 7↓ 08 −7 14 − 14 00 Quotient = 112 Remainder = 0 7 × 112 + 0 = 784 784 + 0 = 784 784 = 784 (True) Application Division of 2-digit numbers and 3-digit numbers is used in many real-life situations. Let us consider a few examples. Example 5: A school has 634 students, who are equally grouped into 4 houses. How many students are there in a house? Are there any students who are not grouped into a house? 18 Hazelwood_G3_Maths_TB_Part 2.indb 18 06-08-2023 00:06:23
Solution: Number of students = 634 158 Number of houses = 4 Number of students in a house = 634 ÷ 4 4)634 − 4↓ 23 Number of students in each house = 158 − 20 The remainder in the division is 2. 34 Therefore, 2 students are not grouped into any house. − 32 02 Example 6: A football game had 99 spectators. If each row has only 9 seats, how Solution: many rows would the spectators occupy? 11 Number of spectators = 99 9) 99 Number of seats in each row = 9 − 9↓ Number of rows occupied by the spectators = 99 ÷ 9 = 11 09 Therefore, 11 rows are occupied by the spectators. −9 0 Higher Order Thinking Skills (H.O.T.S.) In all the division sums we have seen so far, we did not have a 0 (zero) in dividend or quotient. When a dividend has a zero, we place a 0 in the quotient in the corresponding place. Then, get the next digit of the dividend down and continue the division. Let us now understand division of numbers that have a 0 (zero) in dividend or quotient, through these examples. Example 7: Solve: 505 ÷ 5 Solution: Follow these steps for division of numbers having 0 in dividend. Solved Solve this 101 4) 804 5)505 − − 5↓ − 00 − − 00 05 − 05 00 Division 19 Hazelwood_G3_Maths_TB_Part 2.indb 19 06-08-2023 00:07:04
Drill Time Concept 8.1: Divide 2-digit and 3-digit Numbers by 1-digit Numbers 1) Divide 2-digit numbers by 1-digit numbers (1-digit quotient). a) 12 ÷ 2 b) 24 ÷ 6 c) 36 ÷ 6 d) 40 ÷ 8 e) 10 ÷ 5 f) 12 ÷ 4 2) Divide 2-digit numbers by 1-digit numbers (2-digit quotient). a) 12 ÷ 1 b) 99 ÷ 3 c) 48 ÷ 2 d) 65 ÷ 5 e) 52 ÷ 4 f) 84 ÷ 6 3) Divide 3-digit numbers by 1-digit numbers (2-digit quotient). a) 123 ÷ 3 b) 102 ÷ 2 c) 497 ÷ 7 d) 111 ÷ 3 e) 256 ÷ 4 f) 648 ÷ 8 4) Divide 3-digit numbers by 1-digit numbers (3-digit quotient). a) 456 ÷ 2 b) 112 ÷ 1 c) 306 ÷ 3 d) 448 ÷ 4 e) 555 ÷ 5 f) 744 ÷ 4 5) Word Problems a) 260 chocolates have to be equally distributed among 4 students. How many chocolates will each student receive? b) There are 24 people in a bus. Each row in the bTursaciann sMeayt 2Bpreaoipnle. How many rows in the bus are occupied? Connect the Dots Science Fun Some fruits have one seed. Some have more than one seed. Pea pods have more than one seeds. Go back home. Take four pea pods and count the total number of peas. Divide the peas equally among your family members.What is the quotient? What is the remainder? 20 06-08-2023 00:07:06 Hazelwood_G3_Maths_TB_Part 2.indb 20
Chapter Fractions 9 Let Us Learn About • fractions as a part of a whole and their representation. • identify parts of fractions. • fractions of a collection. • applying the knowledge of fractions in real life. Concept 9.1: Fraction as a Part of a Whole Think Farida and her three friends, Joseph, Salma and Rehan, went on a picnic. Farida had only one apple with her. She wanted to share it equally with everyone. What part of the apple does each of them get? Recall Look at the rectangle shown below. We can divide the whole rectangle into many equal parts. Consider the following: Hazelwood_G3_Maths_TB_Part 2.indb 21 21 06-08-2023 00:07:08
1 part: 2 equal parts: 3 equal parts: 4 equal parts: 5 equal parts: and so on. Let us understand the concept of parts of a whole through an activity. & Remembering and Understanding Suppose we want to share an apple with our friends. First, we the number of our friends with whom we want to share the apple. Then, we cut it into as many equal pieces as the number of persons. Thus, each person gets an equal part of the apple after division. Parts of a whole A complete or full object is called a whole. Observe the following parts of a chocolate bar: whole 2 equal parts 3 equal parts 4 equal parts We can divide a whole into equal parts as shown above. Each such division has a different name. To understand this better, let us do an activity. 22 06-08-2023 00:07:09 Hazelwood_G3_Maths_TB_Part 2.indb 22
Activity: Halves Take a square piece of paper. Fold it into two equal parts as shown. Each of the equal parts is called a ‘half’. ‘Half’ means 1 out of 2 equal parts. Putting these 2 equal parts together makes the complete piece of paper. We write ‘1 out of 2 equal parts’ as 1 . 2 In 1 , 1 is the number of parts taken and 2 is the total number of equal parts the whole 2 is divided into. Note: 1 and 1 make a whole. 2 2 Thirds In figure (a), observe that the three parts are not equal. We can also divide a whole into three equal parts. Fold a rectangular piece of paper as shown in figures (b) and (c). 11 1 33 3 three parts three equal parts Fig. (c) Fig. (a) Fig. (b) Each equal part is called a third or one-third. The shaded part in figure (c) is one out of three equal parts. So, we call it a one-third. Two out of three equal parts of figure (c) are not shaded. We call it two-thirds (short form of 2 one-thirds). We write one-third as 1 and two-thirds as 2 . 3 3 Fractions 23 Hazelwood_G3_Maths_TB_Part 2.indb 23 06-08-2023 00:07:09
Note: 1 , 1 and 1 or 1 and 2 makes a whole. 3 3 3 3 3 Fourths Similarly, fold a square piece of paper into four equal parts. Each of them is called a fourth or a quarter. In figure (d), the four parts are not equal. In figure (e), each equal part is called a fourth or a quarter and is written as 1 . 4 1 Four parts 4 Fig. (d) 1 4 1 4 1 4 Four equal parts Fig. (e) Two out of four equal parts are called two-fourths and three out of four equal parts are called three-fourths, written as 2 and 3 respectively. 44 Note: Each of 1 and 3; 1 , 1 , 1 and 1 and 1 , 1 and 2 make a whole. 4 4 444 4 44 4 The total number of equal parts a whole is divided into is called the denominator. The number of such equal parts taken is called the numerator. Representing the parts of a whole as Numerator is called a fraction. Numbers of Denominator the form Numerator are called fractions. Thus, a fraction is a part of a whole. Denominator 24 Hazelwood_G3_Maths_TB_Part 2.indb 24 06-08-2023 00:07:10
For example, 1 , 1 , 1, 2 and so on are fractions. 2 3 4 3 Let us now see a few examples. Example 1: Identify the numerator and denominator in each of the following fractions: a) 1 b) 1 c) 1 2 3 4 Solution: S. No Fractions Numerator Denominator a) 1 1 2 2 b) 1 1 3 3 c) 1 1 4 4 Example 2: Identify the fraction for the shaded parts in the figures below. a) b) Solution: Steps Solved Solve this a) b) Step 1: Count the number of equal parts, the figure is divided into Total number of Total number of equal (Denominator). parts = _______ equal parts = 8 Number of parts shaded Step 2: Count the number of Number of parts = ______ shaded parts (Numerator). shaded = 5 Fractions 25 Hazelwood_G3_Maths_TB_Part 2.indb 25 06-08-2023 00:07:11
Step 3: Write the fraction Fraction = 5 Numerator . 8 Denominator Fraction = Example 3: The circular disc shown in the figure is divided into equal parts. What fraction of the disc is painted yellow? Write the fraction of the disc that is painted white. Solution: Total number of equal parts of the disc is 16. The fraction of the disc that is painted yellow = Number of parts painted yellow = 3 Total number of equal parts 16 The fraction of the disc that is painted white = Number of parts painted white = 7 Total number of equal parts 16 Example 4: Find the fraction of parts that are not shaded in the following figures. a) b) c) Solution: We can find the fractions as: Steps Solved Solve these a) b) c) Total number of equal parts 2 Number of parts not shaded 1 Number of parts not shaded 1 2 Fraction = Total number of equal parts 26 06-08-2023 00:07:12 Hazelwood_G3_Maths_TB_Part 2.indb 26
Application We have learnt to identify the fraction of a whole using the shaded parts. We can learn to shade a figure to represent a given fraction. Let us see some examples. Example 5: Shade a square to represent these fractions: 1 23 1 a) 4 b) 3 c) 5 d) 2 Solution: We can represent the fractions as: Steps Solved 2 Solve these 1 1 3 3 2 Step 1: Identify the Denominator 5 Denominator denominator and the 4 = = numerator. Denominator Numerator Denominator Numerator =4 = = Numerator = 1 = Numerator = Step 2: Draw the required shape. Divide it into as many equal parts as the denominator. Step 3: Shade the number of equal parts as the numerator. This shaded part represents the given fraction. Example 6: Colour the shapes to represent the given fractions. Fractions 1 2 1 4 5 2 Shapes Fractions 27 Hazelwood_G3_Maths_TB_Part 2.indb 27 06-08-2023 00:07:14
Solution: We can represent the fractions as: Fractions 1 2 1 4 5 2 Shapes Higher Order Thinking Skills (H.O.T.S.) Let us see an example of a real-life situation involving fractions. Example 7: A square shaped garden has coconut trees in a quarter of its land. It has mango trees in two quarters and neem trees in another quarter. Draw a figure of the garden and represent its parts. Solution: Fraction of the garden covered by Coconut coconut trees = Quarter = 1 trees 4 Neem trees Fraction of the garden covered by Mango 1 trees mango trees = 2 Quarters = 2 Fraction of the garden covered by neem trees = Quarter = 1 4 So, the square garden is as shown in the figure. 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 4 5 3 d) 9 e) 7 f) 8 28 Hazelwood_G3_Maths_TB_Part 2.indb 28 06-08-2023 00:07:15
2) Identify the fractions of the coloured parts. a) b) c) d) e) Concept 9.2: Fraction of a Collection Think Farida has a bunch of roses. Some of them are red, some white and some yellow. Farida wants to find the fraction of roses of each colour. How can she find that? Recall We know that a complete or a full object is called a whole. We also know that we can divide a whole into equal number of parts. Let us answer these to revise the concept. Divide these into equal number of groups as given in the brackets. Draw circles around them. a) [3 groups] b) [2 groups] c) [5 groups] Fractions 29 Hazelwood_G3_Maths_TB_Part 2.indb 29 06-08-2023 00:07:18
& Remembering and Understanding To find the part or the fraction of a collection, find the number of each type of object out of the total collection. Finding a half We can find different fractions of a collection. Suppose there are 10 pens in a box. To find half of them, we divide them into two equal parts. Each equal part is a half. Each equal part has 5 pens, as 10 ÷ 2 = 5. So, 1 of 10 is 5. 2 Finding a third One-third is 1 out of 3 equal parts. In the given figure, there are 12 bananas. To find a third, we divide them into three equal parts. Each equal part is a third. Each equal part has 4 bananas, as 12 ÷ 3 = 4. Train My Brain So, 1 of 12 is 4. 3 11 1 33 3 Finding a fourth (or a quarter) One-fourth is 1 out of 4 equal parts. In the figure, there are 8 books. 30 06-08-2023 00:07:23 Hazelwood_G3_Maths_TB_Part 2.indb 30
To find a fourth, divide the number of books into 4 equal parts. 1 1 1 1 444 4 Each equal part has 2 books, as 8 ÷ 4 = 2. So, 1 of 8 is 2. 4 Let us see an example to find the fraction of a collection. Example 8: Find the fraction of the coloured parts of the shapes. Shapes Fractions Solution: The fractions of the coloured parts of the shapes are: Shapes Fractions 2 6 3 6 5 8 Application We can apply the knowledge of fractions in many real-life situations. Let us see a few examples. Fractions 31 Hazelwood_G3_Maths_TB_Part 2.indb 31 06-08-2023 00:07:24
Example 9: A basket has 64 flowers. Half of them are roses, a quarter of them are marigolds and a quarter of them are lotuses. How many roses, marigolds and lotuses are there in the basket? Solution: Total number of flowers = 64 Half of the flowers are roses. The number of roses = 1 of 64 = 64 ÷ 2 = 32 2 A quarter of the flowers are marigolds. 1 The number of marigolds = 4 of 64 = 64 ÷ 4 = 16 A quarter of the flowers are lotuses. 1 The number of lotuses = 4 of 64 = 64 ÷ 4 = 16 Therefore, there are 32 roses, 16 marigolds and 16 lotuses in the basket. Example 10: A set of 48 pens has 13 blue, 15 red and 11 black ink pens. The remaining are green ink pens. What fraction of the pens is green? Solution: Total number of pens = 48 Total number of blue, red and black ink pens = 13 + 15 + 11 = 39 Number of green ink pens = 48 – 39 = 9 Fraction of green ink pens == Number of green ink pens = 9 Total number of pens 48 Example 11: There is a bunch of balloons with three different colours. Write the fraction of balloons of each colour. Solution: Total number of balloons = 15 Number of green balloons = 2 2 Therefore, fraction of green balloons is 15 . Number of yellow balloons = 3 3 Therefore, fraction of yellow balloons is 15 . Number of red balloons = 10 10 Therefore, fraction of red balloons = 15 32 06-08-2023 00:07:25 Hazelwood_G3_Maths_TB_Part 2.indb 32
Higher Order Thinking Skills (H.O.T.S.) In some real-life situations, we need to find a fraction of some goods such as fruits, vegetables, milk, oil and so on. Let us now see one such example. Example 12: One kilogram of apples costs `16 and one kilogram of papayas costs `20. If Rita buys 1 kg of apples and 1 kg of papaya, how much money 2 4 did she spend? Solution: Cost of 1 kg apples = `16 Cost of 1 kkg apples = 1 of `16 = `16 ÷2 = `8 2 2 (To find a half, we divide by 2) Cost of 1 kg papaya = `20 Cost of 1 kkg papaya = 1 okfg`20 = `20 ÷4 = `5 4 4 (To find a fourth, we divide by 4) Therefore, the money spent by Rita = `8 + `5 = `13 Example 13: Sujay completed 2 of his Maths homework. If he had to solve 25 5 problems, how many did he complete? Solution: Fraction of homework completed = 2 5 Total number of problems to be solved = 25 Number of problems Sujay solved = 2 of 25 = (25 ÷ 5) × 2 =5 × 2= 10 5 Therefore, Sujay completed 10 problems. Drill Time Concept 9.2: Fraction of a Collection 1) Find fraction of coloured parts. Fractions 33 Hazelwood_G3_Maths_TB_Part 2.indb 33 06-08-2023 00:07:26
a) b) c) d) e) 2) Find 1 and 1 of the following collection. 2 4 3) Word Problems a) A circular disc is divided into 12 equal parts. Venu shaded 1 of the disc 4 pink and 1 of the disc green. How many parts of the disc are shaded? How 3 b) many parts are not shaded? them are unruled and 1 of them are four-ruled. J ohn has 24 notebooks. 1 of 6 2 How many books are (a) unruled and (b) four-ruled? c) Navya has 26 story books. She gives half of the books to her cousins. How many books does she give? Connect the Dots English Fun Think of at least two words that rhyme with each ‘numerator’ and ‘denominator’. 34 06-08-2023 00:07:27 Hazelwood_G3_Maths_TB_Part 2.indb 34
Chapter Money 10 Let Us 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 Think Farida has `38 in her piggy bank. She wants to know how many paise she has. Do you know? 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 Hazelwood_G3_Maths_TB_Part 2.indb 35 35 06-08-2023 00:07:30
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) & Remembering and Understanding 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. 36 06-08-2023 00:07:32 Hazelwood_G3_Maths_TB_Part 2.indb 36
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. 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 c) `9 = 9 × 100 paise = 900 paise Similarly, we can convert paise into rupees. Converting paise into rupees is the reverse process of converting rupees into paise. Example 2: Convert 360 paise to rupees. Solution: We can convert paise to rupees as: Steps Solved Solve this 360 paise 380 paise Step 1: Write the given 360 paise paise as hundreds of paise. = 300 paise + 60 paise Step 2: Rearrange 300 paise as a product of 100 300 paise paise. = (3 × 100) paise + 60 paise Step 3: Write in rupees. `3 + 60 paise = 3 rupees 60 paise Application 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 So, 10 rupees = 10 × 100 paise = 1000 paise Therefore, Anil has 1000 paise with him. Money 37 Hazelwood_G3_Maths_TB_Part 2.indb 37 06-08-2023 00:07:33
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. Higher Order Thinking Skills (H.O.T.S.) Observe this example 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. 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 38 Hazelwood_G3_Maths_TB_Part 2.indb 38 06-08-2023 00:07:33
10.2: Add and Subtract Money with Conversion Leena purchased a book for `35, a pencil for `20 and a sheet of chart paper for `10.50. • What will you do to calculate the total cost of the three items? • When she gives `100 to the shopkeeper, what will the shopkeeper do to return the balance amount to Leena? You remember that in the column method, two or more numbers are added or subtracted by writing them one below the other, don’t you? Now, let’s try to add and subtract money using the column method as well. How do we write an amount? Paise is always written in two Money can be counted in rupees and paise. While writing digits after the an amount, rupees and paise are separated using a dot or a point. point. Solve these How do we add money using the column method? `p In the column method, we write money in a way such that the dots or points are placed 4 1. 5 0 exactly one below the other. While adding and + 4 5. 7 5 subtracting money, the rupees are placed under rupees and the paise under paise. Let us understand this through some examples. Add: `14.65 and `23.80 You can add the two amounts using the following steps: Steps Solved Step 1: Write the given numbers `p with the points exactly one below 1 4. 6 5 the other, as shown. + 2 3. 8 0 Money 39 Hazelwood_G3_Maths_TB_Part 2.indb 39 06-08-2023 00:07:37
Step 2: First add the paise. `p `p Regroup the sum if needed. Write 1 3 8. 4 5 the sum under paise. Place the 1 4. 6 5 + 3 5. 6 0 dot just below the dot. + 2 3. 8 0 `p Step 3: Add the rupees. Add the . 45 2 3. 6 5 carry forward (if any) from the + 1 4. 5 2 previous step. Write the sum under `p rupees. 1 1 4. 6 5 Step 4: Write the sum of the given + 2 3. 8 0 amounts. 3 8. 4 5 `14.65 + `23. 80 = `38.45 1) Solve the following: b) `32.35 + `65.65 a) `28.65 + `62.35 d) `38.45 + `35.60 c) `41.50 + `45.75 2) R amu has `12.75 with him. His friend has `28.50 with him. What is the amount both of them have in total? How do we subtract money using the column method? We can subtract money in the same way as we add money. Let us understand this through an example. Subtract: `73.50 – `52.80 You can subtract the two amounts using the following steps: Steps Solved Step 1: Write the given numbers with the ` p dots exactly one below the other, as 7 3. 50 shown. − 5 2. 80 40 06-08-2023 00:07:37 Hazelwood_G3_Maths_TB_Part 2.indb 40
Steps Solved Step 2: First subtract the paise. Regroup `p if needed. Write the difference under 2 15 paise. Place the dot just below the dot. 7 3. 5 0 Step 3: Subtract the rupees. Write the − 5 2. 8 0 difference under rupees. 70 Step 4: Write the difference of the given amounts. `p 2 15 7 3. 5 0 − 5 2. 8 0 2 0. 7 0 `73. 50 – `52. 80 = `20.70 1) Solve the following: a) `70.75 – `62.45 b) `73.50 – `56.60 c) `80.75 + `41.50 d) `60.75 + `32.50 2) A run had `45.50 with him. He gave `23.50 to Amar. How much money is left with Arun? Reflection Time! 1) What are the different denominations of notes and coins that you have seen? Ask your parents to show you all of them. 2) Which is the highest denomination of a single note which is in use currently ? 3) Do you get pocket money? If yes, how do you spend it? How much do you save? Do you have a piggy bank? Why is it important to have one? Money 41 Hazelwood_G3_Maths_TB_Part 2.indb 41 06-08-2023 00:07:41
Drill Time 10.2: Add and Subtract Money with Conversion 1) Add: a) `23.24 + `10.80 b) `31.20 + `19.16 c) `61.21 + `29.20 d) `11.10 + `12.90 e) `60.90 + `24.23 f) `40.43 + `39.75 2) Subtract: a) `87.10 – `23.20 b) `20.12 – `10.13 c) `31.55 – `22.44 d) `99.99 – `22.22 e) `56.13 – `12.03 f) `60.30 – `17.21 10.3: Multiply and Divide Money You have learned multiplication and division of numbers so far. Do you know that multiplication and division of money is similar to that of numbers? How do we multiply a given amount of money? Sometimes, we might want to multiply an amount with a number to find the total amount. It is the same amount as adding the given amount a specified number of times. For example, if a pen costs `12 and we want to buy 2 such pens, we can find out how much to pay for them by multiplying: `12 × 2 = `24. Notice how multiplying `12 by 2 is like adding `12 twice or doubling `12. To multiply money with a given number, first multiply the numbers under paise with the specified number, write down the amount and place the point. Then multiply the number under rupees with the specified number. Now, let us understand multiplying money using an example. ` 1 Multiply `72 by 8. 72 ×8 To find the total amount, multiply the number under rupees like you would 576 do for multiplication of a 2-digit number by a 1-digit number. Therefore, `72 × 8 = `576 42 06-08-2023 00:07:44 Hazelwood_G3_Maths_TB_Part 2.indb 42
How do we divide an amount with a given number? In multiplication, start multiplying To divide an amount, we divide the numbers under rupees from the rightmost and place the point in the quotient. Then, we divide the digit. In division, number under paise. We divide an amount with a specified start dividing from number just how we divide a 2-digit number by a 1-digit the leftmost digit. number. Let us see how with an example. 5 Divide `35 by 7. So, `35 ÷ 7 = `5 7) 35 − 35 00 1) Solve the following: a) `28 × 5 b) `70 ÷ 2 c) `44 × 5 2) If 1 book costs `29, what is the cost of 6 such books? 3) The cost of a dozen pencils is `48. a) What is the cost of three dozen pencils? b) What is the cost of one pencil? Reflection Time! 1) Did you know that multiplication is related to addition and division is related to subtraction? Solve `50 × 4 by both multiplication and repeated addition. Also, solve `75 ÷ 5 by both division and repeated subtraction. 2) For each of the questions given below, first write the operation and then find the solution. A dozen bananas cost `36. a) What is the cost of 6 bananas? b) How many bananas can you take home for `120? c) What is the cost of 3 dozen bananas Money 43 Hazelwood_G3_Maths_TB_Part 2.indb 43 06-08-2023 00:07:49
Drill Time 10.3: Multiply and Divide Money 1) Solve the following: a) `23 × 2 b) `10 × 3 c) `21 ÷ 7 f) `96 ÷ 6 d) `34 × 4 e) `84 ÷ 4 10.4: Rate Charts and Bills Have you ever noticed your parents collecting pamphlets from different grocery stores? This is because supermarkets circulate such pamphlets to provide customers with the rate charts of groceries, vegetables and household supplies. Rate charts help customers compare the prices (also called rates) of things at different supermarkets, so that they can buy the things they need from the shop that offers them the best prices. But what are rate charts? A rate chart is a list of different items available in a shop and their prices. A rate chart makes it easier for us to know and compare the prices of the items in a shop. Look at the two rate charts given below and answer the following questions. Item Rate (in ₹) Item Rate (in ₹) 1 kg sugar 40 1 litre milk 44 Tomato ketchup 147 1 kg wheat 48 Chocolate bar 50 1 kg oranges 80 Soap bar 34 1 kg apples 150 1 kg tea 240 1 kg pineapple 50 Honey 149.50 1 dozen bananas 20 1) Which fruit is the most affordable? 2) Would you prefer to buy sugar or honey if you have only `130 with you ? 44 06-08-2023 00:07:55 Hazelwood_G3_Maths_TB_Part 2.indb 44
After comparing rate charts, we decide to buy the things we need from a shop. You must have seen that the shopkeeper gives us a bill when we pay for the things we buy. Do you know what a bill is? A bill is a list of items along with their prices. A bill tells us the cost of each item we bought and the total money to be paid to the shopkeeper. Do you know how to make a bill? To make a bill, we write the rate or price of the items bought and the number or quantity of the items. We then multiply the rate of each item with the quantity to find the total cost for that item. For example, you may have bought 7 pens that cost `10 each. So, the total cost of the pens you bought is: `10 × 7 = `70. Lastly, we add the item-wise costs to find the total bill amount. Let us understand how to make bills through an example. Sunil bought the following stationery items at a shop. Item pencil water colour pen scissors Quantity 3 1 4 2 Here is the rate chart of the things Sunil bought. Pencils `3 each Pens `10 each Water colours `100 Scissors `25 We can use the following steps to make a bill. Step 1: Write the items and their quantities in the bill. Step 2: Then write the rate or the price of each item. Money 45 Hazelwood_G3_Maths_TB_Part 2.indb 45 06-08-2023 00:07:57
Step 3: Find the total cost of each item by multiplying the Addition of number of items by their rates/price. amounts is similar to the addition of Step 4: Find the total bill amount by adding the cost of each numbers with two item. or more digits. Take a look at the bill that Sunil was given by the shopkeeper of the stationery shop for the items he bought. Name: Sunil P Bill Date: 12 July S.No. Item Quantity Rate per item Amount 3 `3.00 ₹p 1 `100.00 1) pencil 4 `10.00 9 00 2) water colour 2 `25.00 3) pen 100 00 4) scissors Total 40 00 50 00 `199 00 1) Make a bill for the following items. cake – `100; 10 birthday caps – `5 each; candle – `25; 10 small gifts – `15 each 2) Mr Kumar’s family went to a restaurant for lunch. They ordered 1 pav bhaji for `45, 2 burgers for `40 each, 2 sandwiches for `20.50 each, 3 mango shakes for `25.50 each and 2 ice creams for `22.50 each. What would the restaurant bill total be? Reflection Time! 1) My parents always cross-check the bill and the items that we got after we come home from the market. Do you think this is a good practice? Why? 46 06-08-2023 00:07:59 Hazelwood_G3_Maths_TB_Part 2.indb 46
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