Passport-G3-FoundationMax-Maths-FY_opt

English Fun Compose a poem on multiplication. One example is shown in the picture to the right. A Note to Parent Multiplication is used in many situations in our day-to -day activities. Calculating time, distance, money to be paid in a departmental store, the area of a room and so on are a few examples. Encourage your child to actively engage in these scenarios and help you with the calculations. Drill Time Concept 6.1: Multiply 2-digit Numbers 1) Multiply 2-digit numbers by 2, 3, 4, 5 and 6 a) 56 × 3 b) 23 × 2 c) 77 × 6 d) 50 × 5 e) 62 × 4 2) Multiply 2-digit numbers by 7, 8 and 9 a) 23 × 9 b) 12 × 7 c) 76 × 8 d) 84 × 8 e) 83 × 9 3) Word problems a) There were 23 boys in one group. The school had 4 such groups. How many boys were there in all the groups? b) Viraj travelled for 30 km in one day. He travelled for 7 days. How many kilometres did he travel in 7 days? Multiplication 95 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 95 1/12/2017 10:17:02 PM

Drill Time Concept 6.2: Multiply 3-digit Numbers by 1-digit and 2-digit Numbers 4) Multiply a 3-digit number by a 1-digit number (without regrouping). a) 101 × 8 b) 212 × 4 c) 414 × 2 d) 111 × 5 e) 323 × 3 5) Multiply 3-digit numbers by 1-digit numbers (with regrouping). a) 225 × 7 b) 762 × 4 c) 868 × 8 d) 723 × 5 e) 429 × 2 6) Multiply 3-digit numbers by 2-digit numbers. a) 769 × 21 b) 759 × 10 c) 578 × 42 d) 619 × 66 e) 290 × 30 7) Word problems a) Seema drove 462 km every day for a week. What distance does she drive in that week? b) Suraj spends ` 616 for a set of books. How much will he spend on 24 such sets? Concept 6.3: Double 2-digit and 3-digit Numbers Mentally 8) Double the given numbers mentally. a) 23 b) 52 c) 61 d) 10 e) 74 9) Word problems a) Rohan bought 42 books in Year I and doubled the number in Year II. How many books did he buy in Year II? b) Sonal earned ` 28 on Monday. She earned double the amount on Tuesday. How much did she earn on Tuesday? 96 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 96 1/12/2017 10:17:02 PM

Ti Timeme I Will Learn Concepts 7.1: Read a Calendar 7.2: Read Time Correct to the Hour Ch_7_time.indd 97 1/12/2017 10:23:56 PM

Concept 7.1: Read a Calendar I Think Neena and her friends are playing a game using a calendar. They split into two groups. Each group says a date or day of a particular month. The other group answers with the corresponding day or date of another month. Can you also play such a game? To answer this, we must know about reading a calendar. 7.1 I Recall Let us recall days in a week and months in a year. There are 7 days in a week. They are: 1) Sunday 2) Monday 3) Tuesday 4) Wednesday 5) Thursday 6) Friday 7) Saturday There are 12 months in a year. They are: 1) January 2) February 3) March 4) April 5) May 6) June 7) July 8) August 9) September 10) October 11) November 12) December 7.1 I Remember and Understand Reading a calendar, we can find the day of a given date. We can also find dates that fall on a particular day of the month. Let us do an activity to understand this concept better. 98 Ch_7_time.indd 98 1/12/2017 10:23:58 PM

Activity: 1) List out the birthdays of your parents, grandparents, brothers and sisters. The calendar that we use is called the 2) Arrange them in a table as they appear in a calendar Gregorian calendar. month-wise. 3) Note the days on which the birthdays appear. Stick this on your writing table. This will remind you to wish your family members a “HAPPY BIRTHDAY”. Your tables could be similar to the one given below. Birthdays of my family members Birthday (2017) Member of the family Day 08-January Brother Sunday 10-March Mother Friday 16-June MINE Friday 03-August Father Thursday 04-October Grand father Wednesday 12-December Grand mother Tuesday Example 1: Observe the given calendar and answer the questions: a) How many days are there in this month? b) How many Sundays are there in this JANUARY 2017 month? SUN MON TUE WED THU FRI SAT 1 2 3 7 5 6 4 c) Which day appears 5 times? 8 9 10 11 12 13 14 d) On which day is the 15 16 17 18 19 20 21 Republic day? 22 23 24 25 26 27 28 29 30 31 e) On which date is the second Saturday? Solution: a) There are 31 days in this month. b) There are five Sundays in this month. c) Sunday, Monday and Tuesday appear five times. Time 99 Ch_7_time.indd 99 1/12/2017 10:23:58 PM

d) The Republic day is on Thursday. e) Second Saturday is on 14 . th Example 2: From the calendar for the year 2017, write the days of the following events. a) Independence Day - ____________ b) Republic Day - _____________ c) Christmas Day - ____________ d) Teachers’ Day - _____________ e) Children’s Day - _____________ Solution: a) Independence Day - Tuesday b) Republic Day - Thursday c) Christmas Day - Tuesday d) Teachers’ Day - Tuesday e) Children’s Day - Tuesday Train My Brain Answer the following: a) When is your father’s birthday? b) On which day is your birthday this year? c) When do you have Dussehra vacation for school? 7.1 I Apply We use the calendar on a daily basis. Events like planning holidays, conducting sports and examinations in school are a few examples. 100 Ch_7_time.indd 100 1/12/2017 10:23:58 PM

Example 3: Renu wants to plan her 5-day holiday to October 2017 New Delhi. On the calendar, mark the SUN MON TUE WED THU FRI SAT days when Renu can plan her holiday. She 1 2 3 4 5 6 7 wants to start on a Friday and travel 8 15 9 16 10 11 12 13 14 17 21 20 19 18 overnight to New Delhi. 22 23 24 25 26 27 28 29 30 31 Solution: A 5-day trip starting on a Friday night will end on Wednesday. So, Renu can book her tickets for Friday night and Wednesday night. Fridays in this month: 6, 13, 20, 27 October 2017 Wednesdays in this month: 4, 11, 18, 25 SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 Renu’s trip could be planned for 6 to 8 9 10 11 12 13 14 th 11 , 13 to 18 or 20 to 25 as marked 15 16 17 18 19 20 21 th th th th th on the calendar. 22 23 24 25 26 27 28 29 30 31 Note: If she plans to go on 27 , she would th return on 1 November. st Example 4: Use the January 2017 calendar shown to answer the question. Rupali is a clerk in a bank. She has 2017 JANUARY holidays on Sundays and on the first and SUN MON TUE WED THU FRI SAT the third Saturdays of the month. She also 1 2 3 4 5 6 7 has holidays on the New Year Day and 8 9 10 11 12 13 14 21 18 16 15 20 17 19 Republic Day. How many holidays does 22 23 24 25 26 27 28 she have in the month of January? 29 30 31 Solution: Republic day is on 26 January. th New Year day is on 1 January. st The first and the third Saturday falls on 7 and 21 January respectively. st th Sundays fall on 1 , 8 , 15 , 22 and 29 January. th nd st th th Rupali has holidays on 1 , 7 , 8 , 15 , 21 , 22 , 26 and 29 January. th st st nd th th th th Therefore, she has 8 holidays in January. Time 101 Ch_7_time.indd 101 1/12/2017 10:23:58 PM

7.1 I Explore (H.O.T.S.) Observe the calendar for the month of February of different years. February 1992 February 1993 February 1994 SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT 1 1 2 3 4 5 6 1 2 3 4 5 2 3 4 5 6 7 8 7 8 9 10 11 12 13 6 7 8 9 10 11 12 9 10 11 12 13 14 15 14 15 16 17 18 19 20 13 14 15 16 17 18 19 16 17 18 19 20 21 22 21 22 23 24 25 26 27 20 21 22 23 24 25 26 23 24 25 26 27 28 29 28 27 28 February 1995 February 1996 February 1997 SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT 1 2 3 4 1 2 3 1 5 6 7 8 9 10 11 4 5 6 7 8 9 10 2 3 4 5 6 7 8 12 13 14 15 16 17 18 11 12 13 14 15 16 17 9 10 11 12 13 14 15 19 20 21 22 23 24 25 18 19 20 21 22 23 24 16 17 18 19 20 21 22 26 27 28 25 26 27 28 29 23 24 25 26 27 28 February 1998 February 1999 February 2000 SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 1 2 3 4 5 6 1 2 3 4 5 8 9 10 11 12 13 14 7 8 9 10 11 12 13 6 7 8 9 10 11 12 15 16 17 18 19 20 21 14 15 16 17 18 19 20 13 14 15 16 17 18 19 22 23 24 25 26 27 28 21 22 23 24 25 26 27 20 21 22 23 24 25 26 28 27 28 29 We observe that February has 29 days in the years 1992, 1996 and 2000. In the other years, February has 28 days. Every four years, an extra day is added to the month of February. This is due to the revolution of the Earth around the Sun. • The Earth takes 365 and a quarter days to go around the Sun. • An ordinary year is taken as 365 days only.  1 1 1 1 • Four quarters put together  + + +  make an extra day for every four years.  4 4 4 4  102 Ch_7_time.indd 102 1/12/2017 10:23:59 PM

• This is added on to get the leap year. So, there are 365 + 1 = 366 days in a leap year. Example 5: Find the leap year in the following years: 2011, 2012, 2015, 2016, 2020 Solution: A year is said to be a leap year if the number formed by the last two digits is divisible by 4. In other words, when we divide a year by 4 and if it leaves no remainder, then the year is called a leap year. 2011 ÷ 4 = 502, R = 3 2012 ÷ 4 = 503, R = 0 2015 ÷ 4 = 503, R = 3 2016 ÷ 4 = 504, R = 0 2020 ÷ 4 = 505, R = 0 Thus, 2012, 2016 and 2020 are the leap years. Example 6: How many days were there from Christmas 2010 to Christmas 2011? Solution: 2011 was not a leap year. So, the number of days from Christmas 2010 to Christmas 2011 was 365. Maths Munchies Every year whose number is perfectly divisible by four is a leap year. But, 2 3 1 years divisible by 100 but not by 400 are not leap years. The second part of the rule affects century years. For example, the century years, 1600 and 2000, are leap years. But the century years, 1700, 1800 and 1900, are not. Time 103 Ch_7_time.indd 103 1/12/2017 10:23:59 PM

Concept 7.2: Read Time Correct to the Hour I Think Neena’s teacher taught her to read time. She now knows the units of time. Neena reads time when her dad moves the hands of a clock to different numbers. Can you also read time from a clock? To know time using a clock, we must learn to read time correct to the hour. 7.2 I Recall We have 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 round the clock. c) The _______________ hand is the short hand on the clock. d) The time is _______________ when both the hour hand and the minute hand are on 12. e) 2 hours before 10 o’clock is _______________. 7.2 I Remember and Understand 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 1 hour = 60 minutes to go round the clock face once. 104 Ch_7_time.indd 104 1/12/2017 10:24:00 PM

The minute hand takes 5 minutes to go from one number to the next number on the clock face. We multiply the number at which the minute hand points by 5 to get the minutes. For example, the minute hand in the figure is at 4. So, it denotes 4 × 5 = 20 minutes past the hour (Here, after 3.) Therefore, the time is read as 20 minutes after 3. The hour hand takes one hour to move from one number to the other. Let us now read the time from these clocks. a) b) c) d) In figure a), the minute hand is at 5. The hour hand is in between 1 and 2 . The number of minutes is 5 × 5 = 25. Thus, the time shown is 1:25. In figure b), the minute hand is at 2. The number of minutes is 2 × 5 = 10. The hour hand is between 7 and 8. Therefore, the time shown is 7:10. In figure c), the minute hand is at 9. The number of minutes is 9 × 5 = 45. The hour hand is between 1 and 2. Therefore, the time shown is 1:45. In figure d), the minute hand is at 6. So, the number of minutes is 6 × 5 = 30. The hour hand is between 3 and 4. Therefore, the time shown is 3:30. Example 7: 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 Time 105 Ch_7_time.indd 105 1/12/2017 10:24:00 PM

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, 1 ‘quarter’ means . 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) The time shown is 2:15 or 15 minutes past 2 or quarter past 2. 1 ‘Half’ means . 2 In Fig (b), the minute hand has travelled 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) If the minute hand has to travel a quarter of the clock before it completes one hour, we call it quarter to the hour. Train My Brain The time shown is 7:45 or 45 minutes past 7 or quarter to 8. Fig (c) Example 8: Read the time in each of the given clocks and write it in two different ways. Fig (a) Fig (b) Fig (c) Fig (d) 106 Ch_7_time.indd 106 1/12/2017 10:24:02 PM

Solution: To read time, observe the position of the hour and the minute hands. Solved Solve this Solve this Solve this 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 _____ between _____ and between _____ So, the minutes are and _____. The _____. The minutes and _____. The after 3 hours. The minutes are after are after ____hours. minutes are after minute hand is at ____hours. The The minute hand ____hours. The 6. So, the time is 30 minute hand is at is at _____. So, minute hand is at minutes after 3. We _____. So, the time the time is _____ _____. So, the time write it as 3:30 or is _____ minutes minutes after _____. is _____ minutes half-past 3. after _____. We We write it as _____ after _____. We write it as _____ or or _____. write it as _____ _____. or _____. Train My Brain Answer the following: a) Write the time: quarter past 7. b) How many numbers do you see on the clock? c) How much time does the hour hand take to move from one number to the next? 7.2 I Apply We have learnt how to read the time. Now let us draw hands on the clocks when time is given. Time 107 Ch_7_time.indd 107 1/12/2017 10:24:02 PM

Example 9: 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. Fig (a) Fig (b) Fig (c) Fig (d) Example 10: Draw the hands of a clock to show the given time. a) Quarter to 6 b) Half past 3 c) Quarter past 8 Solution: Fig (a) Fig (b) Fig (c) 7.2 I Explore (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. Example 11: The clocks given show the start time and the end time of the Maths class. How long was the class? 108 Ch_7_time.indd 108 1/12/2017 10:24:04 PM

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 is 45 minutes. Example 12: Sanjay spends an hour between 4:30 and 5:30 for 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 having 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 having milk at 4:45. b) Sanjay 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. Time 109 Ch_7_time.indd 109 1/12/2017 10:24:05 PM

Maths Munchies People in the past had different ways of reading time. The position of the 2 3 1 stars in the sky showed the time. The night had 20 hours. The days in the past had ten hours. To keep a track of the hours in a day, people used a shadow clock. Shadow clock is also known as sundial. 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? 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. English Fun A poem to remember what a calendar tells us: When we see the calendar we learn the month, the date, the year. Every week day has a name there are lots of numbers that look the same. So let’s begin to show you how we see the calendar right now. A Note to Parent Whenever you visit a railway station with your child, make him or her note down the time of various trains arriving at the station. 110 Ch_7_time.indd 110 1/12/2017 10:24:06 PM

Drill Time Concept 7.1: Read a Calendar 1) Observe the calendar and answer the following 2017 JANUARY questions. SUN MON TUES WED THU FRI SAT 1 2 3 4 5 6 7 a) How many weekend days and weekdays are 8 9 10 11 12 13 14 there in the month shown in the calendar? 15 16 17 18 19 20 21 Consider Saturday and Sunday as weekend 22 23 24 25 26 27 28 days. 29 30 31 b) Write the day and date before two days of fourth Saturday of January. c) On which day does the month end? 2) Word Problems a) Raju bought a new dress on 1 of September. 2017 SEPTEMBER st He bought another new dress 10 days after first SUN MON TUES WED THU FRI SAT day of the month. On which date did he buy 1 2 the other dress? 3 4 5 6 7 8 9 11 16 15 12 13 10 14 b) Sonu’s birthday was on 2 of September. What 17 18 19 20 21 22 23 nd is the date, if he celebrated it on the same day 24 25 26 27 28 29 30 of the third week? c) Ram solved problems from one chapter of his book on 9 of September. He th 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 3) Draw the hands of a clock to show the given time. a) Half past 2 b) 4:15 c) Quarter to 12 d) 4:25 e) 6:20 Time 111 Ch_7_time.indd 111 1/12/2017 10:24:06 PM

Drill Time 4) What is the time shown on each of these clocks? a) b) c) d) 5) 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. From the figures, answer the following questions. (A) When did Ram wake up? (B) For how many minutes did Ram drink milk? (C) How much time did Ram spend for getting ready? (D) For how long did Ram study? 112 Ch_7_time.indd 112 1/12/2017 10:24:06 PM

D Divisionivision I Will Learn Concepts 8.1: Division as Equal Grouping and Relate Division to Multiplication 8.2: Divide 2-digit and 3-digit Numbers by 1-digit Numbers L08_V2_PPS_Math_G3_TB_08112016_V1.indd 113 1/12/2017 10:33:44 PM

Concept 8.1: Division as Equal Grouping and Relate Division to Multiplication I Think Neena wants to distribute 8 sticks equally among 4 of her friends. How can she distribute? To answer this question, we must know equal grouping. 8.1 I Recall In the previous chapter, we have learnt multiplication. Multiplication is finding the total number of objects that have been grouped equally. Let us use this to distribute objects equally in groups. Consider 12 bars of chocolate. The different ways in which they can be distributed are as follows. Distributing in 1 group: 1 × 12 = 12 Distributing in 2 groups: 2 × 6 = 12 Distributing in 3 groups: 3 × 4 = 12 Distributing in 4 groups: 4 × 3 = 12 114 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 114 1/12/2017 10:33:46 PM

Distributing in 6 groups: 6 × 2 = 12 Distributing in 12 groups: 12 × 1 = 12 Distributing a given number of objects into equal groups is called division. We can understand division better by using equal sharing and equal grouping. 8.1 I Remember and Understand Equal sharing means having equal number of objects or things in a group. We use division to find the number of things in a group and the number of groups. Suppose 9 balloons are to be shared equally by 3 girls. Let us use repeated subtraction to distribute the balloons. 1 round: 1 balloon is taken by each girl. st 9 – 3 = 6. So, 6 balloons remain. 2 round: 1 more balloon is taken by each nd girl. Now, each of them has 2 balloons. 6 – 3 = 3. So, 3 balloons remain. 3 round: 1 more balloon is taken by each rd girl. Now, each of them has 3 balloons. 3 – 3 = 0. So, 0 balloons remain. Each girl gets 3 balloons. Division 115 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 115 1/12/2017 10:33:48 PM

We can write it as 9 divided by 3 equals 3. The symbol for ‘is divided by’ is ÷. 9 divided by 3 equals 3 is written as In division of two numbers, the 9 ÷ 3 = 3 number written to the left of ÷ symbol is called Dividend. [Total number] ÷ [Number in each group] = [Number of groups] The number written to the right of ÷ symbol is called Divisor. Dividend ÷ Divisor = Quotient The number written to the right In a division, the number that is divided is of = symbol is called Quotient. called the dividend. The number that divides is called the divisor. The answer in division is called the quotient. The number (part of the dividend) that remains is called the remainder. 9 ÷ 3 = 3 is called a division fact. In this, 9 is the dividend, 3 is the divisor and 3 is the quotient. Note: Representing the dividend, divisor and quotient using the symbols ÷ and = is called a division fact. We use multiplication tables to find the quotient in a division. We find the factor which when multiplied by the divisor gives the dividend. Let us understand this through a few examples. Example 1: 18 pens are to be shared equally by 3 children. How many pens does each of them get? Solution: Total number of pens = 18 Number of children = 3 Number of pens each child gets = 18 ÷ 3 = 6 (since 6 × 3 = 18) Therefore, each child gets 6 pens. Example 2: 10 flowers are put in some vases. If each vase has 2 flowers, how many vases are used? Solution: Number of flowers = 10 Number of flowers in each vase = 2 116 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 116 1/12/2017 10:33:48 PM

Number of vases used = 10 ÷ 2 = 5 (since 2 × 5 = 10) Therefore, 5 vases are used to put 10 flowers. We get two division facts from a multiplication fact. The divisor and the quotient are the factors of the dividend. Observe the following: Dividend ÷ Divisor = Quotient Multiplicand × Multiplier = Product 18 ÷ 6 = 3 6 × 3 = 18 ↓ ↓ ↓ ↓ ↓ ↓ Product Factor Factor Divisor Quotient Dividend (Multiplicand) (Multiplier) From the multiplication fact 6 × 3 = 18, we can write two division facts: a) 18 ÷ 3 = 6 and b) 18 ÷ 6 = 3 Multiplication and division are reverse operations. Let us now understand this through an activity. We can show a multiplication fact on the number line. For example, 3 × 5 = 15 means 5 times 3 is 15. To show 5 times 3 on the number line, we take steps of 3 for 5 times. We go forward from 0 to 15. Division 117 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 117 1/12/2017 10:33:49 PM

Similarly, we can show the division fact 15 ÷ 3 = 5 on the number line . To show 15 divided by 3 on the number line, we take steps of 3 for 5 times. We go backward from 15 to 0 as shown. Train My Brain Write two multiplication facts for each of the following: a) 20 ÷ 5 = 4 b) 49 ÷ 7 = 7 c) 10 ÷ 2 = 5 8.1 I Apply Equal sharing and equal grouping are used in some real-life situations. Consider the following situations. Example 3: 25 buttons are to be stitched on 5 shirts. If each shirt has the same number of buttons, how many buttons are there on each shirt? Solution: Total number of buttons = 25 Number of shirts = 5 The division fact for 25 buttons distributed to 5 shirts = 25 ÷ 5 = 5. Therefore, each shirt has 5 buttons on it. Example 4: 24 marbles are to be divided in 4 friends. How many marbles will each friend get? Solution: Total number of marbles = 24 Number of friends = 4 Number of marbles each friend will get = 24 ÷ 4 = 6 Therefore, each friend will get 6 marbles. 118 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 118 1/12/2017 10:33:49 PM

8.1 I Explore (H.O.T.S.) Division is used in many situations in our day-to-day lives. Let us see some examples. Example 5: Aman spends 14 hours a week for tennis practice. He spends 21 hours a week for doing homework and 48 hours a week at school. How much time does he spend in a day for these activities? (Hint: 1 week = 7 days. The school works for 6 days a week.) Solution: Time spent for tennis practice per day = 14 hours ÷ 7 = 2 hours Time spent for doing homework per day = 21 hours ÷ 7 = 3 hours Time spent at school per day = 48 hours ÷ 6 = 8 hours (School works for 6 days a week) Thus, the total time spent by Aman in a day for all the activities = (2 + 3 + 8) hours = 13 hours (except Sunday) Example 6: Deepa shares 15 lollipops among her 5 friends. Instead, if she shares among only 3 of them, how many more lollipops does each of them get? Solution: Number of lollipops = 15 If Deepa shares the lollipops among her five friends, the number of lollipops each of them would get = 15 ÷ 5 = 3 If Deepa shares the lollipops among only three of them, the number of lollipops each of them gets = 15 ÷ 3 = 5 Difference in the number of lollipops = 5 – 3 = 2 Therefore, her friends would get 2 more lollipops. Division 119 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 119 1/12/2017 10:33:49 PM

Maths Munchies Why is division of a number by 0 not possible? 2 3 1 We know that division and multiplication are related. If we have to find 6 ÷ 3, we get the answer 2, because 2 × 3 = 6. Similarly, if we have to find 6 ÷ 0, what would be the answer? We must get a number which when multiplied by 0 gives 6. But any number when multiplied by 0 results in 0. Therefore, 6 ÷ 0 is not possible. Division by zero is undefined. Concept 8.2: Divide 2-digit and 3-digit Numbers by 1-digit Numbers I Think Neena has 732 stickers. She wants to distribute them equally among her three friends. How will she distribute? To answer this, we must learn how to divide a 3-digit number by a 1-digit number. 8.2 I Recall In the previous section, 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 ______________________. 120 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 120 1/12/2017 10:33:50 PM

c) The division facts for the multiplication fact 2 × 4 = 8 are ________________ and __________________. d) 14 ÷ 2 = __________ e) 10 ÷ 5 = __________ 8.2 I Remember and Understand We can make equal shares or groups and divide with the help of vertical arrangement. Let us see some examples. The quotient when 1) Dividing a 2-digit number by a 1-digit number (1-digit a number is divided quotient) by itself is always 1. Example 7: Divide: 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 divisor as shown: DivisorDividend 545 ) ) Dividend = _____ Step 2: Find the multiplication fact 45 = 5 × 9 8 ) 56 Divisor = ______ which has the dividend and divisor. Step 3: Write the other factor as 9 - Quotient = ____ quotient. Write the product of the 545 ) factors below the dividend. Remainder = _____ − 45 Step 4: Subtract the product 9 from the dividend and write the 545 Dividend = _____ ) difference below the product. − 45 436 Divisor = ______ ) This difference is called the remainder. 00 - Quotient = ____ 45 = Dividend 5 = Divisor Remainder = _____ 9 = Quotient 0 = Remainder Note: If the remainder is zero, the divisor is said to divide the dividend exactly. Division 121 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 121 1/12/2017 10:34:02 PM

Checking for correctness of division: The multiplication fact of the division is used to check its correctness. 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 7 is correct or not. Step 1: Remainder < Divisor 0 < 5 (True) Step 2: Quotient × Divisor 9 × 5 Step 3: (Quotient × Divisor) + Remainder = 45 + 0 = 45 = Dividend Note: The division is incorrect if a) Remainder > or = divisor b) (Quotient × Divisor) + Remainder ≠ Dividend 2-digit quotients 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. Train My Brain Example 8: Divide: 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 dividend is greater than the divisor. 5 Step 2: Divide the tens and write the 1 ) 60 quotient. 357 − ) Write the product of quotient and divisor, below the tens digit of the dividend. − 3 − 122 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 122 1/12/2017 10:34:04 PM

Steps Solved Solve these Step 3: Subtract and write the difference. 1 357 ) − 3 Dividend = _____ 2 Step 4: Check if difference < divisor is true. 2 < 3 (True) Divisor = ______ Quotient = ____ Step 5: Bring down the ones digit of the 1 dividend and write it beside the remainder. 357 Remainder = ___ ) − 3 ↓ 27 Step 6: Find the largest number in the 3 × 8 = 24 19 multiplication table of the divisor that can 3 × 9 = 27 357 ) be subtracted from the 2-digit number in 3× 10 = 30 the previous step. 24 < 27 <30. − 3 ↓ ) So, 27 is the 27 342 required − number. Step 7: Write the factor of required 19 number, other than the divisor, as quotient. 357 − ) Write the product of divisor and quotient below the 2-digit number. Subtract and − 3 ↓ write the difference. 27 − 27 00 Dividend = _____ Step 8: Check if remainder < divisor is true. 0 < 3 (True) Stop the division. Divisor = ______ (If this is false, the division is incorrect.) Quotient = ____ Step 9: Write the quotient and remainder. Quotient = 19 Remainder = 0 Remainder = ___ Step 10: Check if (Divisor × Quotient) + 3 × 19 + 0 = 57 Remainder = Dividend is True. 57 + 0 = 57 (If this is false, the division is incorrect.) 57 = 57 (True) Division 123 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 123 1/12/2017 10:34:11 PM

2) Divide 3-digit numbers by 1-digit numbers (2-digit Quotients) 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 9: Divide: a) 265 ÷ 5 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 the divisor. If it is not, consider the tens ) 5 265 4 244 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 5 26 5 − number of the dividend. Write the ) quotient. − 2 5 Write the product of the quotient and divisor below the dividend. 5 × 4 = 20 5 × 5 = 25 Dividend = _____ 5 × 6 = 30 25 < 26 Divisor = ______ Step 3: Subtract and write the 5 Quotient = ____ difference. 5 26 5 Remainder = ___ ) − 2 5 1 Step 4: Check if difference < divisor 1 < 5 (True) ) is true. (If it is false, the division is 9 378 incorrect.) − Step 5: Bring down the ones digit 5 of the dividend. Write it beside the 5 26 5 ) remainder. − − 2 5↓ 15 124 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 124 1/12/2017 10:34:19 PM

Steps Solved Solve these Step 6: Find the largest number in 5 Dividend = _____ the multiplication table of the divisor 5 26 5 ) that can be subtracted from the Divisor = ______ 2-digit number in the previous step. − 2 5↓ Quotient = ____ 15 5 × 2 = 10 Remainder = ___ 5 × 3 = 15 5 × 4 = 20 15 is the required number. 5 245 ) Step 7: Write the factor of required 53 − number, other than the divisor, as 5 26 5 ) quotient. Write the product of divisor − 2 5↓ and quotient below the 2-digit 15 − number. Then, subtract them. − 15 00 Step 8: Check if remainder < divisor is true. Stop the division. (If this is false, 0 < 5 (True) Dividend = _____ the division is incorrect.) Step 9: Write the quotient and Quotient = 53 Divisor = ______ remainder. Remainder = 0 Quotient = ____ Step 10: Check if (Divisor × 5 ×53 + 0 = 265 Quotient) + Remainder = Dividend 265 + 0 = 265 Remainder = ___ is true. (If this is false, the division is 265 = 265 (True) incorrect.) 3-digit quotients Example 10: Divide: 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 7 784 ) to the divisor. 7 = 7 Division 125 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 125 1/12/2017 10:34:24 PM

Steps Solved Solve these Step 2: Divide the hundreds and 1 write the quotient in the hundreds 7 784 ) place. Write the product of the quotient − 7 8 984 and the divisor under the hundreds ) place of the divided. − Step 3: Subtract and write the 1 difference. 7 784 − ) − 7 0 − Step 4: Check if difference < divisor 0 < 7 (True) is true. Step 5: Bring down the next digit of 1 the dividend. Check if it is greater 7 784 ) than or equal to the divisor. Dividend = _____ − 7 ↓ 08 Divisor = ______ 8 > 7 Quotient = ____ Step 6: Find the largest number in the 11 Remainder = ___ multiplication table of the divisor that 7 784 ) can be subtracted from the 2-digit 7 number in the previous step. −↓ Write the factor other than the divisor 08 as quotient. − 7 5 ) 965 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 11 difference. Bring down the next digit 7 784 ) (ones digit) of the dividend. − 7 Check if the dividend is greater than −↓ or equal to the divisor. 08 − 7 14 14 > 7 126 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 126 1/12/2017 10:34:35 PM

Steps Solved Solve these Step 8: Find the largest number in 112 Dividend = _____ the multiplication table of the divisor 7 784 ) that can be subtracted from the Divisor = ______ 7 2-digit number in the previous step. −↓ Quotient = ____ Write the factor other than the 08 divisor as the quotient. − 7 Remainder = ___ Write the product of the quotient 14 and the divisor below it. − 14 7 × 2 = 14 The required number 2 ) 246 is 14. − Step 9: Subtract and write the 112 difference. 7 784 ) Check if it is less than the divisor. −↓ − 7 Stop the division. 08 − 7 − 14 − 14 00 Dividend = _____ Step 10: Write the quotient and the Quotient = 112 Divisor = ______ remainder. Remainder = 0 Step 11: Check if (Divisor × Quotient) Quotient = ____ + Remainder = Dividend is true. (If it 7 × 112 + 0 = 784 Remainder = ___ is false, the division is incorrect.) 784 + 0 = 784 784 = 784 (True) Train My Brain Solve the following: a) 12 ÷ 4 b) 648 ÷ 8 c) 744 ÷ 4 Division 127 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 127 1/12/2017 10:34:41 PM

8.2 I Apply Division of 2-digit numbers and 3-digit numbers is used in many real-life situations. Let us consider a few examples. Example 11: 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? Solution: Number of students = 634 158 4 634 ) Number of houses = 4 4 −↓ Number of students in a house = 634 ÷ 4 23 − 20 Number of students in each house = 158 34 The remainder in the division is 2. − 32 02 Therefore, 2 students are not grouped into any house. Example 12: A football game had 99 spectators. If each row has only 9 seats, how many rows would the spectators occupy? Solution: Number of spectators = 99 11 9 99 ) Number of seats in each row = 9 9 −↓ Number of rows occupied by the spectators = 99 ÷ 9 = 11 09 − 9 Therefore, 11 rows were occupied by the spectators. 0 8.2 I Explore (H.O.T.S.) In all the divisions 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. 128 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 128 1/12/2017 10:34:44 PM

Let us now understand division of numbers that have a 0 (zero) in dividend or quotients, through these examples. Example 13: Divide: 505 ÷ 5 Solution: Follow these steps for division of numbers having 0 in dividend. Solved Solve this 505 ÷ 5 804 ÷ 4 101 4 804 5 505 ) ) 5 −↓ − 00 − 00 − 05 − 05 00 − Maths Munchies Dividing a 2-digit number or a 3-digit number by 10: 1 2 3 Observe the pattern in the division of the following examples: a) 562 ÷ 10 = Q 56 and R 2 b) 325 ÷ 10 = Q 32 and R 5 c) 687 ÷ 10 = Q 68 and R 7 We observe that the ones digit of the dividend is the remainder and the number formed by its remaining digits is the quotient. This helps us to do the divisions quickly. Division 129 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 129 1/12/2017 10:34:47 PM

Connect the Dots Science Fun Some fruits have one seed. Some have more than one seed. Peas have more than one seeds. Take four peas and take out all peas seeds. Divide them equally among your family. What is the quotient? What is the remainder? Social Studies Fun Division mean equal sharing. It exists in our neighbourhood and families also. The members of a family share the works or tasks in a family. What kind of division of work do you see in your neighbourhood? A Note to Parent Engage your child in the activities that involve division in day to day life like dividing chapatis amongst all on a dinner table, splitting pocket money or some chocolates with his or her sibling or even putting flowers into vases at home. Drill Time Concept 8.1: Division as Equal Grouping and Relate Division to Multiplication 1) Divide the number in equal groups. a) 16 in 4 equal groups b) 18 in 9 equal groups c) 20 in 5 equal groups d) 32 in 8 equal groups e) 10 in 2 equal groups 130 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 130 1/12/2017 10:34:48 PM

Drill Time 2) Word Problems a) 26 students are to be divided in 2 groups. How many students will be there in each group? b) 14 pencils must be distributed among 7 children. How many pencils will each student receive? Concept 8.2: Divide 2-digit and 3-digit Numbers by 1-digit Numbers 3) 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 4) 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 5) 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 6) 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 7) Word Problems a) There are 260 chocolates in a jar that have to be distributed equally among 4 students. How many chocolates will each student receive? b) There are 24 people in a bus. Each row in the bus can seat 2 people. How many rows in the bus are occupied? Division 131 L08_V2_PPS_Math_G3_TB_08112016_V1.indd 131 1/12/2017 10:34:48 PM

F Fractionsractions I Will Learn Concepts 9.1: Fraction as a Part of a Whole 9.2: Fraction of a Collection L09_V2_PPS_Maths_G3_TB.indd 132 1/12/2017 5:21:54 AM

Concept 9.1: Fraction as a Part of a Whole I Think Neena and her three friends share an apple equally. What part of the apple does each of them get? To answer this question, we must learn to find fraction of a whole. 9.1 I Recall Look at the rectangle shown below. We can divide the whole rectangle into many equal parts. Consider the following: 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. Fractions 133 L09_V2_PPS_Maths_G3_TB.indd 133 1/12/2017 5:21:55 AM

9.1 I Remember and Understand Suppose we want to share an apple with our friends. First, we count 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: 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. Activity: Halves Take a square piece of paper. Fold it into two equal parts as shown. 134 L09_V2_PPS_Maths_G3_TB.indd 134 1/12/2017 5:21:56 AM

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 1 In , 1 is the number of parts taken and 2 is the total number of equal parts the 2 whole is divided into. 1 1 Note: and 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). 1 1 1 3 3 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). 1 2 We write one-third as and two-thirds as . 3 3 1 1 1 1 2 Note: , and or and 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. Fractions 135 L09_V2_PPS_Maths_G3_TB.indd 135 1/12/2017 5:21:56 AM

In figure (a), the four parts are not 1 equal. In figure (b), each equal part 4 is called a fourth or a quarter and is 1 written as . 1 4 4 Two out of four equal parts are called 1 two-fourths and three out of four 4 equal parts are called three-fourths, 1 3 written as 2 and respectively. 4 4 4 Four parts Four equal parts 1 Note: Each of and Fig (a) Fig (b) 4 3 ; 1 1 1 and 1 and , and 2 1 1 , , 4 4 4 4 4 4 4 4 makes a whole. 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. Numerator Representing the parts of a whole as Denominator is called a fraction. Thus, a fraction is a part of a whole. 1 1 1 2 For example, , , , and so on are fractions. 2 3 4 3 Numbers of the form Let us now see a few examples. Numerator are Example 1: Identify the numerator and denominator Denominator in each of the following fractions: called fractions. 1 1 1 a) b) c) 2 3 4 Solution: S. No Fractions Numerator Denominator 1 a) 1 2 2 1 b) 3 1 3 1 c) 1 4 4 136 L09_V2_PPS_Maths_G3_TB.indd 136 1/12/2017 5:21:58 AM

Example 2: Identify the fraction for the shaded parts in the figures below. a) b) Solution: Solved Solve this Steps a) b) Step 1: Count the number of Total number of Total number of equal equal parts, the figure is divided equal parts = 8 parts = _______ into (Denominator). Step 2: Count the number of Number of parts Number of parts shaded = shaded parts (Numerator). shaded = 5 ______ Step 3: Write the fractions. 5 Numerator Fraction = 8 Fraction = Denominator 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. Number of parts painted yellow is 3. The fraction of the disc that is painted yellow = Number of parts paintedyellow = 3 Totalnumberofequal parts 16 The fraction of the disc that is painted white Number of parts paintedwhite 6 = = Totalnumberofequal parts 16 Fractions 137 L09_V2_PPS_Maths_G3_TB.indd 137 1/12/2017 5:21:59 AM

Example 4: Find the fraction of parts not shaded in the following figures. a) b) c) Solution: a) Total number of equal parts = 2 Number of parts not shaded = 1 Number of parts not shaded 1 Fraction = = Total number of equal parts 2 Complete the table given. Steps b) c) Total number of equal parts Number of parts not shaded Fraction = Number of parts not shaded Total number of equal parts Train My Brain Identify the fraction of the shaded parts in the given figures. a) b) c) 9.1 I Apply 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. 138 L09_V2_PPS_Maths_G3_TB.indd 138 1/12/2017 5:21:59 AM

Example 5: Shade a square to represent these fractions: 1 2 3 1 a) b) c) d) 2 4 5 3 Solution: We can represent the fractions as: Solved Solve these Steps 1 2 3 1 4 3 5 2 Step 1: Identify the Denominator Denominator Denominator Denominator denominator and = 4 = = = the numerator. Numerator Numerator = Numerator = Numerator = = 1 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 Shapes 1 4 2 5 1 2 Fractions 139 L09_V2_PPS_Maths_G3_TB.indd 139 1/12/2017 5:22:01 AM

Solution: We can represent the fractions as: Fractions Shapes 1 4 2 5 1 2 9.1 I Explore (H.O.T.S.) Let us see some examples of real-life situations 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 trees = Quarter = 1 4 1 Fraction of the garden covered by mango trees = 2 Quarters = 2 1 Fraction of the garden covered by neem trees = Quarter = 4 So, the square garden is as shown in the figure. Coconut trees Mango trees Neem trees 140 L09_V2_PPS_Maths_G3_TB.indd 140 1/12/2017 5:22:02 AM

Example 8: Answer the following questions: a) How many one-sixths are there in a whole? b) How many one-fifths are there in a whole? c) How many halves make a whole? Solution: a) There are 6 one-sixths in a whole. b) There are 5 one-fifths in a whole. c) 2 halves make a whole. 1 1 1 1 6 6 5 5 1 6 1 1 1 6 1 1 2 2 5 5 1 1 1 6 6 5 Maths Munchies We have learnt parts of a whole such as half and fourths. We can divide 2 3 1 a whole into more number of equal parts such as fifths, sixths, sevenths, eighths, ninths and tenths. Train My Brain Fraction Name Fraction Name 1 one-fifths 1 one-eighths 5 8 1 one-sixths 1 one-ninths 6 9 1 one-sevenths 1 one-tenths 7 10 Try these Write the following fractions: a) one-hundredths b) one-thousandths c) one -fiftyfifths Fractions 141 L09_V2_PPS_Maths_G3_TB.indd 141 1/12/2017 5:22:03 AM

Concept 9.2: Fraction of a Collection I Think Neena has a bunch of roses. Some of them are red, some white and some yellow. Neena wants to find the fraction of roses of each colour. How can she find that? To answer that, we must know the fraction of a collection. 9.2 I 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) [ 2 groups] b) [3 groups] c) [2 groups] d) [5 groups] 142 L09_V2_PPS_Maths_G3_TB.indd 142 1/12/2017 5:22:05 AM

9.2 I Remember and Understand Finding a half We can find different fractions of a collection. Suppose To find the part or the there are 10 pens in a box. To find a half of them, we fraction of a collection, find divide them into two equal parts. Each equal part is a the number of each type half. of object out of the total collection. 1 Each equal part has 5 pens, as 10 ÷ 2 = 5. So, of 10 is 5. 2 Finding a third One-third is 1 out of 3 equal parts. In the given figure, there are12 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. 1 So, of 12 is 4. 3 Fractions 143 L09_V2_PPS_Maths_G3_TB.indd 143 1/12/2017 5:22:06 AM

Finding a fourth (or a quarter) One-fourth is 1 out of 4 equal parts. In the figure, there are 8 books. To find a fourth, divide the number of books into 4 equal parts. 1 1 1 1 4 4 4 4 1 Each equal part has 2 books, as 8 ÷ 4 = 2. So, of 8 is 2. 4 Let us see a few examples to find the fraction of a collection. Example 9: 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 6 144 L09_V2_PPS_Maths_G3_TB.indd 144 1/12/2017 5:22:07 AM