Passport-G3-Textbook-Maths-FY

Drill Time Concept 7.1: Read a Calendar 1) Observe the calendar and answer the following questions. a) H ow many weekends and weekdays are 2019 JANUARY there in the month shown in the calendar? SUN MON TUES WED THU FRI SAT Consider Saturday and Sunday as weekend 12345 days. 6 7 8 9 10 11 12 13 14 15 16 17 18 19 b) W rite the day and date before two days of 20 21 22 23 24 25 26 the fourth Saturday of January. 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. 2018 SEPTEMBER He bought another new dress 10 days SUN MON TUES WED THU FRI SAT after first day of the same month. On 1 which date did he buy the other dress? 2 3 45678 9 10 11 12 13 14 15 b) S hane’s birthday was on 2nd September. 16 17 18 19 20 21 22 What is the date, if he celebrated it on the 23 24 25 26 27 28 29 same day of the third week. 30 c) A rif solved problems from one chapter of his book on 9th of 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 3) 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 4) What is the time shown on each of these clocks? Time 97

Drill Time 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. wake up brush have bath Wear uniform study breakfast From the figures, answer the following questions. a) When did Ram wake up? b) How much time did Ram spend for wearing his school uniform? c) When did Ram start studying? d) At what time did Ram had his breakfast? A Note to Parent Whenever you visit a railway station with your child, make him or her note down the arrival and departure times of various trains arriving at the station. 98

Chapter Division 8 I Will Learn About • equal grouping and sharing. • repeated subtraction and division facts. • dividing 2-digit number by 1-digit number. • checking the correctness of division. Concept 8.1: Division as Equal Grouping I Think Farida and her brother Piyush got a chocolate bar with 14 pieces for Christmas. Piyush divided it and gave Farida 6 pieces. Do you think Farida got an equal share? How can we find out? 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. 99

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 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. 100

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 1st round: 1 balloon is taken by each equally among 3 friends. Let us use friend. repeated subtraction to distribute the balloons. 9 – 3 = 6. So, 6 balloons remain. 2nd round: From the remaining 6 balloons, 3rd round: From the remaining 3 balloons, 1 more balloon is taken by each friend. 1 more balloon is taken by each friend. Now, each of them has 3 balloons. Now, each friend has 2 balloons. 3 – 3 = 0. So, 0 balloons remain. Each friend gets 3 balloons. 6 – 3 = 3. So, 3 balloons remain. Division 101

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 ↓ ↓ ↓ Total Number of Number of number of objects in each groups objects group Dividend Divisor Quotient In a division, the number that is divided is 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 = 2 102

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 table: Dividend ÷ Divisor = Quotient Multiplicand × Multiplier = Product 6 × 3 = 18 18 ÷ 6 = 3 ↓↓ ↓ ↓↓ ↓ Divisor Quotient Dividend Product Factor Factor (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. Division 103

To show 5 times 3 on the number line, we take steps of 3 for 5 times. We go forward from 0 to 15. 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 division facts. 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 among 5 shirts = 25 ÷ 5 = 5 Therefore, each shirt has 5 buttons on it. Example 4: 24 marbles are to be divided among 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. 104

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 the lollipops 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. Concept 8.2: Divide 2-digit and 3-digit Numbers by 1-digit Numbers I Think Farida has 732 stickers. She wants to distribute them equally among her three friends. How will she distribute? Division 105

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 ______________________. c) The division facts for the multiplication fact 2 × 4 = 8 are ________________ and __________________. 8.2 I Remember and Understand We can make equal shares or groups and divide with the help A number of vertical arrangement. Let us see some examples. divided by the same number is Dividing a 2-digit number by a 1-digit number always 1. (1-digit quotient) Example 7: 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 − 45 106

Steps Solved Solve these 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. 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 = 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 8: Solve: 57 ÷ 3 Solution: Follow these steps to divide a 2-digit number by a 1-digit number. Division 107

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 = _____ Divisor = ______ Step 4: Check if difference < divisor is true. 3)57 Quotient = ____ Step 5: Bring down the ones digit of the Remainder = ___ dividend and write it beside the remainder. −3 2 2 < 3 (True) 1 3)57 − 3↓ 27 Step 6: Find the largest number in the 3 × 8 = 24 19 multiplication table of the divisor that can be subtracted from the 2-digit number in )3 × 9 = 27 3 57 Brain the previous step. )32So4×,<217027i=s<t3h30Te0r.a−in237↓My 3 42 required number. − Step 7: Write the factor of required number, 19 − other than the divisor, as the quotient. Write the product of the divisor and the quotient 3)57 below the 2-digit number. Subtract and write the difference. − 3↓ 27 − 27 00 108

Steps Solved Solve these Step 8: Check if remainder < divisor is true. 0 < 3 (True) Stop the division. Dividend = _____ Divisor = ______ (If this is false, the division is incorrect.) Quotient = 19 Quotient = ____ Step 9: Write the quotient and the Remainder = 0 Remainder = ___ 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 9: Solve: 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 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 = ______ Write the product of the quotient and − 25 Quotient = ____ the divisor below the dividend. Remainder = ___ 5 × 4 = 20 Step 3: Subtract and write the 5 × 5 = 25 difference. 5 × 6 = 30 25 < 26 5 5)265 − 25 1 Division 109

Steps Solved Solve these 1 < 5 (True) Step 4: Check if difference < divisor 9) 378 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 Dividend = _____ Divisor = ______ Step 6: Find the largest number in the − 25↓ Quotient = ____ multiplication table of the divisor that 15 Remainder = ___ can be subtracted from the 2-digit number in the previous step. 5 5) 245 Step 7: Write the factor of required 5)265 − number, other than the divisor, as quotient. Write the product of divisor − 25↓ − and quotient below the 2-digit 15 number. Then, subtract them. Dividend = _____ 5 × 2 = 10 Divisor = ______ Step 8: Check if remainder < divisor is 5 × 3 = 15 Quotient = ____ true. Stop the division. (If this is false, 5 × 4 = 20 Remainder = ___ the division is incorrect.) 15 is the required number. 53 5)265 − 25↓ 15 − 15 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) 110

3-digit quotient Example 10: 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. Step 2: Divide the hundreds and write the 7=7 − quotient in the hundreds place. 1 Write the product of the quotient and the − divisor under the hundreds place of the 7)784 dividend. − Step 3: Subtract and write the difference. −7 Dividend = _____ Step 4: Check if difference < divisor is true. 1 Divisor = ______ Step 5: Bring down the next digit of the Quotient = ____ dividend. Check if it is greater than or 7)784 Remainder = ___ equal to the divisor. −7 5) 965 Step 6: Find the largest number in the 0 multiplication table of the divisor that can − be subtracted from the 2-digit number in 0 < 7 (True) the previous step. 1 − Write the factor other than the divisor as quotient. 7)7 84 − Write the product of the quotient and the divisor below it. − 7↓ 08 8>7 11 7)784 − 7↓ 08 −7 7×1=7<8 The required number is 7. Division 111

Steps Solved Solve these Step 7: Subtract and write the difference. 11 Dividend = _____ Bring down the next digit (ones digit) of the Divisor = ______ dividend. 7)784 Quotient = ____ Remainder = ___ Check if the dividend is greater than or − 7↓ equal to the divisor. 08 2) 246 −7 − 14 − − Step 8: Find the largest number in the 14 > 7 multiplication table of the divisor that can Dividend = _____ be subtracted from the 2-digit number in 112 Divisor = ______ the previous step. Quotient = ____ 7)784 Remainder = ___ Write the factor other than the divisor as the quotient. − 7↓ 08 Write the product of the quotient and the divisor below it. −7 14 − 14 Step 9: Subtract and write the difference. 7 × 2 = 14 The required Check if it is less than the divisor. Stop the number is 14. division. 112 7)784 − 7↓ 08 −7 14 − 14 00 Step 10: Write the quotient and the Quotient = 112 remainder. Remainder = 0 Step 11: Check if (Divisor × Quotient) + Remainder = Dividend is true. (If it is false, 7 × 112 + 0 = 784 the division is incorrect.) 784 + 0 = 784 784 = 784 (True) 112

Train My Brain Solve the following: a) 12 ÷ 4 b) 648 ÷ 8 c) 744 ÷ 4 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 Solution: grouped into a house? 158 Number of students = 634 Number of houses = 4 4)634 Number of students in a house = 634 ÷ 4 − 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 12: 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 Number of seats in each row = 9 9) 99 Number of rows occupied by the spectators = 99 ÷ 9 = 11 − 9↓ 09 Therefore, 11 rows were occupied by the spectators. −9 0 8.2 I Explore (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. Division 113

Let us now understand division of numbers that have a 0 (zero) in dividend or quotient, through these examples. Example 13: 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 Maths Munchies 213 Why is division of a number by 0 not possible? 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. Connect the Dots Social Studies Fun Division mean equal sharing. It exists in our neighbourhood and families also. The members of a family share tasks in a family. What kind of division of work do you see in your neighbourhood? 114

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? Drill Time Concept 8.1: Division as Equal Grouping 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 2) Word Problems a) 26 students are to be divided into 2 groups. How many students will be there in each group? b) 1 4 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 Division 115

Drill Time 7) Word Problems a) 2 60 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 bus can seat 2 people. How many rows in the bus are occupied? 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 their siblings or even putting flowers into vases at home. 116

Chapter Fractions 9 I Will 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 I Think Farida and her three friends, Joseph, Salma and Rehan, went on a picnic. Farida had only one apple with him. He wanted to share it equally with everyone. What part of the apple does each of them get? 9.1 I Recall Look at the rectangle shown below. We can divide the whole rectangle into many equal parts. Consider the following: 117

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. 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 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. 118

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 Note: 1 , 1 and 1 or 1 and 2 makes a whole. 3 3 3 3 3 Fractions 119

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 4 1 4 1 4 1 Four parts Fig. (d) 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. Thus, a fraction is a part of a whole.  Denominator  For example, 1 , 1, 1, 2 and so on are fractions. 2 3 4 3 120

Let us now see a few examples. Example 1: Identify the numerator and denominator in Numbers of the form Numerator are each of the following fractions: Denominator a) 1 b) 1 c) 1 2 3 4 called fractions. 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 Fraction = Step 3: Write the fraction Fraction = 5  Numerator  . 8  Denominator  Fractions 121

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 Train My Brain Identify the fraction of the shaded parts in the given figures. a) b) c) 122

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. Example 5: Shade a square to represent these fractions: 1 2 3 d) 1 a) 4 b) 3 c) 5 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 = = Step 2: Draw the Numerator = 1 = required shape. Divide it into as many Numerator 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 123

Solution: We can represent the fractions as: Fractions 1 2 1 4 5 2 Shapes 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 Fraction of the garden covered by mango trees = 2 Quarters = 1 2 Fraction of the garden covered by neem trees = Quarter = 1 So, the square garden is as shown in the figure. 4 Mango Coconut trees trees Neem trees 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? 124

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. 11 66 11 55 1 1 11 11 6 6 55 22 1 1 1 6 6 5 Concept 9.2: Fraction of a Collection I 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? 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] Fractions 125

c)  [2 groups] d)  [5 groups] 9.2 I Remember and Understand To find the part or the fraction of a collection, Finding a half find the number of each We can find different fractions of a collection. Suppose type of object out of the there are 10 pens in a box. To find a half of them, we total collection. 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 Train My Brain 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. So, 1 of 12 is 4. 3 111 333 126

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 1 444 4 1 Each equal part has 2 books, as 8 ÷ 4 = 2. So, 4 of 8 is 2. 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 3 6 5 8 Fractions 127

Example 10: Colour the shapes according to the given fractions. Fractions Shapes 1 5 2 7 3 4 Solution: We can colour the shapes according to the fractions as – Shapes Fractions 1 5 2 7 3 4 Train My Brain What fraction of the collection are: a) Chocolate cupcakes b) Strawberry cupcakes c) Blueberry cupcakes 128

9.2 I Apply We can apply the knowledge of fractions in many real-life situations. Let us see a few examples. Example 11: A basket has 64 flowers. Half of them are roses, a quarter of them are marigolds and a quarter of them are lotus. How many roses, marigolds and lotus 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 lotus. 1 The number of lotus = 4 of 64 = 64 ÷ 4 = 16 Therefore, there are 32 roses, 16 marigolds and 16 lotus in the basket. Example 12: 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 13: 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 . Fractions 129

Number of red balloons = 10 10 9.2 Therefore, fraction of red balloons = 15 I Explore (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 some such examples. Example 14: One kilogram of apples costs ` 16 and one kilogram of papaya costs ` 20. If Rita buys 1 kg of apples and 1 kg of papaya, how much 2 4 money 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 ooff ` 20 = ` 20 ÷ 4 = ` 5 4 4 (To find a fourth, we divide by 4) Therefore, the money spent by Rita = ` 8 + ` 5 = ` 13 Example 15: 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 has solved 10 problems. 130

Maths Munchies Egyptians have a different way to represent fractions. 213 To represent 1 as numerator, they use a mouth picture which literally means ‘part’. So, the fraction ‘one-fifth’ will be shown as given in the image. On the other hand, fractions were only written in words in Ancient Rome. 1 was called unica 6 was called semis 12 12 1 1 was called scripulum 24 was called semunica 144 Connect the Dots Science Fun Around 7 out of 10 parts of air is nitrogen. Oxygen is at the second position. 2 out of 10 parts of air is oxygen. English Fun Think of at least two words that rhyme with each ‘numerator’ and ‘denominator’. Drill Time Concept 9.1: Fraction as a Part of a Whole 1) Find the numerator and the denominator in each of these fractions. 2 b) 1 2 a) 5 7 c) 3 45 d) 9 e) 7 Fractions 131

Drill Time 2) Identify the fractions of the shaded parts. a) b) c) d) e) Concept 9.2: Fraction of a Collection 3) Find fraction of coloured parts. a) b) c) d) e) 4) Find 1 and 1 of the following collection. 2 4 5) Word Problems a) A circular disc is divided into 12 equal parts. Venu shaded 1 of the disc 4 pink and 1 of the disc green. How many parts of the disc are shaded? 3 How many parts are not shaded? are unruled and 1 of them are b) John has 24 notebooks. 1 of them 6 2 four-ruled. How many books are (a) unruled and (b) four-ruled? 132

A Note to Parent Fractions are present all around us. The easiest way to make a child relate to fractions is through food items. Cut fruits such as apples and oranges in different equal parts and use it to help your child understand fractions. Fractions 133

Chapter Money 10 I Will Learn About • converting rupees to paise and vice-versa. • adding and subtracting money. • multiplying and dividing money. • making rate charts and bills. Concept 10.1: Convert Rupees to Paise I Think Farida has ` 38 in her piggy bank. She wants to know how many paise she has. Do you know? 10.1 I Recall We have learnt to identify different coins and currency notes. We have also learnt that 100 paise make a rupee. Let us learn more about money. 1 rupee = 100 paise 100 p = 1 rupee Let us revise the concept about money. a) Identify the value of the given coin.  [ ] (A) ` 1 (B) ` 2 (C) ` 5 (D) ` 10 134

b) The ` 500 note among the following is: [] (A) (B) (C) (D) [] c) The combination that has the greatest value is: (A) (B) (C) (D) 10.1 I Remember and Understand Let us understand the conversion of rupees to paise through an activity. Activity: The students must use their play money (having all play notes and coins). As the teacher writes the rupees on the board, each student picks the exact number of paise in it. There can be many combinations for the same amount of rupees. For example, 1 rupee is 100 paise. So, the students may take two 50 paise coins. Money 135

Let us understand the conversion through some examples. Example 1: Convert the given rupees into paise: a) ` 2 b) ` 5 c) ` 9 Solution: We know that 1 rupee = 100 paise a) ` 2 = 2 × 100 paise = 200 paise b) ` 5 = 5 × 100 paise = 500 paise Converting paise c) ` 9 = 9 × 100 paise = 900 paise into rupees is the Similarly, we can convert paise into rupees. reverse process of Example 2: Convert 360 paise to rupees. converting rupees Solution: We can convert paise to rupees as: into paise. Steps Solved Solve this 380 paise Step 1: Write the given 360 paise paise as hundreds of paise. = 300 paise + 60 paise Step 2: Rearrange 300 300 paise paise as a product of 100 = (3 × 100) paise + 60 paise paise. ` 3 + 60 paise Step 3: Write in rupees. = 3 rupees 60 paise Train My Brain Convert as given. a) 550 paise to rupees b) 25 rupees to paise c) 110 paise to rupees 10.1 I Apply Let us see some real-life examples involving the conversion of rupees into paise and paise to rupees. Example 3: Anil has ` 10 with him. How many paise does he have? Solution: 1 rupee = 100 paise 136 12/22/2017 4:16:48 PM NR_BGM_182110020_Passport-G3-Textbook-Maths-FY_Corrected page.pdf 5

So, 10 rupees = 10 × 100 paise = 1000 paise Therefore, Anil has 1000 paise with him. Example 4: Raj has 670 paise. How many rupees does he have? Solution: Amount with Raj = 670 paise = 600 paise + 70 paise = (6 × 100) paise + 70 paise = ` 6 + 70 paise = 6 rupees 70 paise Therefore, Raj has 6 rupees 70 paise. 10.1 I Explore (H.O.T.S.) Observe these examples where conversion of rupees to paise and that of paise to rupees are mostly useful. Example 5: Vani has ` 4, Gita has ` 5 and Ravi has 470 paise. Who has the least amount of money? Solution: Amount Vani has = ` 4 Amount Gita has = ` 5 Amount Ravi has = 470 paise To compare money, all the amounts must be in the same unit. So, let us first convert the amounts from rupees to paise. ` 4 = (4 × 100) = 400 paise ` 5 = (5 × 100) = 500 paise Now, arranging the money in ascending order, we get 400 < 470 < 500. Therefore, Vani has the least amount of money. Example 6: Ram has 1 rupees 10 paise, Shyam has 1 rupees 40 paise and Rishi has 1 rupees 20 paise. Arrange the amount in ascending order. Who has the most money? Solution: Amount Ram has = 1 rupees 10 paise Amount Shyam has = 1 rupees 40 paise Money 137

Amount Rishi has = 1 rupees 20 paise To compare the money, all of them must be in the same unit. So, let us convert the amounts from rupees to paise. 1 rupees 10 paise = (1 × 100) + 10 = 110 paise 1 rupees 40 paise = (1 × 100) + 40 = 140 paise 1 rupees 20 paise = (1 × 100) + 20 = 120 paise Arranging the amounts in ascending order we get, 110 < 120 < 140. Therefore, Shyam has more money than Ram and Rishi. Concept 10.2: Add and Subtract Money with Conversion I Think Farida’s father bought a toy car for ` 56 and a toy bus for ` 43. How much did he spend altogether? How much change does he get if he gives ` 100 to the shopkeeper? 10.2 I Recall Recall that two or more numbers are added by writing them one below the other. This method of addition is called the column method. We know that rupees and paise are separated using a dot or a point. In the column method, we write money in such a way that the dots or points are placed exactly one below the other. The rupees are placed under rupees and the paise under paise. Let us recall a few concepts about money through these questions. a) 50 paise + 50 paise = ________________ b) ` 50 – ` 10 = _______________ c) ` 20 + ` 5 + 50 paise = ______________ d) ` 20 + ` 10 = _______________ e) ` 50 – ` 20 = _______________ 138

10.2 I Remember and Understand While adding and subtracting money, we write numbers one below Paise is always the other and add or subtract as needed. written in two Let us understand this through some examples. digits after the Example 7: Add: ` 14.65 and ` 23.80 point. Solution: We can add two amounts as: Steps Solved Solve these `p Step 1: Write the given numbers `p with the points exactly one below 1 4. 6 5 4 1. 5 0 the other, as shown. + 2 3. 8 0 + 4 5. 7 5 Step 2: First add the paise. `p `p Regroup the sum if needed. Write 1 the sum under paise. Place the 1 4. 6 5 3 8. 4 5 dot just below the dot. + 2 3. 8 0 + 3 5. 6 0 Step 3: Add the rupees. Add . 45 `p the carry forward (if any) from the previous step. Write the sum `p 2 3. 6 5 under rupees. 1 + 1 4. 5 2 1 4. 6 5 + 2 3. 8 0 3 8. 4 5 Step 4: Write the sum of the given ` 14.65 + ` 23. 80 amounts. = ` 38.45 Example 8: Write in columns and subtract ` 56.50 from ` 73.50. Solution: We can subtract the amounts as: Money 139

Steps Solved Solve these Step 1: Write the given numbers with the ` p `p dots exactly one below the other, as 7 3. 50 8 0. 7 5 shown. − 5 6. 50 − 4 1. 5 0 Step 2: First subtract the paise. Regroup `p `p if needed. Write the difference under 7 3. 5 0 6 0. 7 5 paise. Place the dot just below the dot. − 5 6. 5 0 − 3 2. 5 0 Step 3: Subtract the rupees. Write the difference under rupees. 00 Step 4: Write the difference of the given `p amounts. 6 13 7 3. 5 0 − 5 6. 5 0 1 7. 0 0 ` 73. 50 – ` 56. 50 = ` 17.00 Train My Brain Solve the following: b) ` 32.35 + ` 65.65 c) ` 70.75 – ` 62.45 a) ` 28.65 + ` 62.35 10.2 I Apply Look at some real-life examples where we use addition and subtraction of money. Example 9: Arun had ` 45.50 with him. He gave ` 23.50 to Amar. `p How much money is left with Arun? 4 5. 5 0 − 2 3. 5 0 Solution: Amount Arun had = ` 45.50 2 2. 0 0 Amount Arun gave to Amar = ` 23.50 Difference in the amounts = ` 45.50 – ` 23.50 = ` 22 Therefore, Arun has ` 22 left with him. 140

Example 10: Ramu has ` 12.75 with him. His friend has ` 28.50 with him. What is the amount both of them have? Solution: Amount Ramu has = ` 12.75 ` p Amount Ramu’s friend has = ` 28.50 11 1 2. 75 To find the total amount we have to add both the + 2 8. 50 amounts. 4 1. 25 So, the total amount with Ramu and his friend is ` 41.25. 10.2 I Explore (H.O.T.S.) In some situations, we may need to carry out both addition and subtraction to find the answer. In such cases, we need to identify which operation is to be carried out first. Let us see a few examples. Example 11: Add ` 20 and ` 10.50. Subtract the sum from ` 40. Solution: First add ` 20 and ` 10.50. `p `p ` 20 + ` 10.50 = ` 30.50 2 0. 0 0 4 0. 0 0 + 1 0. 5 0 − 3 0. 5 0 Now, let us find the difference 3 0. 5 0 0 9. 5 0 between ` 30.40 and ` 50. Therefore, ` 40 – ` 30.50 = ` 9.50 Example 12: Surya went to a water park with his parents. The ticket for each ride is: Roller coaster: ` 35, River fall: ` 32, Water ride: ` 20 Surya went on two rides. He gave ` 60 and got a change of ` 5. Which two rides did he go on? Solution: Surya gave ` 60. The change he got is ` 5. The money spent for two rides = ` 60 – ` 5 = ` 55 So, we must add and check which two tickets cost ` 55. ` 35 + ` 32 = ` 67 which is not ` 55. ` 32 + ` 20 = ` 52 which is not ` 55. ` 35 + ` 20 = ` 55 Therefore, the two rides that Surya went on are roller coaster and water ride. Money 141

Concept 10.3: Multiply and Divide Money I Think Farida's father gave her ` 150 on three occasions. Farida wants to share the total amount equally with her brother. How should she find the total amount? How much will Farida and her brother get? 10.3 I Recall While multiplying, we begin from ones place and move to the tens and hundreds places. Sometimes, we may need to regroup the products. We begin division from the largest place and move to the ones place of the number. Let us answer these to revise the concepts of multiplication and division. a) 32 × 4 = _____ b) 11 × 6 = _____ c) 20 ÷ 2 = _____ b) 48 ÷ 3 = _____ e) 10 × 6 = _____ f) 24 ÷ 8 = _____ 10.3 I Remember and Understand Multiplication and division of money is similar to that of numbers. To multiply money, first multiply the numbers under paise, In multiplication, start and place the point. Then multiply the number under multiplying from the rupees. To divide money, we divide the numbers under rightmost digit. rupees and place the point in the quotient. Then, divide In division, start dividing the number under paise. from the leftmost digit. Now, let us understand multiplying and dividing money through a few examples. Example 13: Multiply ` 72 by 8. ` 1 Solution: To find the total amount, multiply the number under rupees as 72 actual multiplication of a 2-digit number by a 1-digit number. ×8 576 Therefore, ` 72 × 8 = ` 576 142

Example 14: Divide ` 35 by 7. 5 Solution: Divide the amount just as you would divide a 2-digit number 7)35 by a 1-digit number. So, ` 35 ÷ 7 = ` 5 − 35 Train My Brain 00 Solve the following: a) ` 28 × 5 b) ` 70 ÷ 2 c) ` 44 × 5 10.3 I Apply We apply multiplication and division of money in many real-life situations. Let us see some examples. Example 15: The cost of a dozen bananas is ` 48. ` a) What is the cost of three dozen bananas? 2 b) What is the cost of one banana? 48 Solution: One dozen = 12 ×3 144 a) Cost of one dozen bananas = ` 48 three dozen bananas = ` 48 × 3 = ` 144 4 one dozen (12) bananas = ` 48Train My Brain 12 48 − 48 )Cost of b) of Cost Cost of one banana = ` 48 ÷ 12 = ` 4 00 (Recall that 10 × 4 = 40. Then, 11 × 4 = 44 and 12 × 4 = 48). Example 16: Rahul went to buy a few chocolates. If a chocolate costs ` 20, how much would 4 such chocolates cost? ` Solution: Cost of one chocolate = ` 20 20 Cost of 4 chocolates = ` 20 × 4 = ` 80 ×4 80 10.3 I Explore (H.O.T.S.) In some situations, we have to carry out more than one operation on money. Consider the following examples. Money 143

Example 17: Nidhi buys 4 bunches of flowers each costing ` 54. She buys 6 candy bars for her brothers at the cost of ` 5 each. If she has ` 8 left with her after paying the amount, how much did she have in the beginning? Solution: Cost of a bunch of flowers = ` 54 Cost of 4 bunches = ` 54 × 4 = ` 216 Cost of each candy bar = ` 5 Cost of 6 candy bars = ` 5 × 6 = ` 30 Total cost of the things she bought = ` 216 + ` 30 = ` 246 Amount she is left with = ` 8 Therefore, amount she had in the beginning = ` 246 + ` 8 = ` 254 Example 18: Bhanu bought some items for ` 362. She has some ` 100 notes. How many notes should she give the shopkeeper? Solution: Cost of the items = ` 362 = ` 300 + ` 62 = (` 100 x 3) + ` 62 As ` 362 has to be paid, Bhanu has to give 3 + 1 = 4 notes of ` 100. Concept 10.4: Rate Charts and Bills I Think Farida went to a mall with her parents. She buys a pair of jeans, 2 shirts, a story book and a ball. How much should she pay? She was given a bill for what she has bought. Can you prepare a bill similar to the one given to her? 10.4 I Recall Recall that we make lists of items when we go shopping. The lists could be of provisions, stationery and items like vegetables or fruits. We can compare the list of items and the items we bought. We can compare their rates and add them to get the total amount to be paid. Let us answer these to revise addition and multiplication of money. a) ` 12 × 2 = __________ b) ` 20 × 3 = __________ c) ` 25 × 4 = __________ d) ` 12 + ` 20 = __________ e) ` 30 + ` 40 = __________ f) ` 21 + ` 10 = __________ 144 NR_BGM_182110020_Passport-G3-Textbook-Maths-FY_Corrected page.pdf 6 12/22/2017 4:16:48 PM

10.4 I Remember and Understand Making bills Addition of A bill is a list of items that we have bought from a shop. A bill amounts is similar tells us the cost of each item and the total money to be paid to to the addition of the shopkeeper. numbers with two or more digits. To make a bill of items, we write the rate of the object and the quantity in the bill. We then find the product of the rate and the quantity. We add the products to find the total bill amount. Let us understand how to make bills through a few examples. Example 19: Look at the rates of the items from a stationery shop in the box below. Geometry Set Sharpener ` 5 ` 140 Colour pencils Notebooks ` 140 ` 40 Pencils ` 3 Pens ` 10 Scissors ` 25 Water colours ` 100 Sunil buys a few items as given in the list. Make a bill for the items he bought. Item Pencil Water colour Sharpener Pen Notebook Quantity 2 14 4 2 Solution: Follow the steps to make the bill. Step 1: Write the items and their quantities in the bill. Step 2: Then write the cost per item. Step 3: Find the total cost of each item by multiplying the number of items by their rates. Money 145 NR_BGM_182110020_Passport-G3-Textbook-Maths-FY_Corrected page.pdf 7 12/22/2017 4:16:48 PM

Step 4: Find the total bill amount by adding the amount of each item. S.No Item Bill Rate per item Amount 1 Pencil Quantity ` 3.00 `p 2 6 00 2 Water colour 1 ` 100.00 100 00 3 Sharpener 4 ` 5.00 20 00 4 Pen 4 ` 10.00 40 00 5 Notebook 2 ` 40.00 80 00 Total 246 00 Making rate charts A rate chart is a chart in which the rate of the different items are written. A rate chart makes it easier for us to see and compare the prices of the items. Example 20: Anil and his friends are playing with play money. Anil runs a supermarket. Some items in his supermarket are given below, along with their rates. ` 40/- per kg ` 147/- ` 50/- ` 34/- ` 240/- per kg ` 149.50/- ` 44/- per litre ` 48/- per kg ` 80/- per kg ` 150/- per kg ` 50/- ` 20/- per dozen He makes a rate chart to display the price of each item. How will the rate chart look? 146