51705015_Maple-G4_Textbook Integrated_Term2

Steps Solved Solve these Step 5: Subtract and write the 15 × 5 = 75 )16 3744 difference. Repeat till all the digits of 15 × 6 = 90 the dividend are brought down. 90 = 90 So, 90 is the required number. 156 )15 2340 − 15↓ Dividend = _____ 84 Divisor = ______ Quotient = _____ − 75 Remainder = _____ 90 − 90 00 Quotient = 156 Remainder = 0 Step 6: Check if (Divisor × Quotient) + 15 × 156 + 0 = 2340 Remainder = Dividend is true. If this is 2340 + 0 = 2340 false, the division is incorrect. 2340 = 2340 (True) Let us see some properties of division. Properties of division 1) Dividing a number by 1 gives the same number as the quotient. For example: 15 ÷ 1 = 15; 1257 ÷ 1 = 1257; 1 ÷ 1 = 1; 0 ÷ 1 = 0 2) Dividing a number by itself gives the quotient as 1. For example: 15 ÷ 15 = 1; 1257 ÷ 1257 = 1; 1 ÷ 1 = 1 3) Division by zero is not possible and is not defined. For example: 10 ÷ 0; 1257 ÷ 0; 1 ÷ 0 are not defined Division 7

Application Division of large numbers can be applied in many real-life situations. Consider these examples. Example 4: 4720 apples are to be packed in 8 baskets. If each basket has the ) 590 same number of apples, how many apples are packed in each Solution: basket? 8 4720 Total number of apples = 4720 − 40↓ 072 Number of baskets = 8 − 072 The number of apples packed in each basket = 4720 ÷ 8 0000 Example 5: Therefore, 590 apples are packed in each basket. − 0000 Solution: 2825 notebooks were distributed equally among 25 students. How many 0b0o0o0ks did each student get? ) 113 Number of notebooks = 2825 Example 6: 25 2 8 2 5 Solution: Number of students = 25 −25↓ Number of books each student got = 2825 ÷ 25 032 Therefore, each student got 113 notebooks. −025 0 075 8308 people watched a hockey match. If 10 people watched − 0075 from each cabin in the stadium, how many cabins were full? How 000 many people were there in the remaining cabin? 830 Number of people = 8308 Number of people in each cabin = 10 )10 8 3 0 8 Number of cabins = 8308 ÷ 10 = 830 Number of people in the remaining cabin = 8 (Remainder in the −80↓ 30 − 30 008 division of 8308 by 10). Therefore, 8 people were remaining in the cabin. Higher Order Thinking Skills (H.O.T.S.) Let us see some more examples of situations where we use division of large numbers. 8

Example 7: A school has 530 students in the primary section, 786 students in the middle school and 658 students in the high school section. If equal number of students Solution: are seated in 6 halls, how many students are seated in each hall? Number of students in the primary section = 530 329 Number of students in the middle school section = 786 Number of students in the high school section = 658 )6 1974 Thus, the total number of students in the school = 530 + 786 + 658 = 1974 −18 Example 8: 1974 children are equally seated in 6 halls. 017 Solution: − 012 54 − 54 00 Therefore, the number of students in each hall = 1974 ÷ 6 = 329 students. Divide the largest 4-digit number by the largest 2-digit number. Write the quotient and the remainder. 10 1 The largest 4-digit number is 9999. The largest 2-digit number is 99. )99 9 9 9 9 The required division is 9999 ÷ 99 −99↓ 009 − 000 99 Quotient = 101; Remainder = 0 − 99 00 Drill Time Concept 7.1: Divide Large Numbers 1) Divide a 4-digit number by a 1-digit number. a) 1347 ÷ 6 b) 4367 ÷ 5 c) 3865 ÷ 4 d) 5550 ÷ 5 2) Divide a 4-digit and 3-digit numbers by a 2-digit number. a) 3195 ÷ 10 b) 612 ÷ 10 c) 2676 ÷ 12 d) 267 ÷ 11 3) Word Problems a) A n amount of ` 1809 is distributed equally among 9 women. How much money did each of them get? b) 10 boxes have 1560 pencils. How many pencils are there in a box? c) A school has 1254 students, who are equally grouped into 14 groups. How many students are there in each group? How many students are remaining? Division 9

Chapter Fractions - I 8 Let Us Learn About • e quivalent fractions. • problems related to equivalent fractions. • like and unlike fractions. • adding and subtracting like fractions. Concept 8.1: Equivalent Fractions Think Jasleen cuts 3 apples into 18 equal pieces. Ravi cuts an apple into 6 equal pieces. Did both of them cut the apples into equal pieces? Recall In Class 3, we have learnt that a fraction is a part of a whole. A whole can be a region or a collection. When a whole is divided into two equal parts, each part is called ‘a half’. 11 22 ‘Half’ means 1 out of 2 equal parts. We write ‘half’ as 1 . 2 10

Two halves make a whole. Numerator Numbers of the form Denominator are called fractions. The total number of equal parts into which a whole is divided is called the denominator. The number of such equal parts taken is called the numerator. Similarly, each of the three equal parts of a whole is called a third. We write one-third as 1 and, two-thirds as 2 . 33 3 Three-thirds or 3 make a whole. Each of four equal parts of a whole is called a fourth or a quarter written as 1 . 4 Two such equal parts are called two-fourths, and three equal parts are called three-fourths, written as 2 and 3 respectively. Four quarters make a whole. 44 2 halves, 3 thirds, 4 fourths, 5 fifths, …, 10 tenths make a whole. So, we write a whole as 2 , 3 , 4 , 5 ,...,10 and so on. 2 3 4 5 10 & Remembering and Understanding Fractions that denote the same part of a whole are called equivalent fractions. Let us now understand what equivalent fractions are. Suppose there is 1 bar of chocolate with Ram and Raj each as shown. chocolate with Ram chocolate with Raj Ram eats 1 of the chocolate. 5 Then the piece of chocolate he gets is Raj eats 2 of the chocolate. 10 Then the piece of chocolate he gets is Fractions - I 11

We see that both the pieces of chocolates are of the same size. So, we say that the fractions 1 and 2 are equivalent. We write them as 1 = 2 . 5 10 5 10 Example 1: Shade the regions to show equivalent fractions. a) [ 1 and 2 ] 36 b) 1 2] [ and 48 Solution: a) 1 3 2 6 b) 1 4 2 8 Example 2: Find the figures that represent equivalent fractions. Also, mention the fractions. a) b) c) d) 12

Solution: The fraction represented by the shaded part of figure a) is 1 . 2 The shaded part of figure b) represents 2 . The shaded part of figure d) 4 represents 1 . 2 So, the shaded parts of figures a), b) and d) represent equivalent fractions. Application Let us see a few examples of equivalent fractions. Example 3: Shade the second figure to give a fraction equivalent to the first. Solution: 2 The fraction denoted in the first figure is . This is half of the given figure. 4 So, to denote a fraction equivalent to the first, shade half of the the second figure as shown. Example 4: Venu paints four-sixths of a cardboard and Raj paints two-thirds of a similar sized cardboard. Who has painted a larger area? Solution: Fraction of the cardboard painted by Venu and Raj are as follows: Venu Raj It is clear that, both Venu and Raj have painted an equal area on each of the cardboards. Fractions - I 13

Higher Order Thinking Skills (H.O.T.S.) We have learnt how to find equivalent fractions using pictures. Let us see a few more examples involving equivalent fractions. Example 5: Find two fractions equivalent to the given fractions. a) 2 b) 33 11 66 Solution: To find fractions equivalent to the given fractions, we either multiply or divide both the numerator and the denominator by the same number. a) 2 11 W e see that 2 and 11 do not have any common factors. So, we cannot divide them to get an equivalent fraction of 2 . 11 T herefore, we multiply both the numerator and the denominator by the same number, say 5. 2 = 2 × 5 = 10 11 11× 5 55 Thus, 10 is a fraction equivalent to 2 . 55 11 2 L ikewise, we can multiply by any number of our choice to get more 11 fractions equivalent to it. b) 33 66 W e see that 33 and 66 have common factors 3, 11 and 33. So, dividing both the numerator and the denominator by 3, 11 or 33, we get fractions equivalent to 33 . 66 33 ÷ 3 = 11 , 33 ÷ 11 = 3 or 33 ÷ 33 = 1 66 ÷ 3 22 66 ÷11 6 66 ÷ 33 2 Therefore, 11 , 3 and 1 are the fractions equivalent to 33 . 2 66 22 6 14

Example 6: Draw four similar rectangles. Divide them into 2, 4, 6 and 8 equal parts. Then Solution: colour 1 2 3 and 5 parts of the rectangles respectively. Compare these , , 246 8 coloured parts and write the fractions using >, = or <. 1 2 2 4 3 6 5 8 From the coloured parts of these rectangles, we can see that all of them except 5 are of the same size. So, the fractions, 1 , 2 and 3 are 8 24 6 equivalent. Therefore, 1 = 2 = 3 . 246 Fractions - I 15

Concept 8.2: Identify and Compare Like Fractions Think Jasleen has a circular disc coloured in blue, green, red and white as shown. She wants to know if there is any special name for the fractions shown by different colours on the circular disc. Do you know any special name for such fractions? Recall In Class 3, we have learnt to represent shaded parts of a whole as fractions. Recall the same through the following example. Jasleen’s colourful circular disc is given here. Find the fractions represented by the following colours: a) Red b) Green c) Blue d) White & Remembering and Understanding 12 3 Fractions such as , and , that have the same denominator are called like fractions. 88 8 Fractions such as 1 , 2 and 3 that have different denominators are called unlike fractions. 84 7 Fractions with numerator ‘1’ are called unit fraction. such as 1 , 1 , 1 and so on. 234 To understand these fractions, consider the following examples. Example 7: Identify like and unlike fractions from the following fractions. 3 ,3 , 1, 5 , 6, 1, 4 7 5 7 7 7 4 11 16

Solution: 3 , 1 , 5 and 6 have the same denominator. So, they are like fractions. 777 7 3 , 1 and 4 have different denominators. So, they are unlike fractions. Example 8: 54 a) 11 Find the fraction of the parts not shaded in these figures. b) c) d) Which of them represent like fractions? Solution: a) Number of parts not shaded = 1 Total number of equal parts = 2 Fraction = Number of parts not shaded = 1 Total number of equal parts 2 b) Number of parts not shaded = 3 Total number of equal parts = 4 Fraction = Number of parts not shaded = 3 Total number of equal parts 4 c) Number of parts not shaded = 3 Total number of equal parts = 5 Fraction = Number of parts not shaded = 3 Total number of equal parts 5 d) Number of parts not shaded = 3 Total number of equal parts = 6 Fraction = Number of parts not shaded = 3 = 1 Total number of equal parts 6 2 a) and d) have denominator equal to 2. They represent like fractions. Fractions - I 17

Application We can compare like fractions and tell which is greater or less than the others. To compare like fractions, we compare their numerators. The fraction with the greater numerator is greater. Let us understand this better through some examples. Example 9: Jai ate 1 of the apple and Vijay ate 2 of the apple. Who ate more? Solution: 33 1 Fraction of apple Jai ate = 3 Fraction of apple Vijay ate = 2 3 Since, 2 > 1, 2 > 1 33 Therefore, Vijay ate more. Example 10: The circular disc shown here is divided into equal parts. The parts are painted in different colours. Write the fraction of each colour on the disc. Compare the fractions and tell which colour is used more and which the least. Solution: Total number of equal parts on the disc is 16. Number of parts painted yellow is 3. Fraction = 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 = 6 Total number of equal parts 16 The fraction of the disc that is painted red = Number of parts painted red = 4 Total number of equal parts 16 The fraction of the disc that is painted blue = Number of parts painted blue = 3 Total number of equal parts 16 18

Comparing the numerators of these fractions, we get 3 < 4 < 6. Since, 6 is 16 the greatest and 3 is the least, white is used the most and blue and yellow 16 are the least. Higher Order Thinking Skills (H.O.T.S.) Let us see a few more examples using comparison of like fractions. Example 11: Colour each figure to represent the given fraction and compare them. 3 2 5 5 Solution: Clearly, the part of the figure represented by 3 is greater than that 5 represented by 2 . Hence, 3 is greater than 2 . 55 5 Let us try to arrange some like fractions in ascending and descending orders. Example 12: Arrange 1 , 6 , 2 , 5 and 4 in the ascending and descending orders. 777 7 7 Solution: Comparing the numerators of the given likeTrfraacintionMs, y Brain we have 1 < 2 < 4 < 5 < 6. 12 4 56 So, < < < < . 77777 Therefore, the required ascending order is 1 , 2 , 4 , 5 , 6 . 77777 We know that, the descending order is just the reverse of the ascending order. So, the required descending order is 6 , 5 , 4 , 2 , 1 . 77 7 7 7 Fractions - I 19

Concept 8.3: Add and Subtract Like Fractions Think Jasleen has a cardboard piece, equal parts of which are coloured in different colours. Some of the equal parts are not coloured. She wants to find the part of the cardboard that has been coloured and left uncoloured. How do you think Jasleen can find that? Recall Recall that like fractions have the same denominators. To compare them, we compare their numerators. Let us answer the following to recall the concept of like fractions. Compare the following using >, < and =. a) 2 ____ 1 b) 4 ____ 8 c) 3 ____ 5 d) 7 ____ 3 e) 1 ____ 4 33 10 10 77 88 55 & Remembering and Understanding While adding or subtracting like fractions, add or subtract only their numerators. Write the sum or difference on the same denominator. Let us understand addition and subtraction of like fractions through some examples. Example 13: In the given figures, find the fractions represented by the shaded parts using addition. Then find the fractions represented by the unshaded parts using subtraction. a) b) c) Solution: We can find the fractions represented by the shaded and the unshaded parts with the following steps. 20

Solved Solve these Steps Step 1: Count the total Total number of equal Total number of Total number of number of equal parts. equal parts = ____ parts = 6 equal parts = ___ Step 2: Count the a) N umber of parts a) Number of parts a) Number of parts number of parts of each coloured pink = 1 coloured yellow coloured violet = colour. = ______ _______ b) Number of parts coloured blue = 2 b) Number of parts b) N umber of parts coloured violet = coloured brown _______ = ______ Step 3: Write the fraction Pink: 1 , Blue: 2 Yellow: ________ Violet: ________ representing the number 66 Violet: ________ Brown: ________ of parts of each colour. Step 4: To add the like The fraction that The fraction that The fraction that fractions in step 3, add represents the their numerators and represents the shaded represents the shaded part of the write the sum on the given figure is same denominator. part of the given shaded part of the ____ + ____=____. figure is given figure is 1 + 2 = 1+ 2 = 3 . ____ + ____=____. 66 6 6 Step 5: Write the whole Like fraction Like fraction Like fraction representing the representing the as a like fraction of the representing the whole = 6 . whole = _______. whole = _______. sum in step 4. Then, to 6 So, the fraction So, the subtract the like fractions, that represents the subtract their numerators. So, the fraction unshaded part of fraction that Write the difference on that represents the the given figure is represents the the same denominator. unshaded part of the unshaded part of given figure is ____ − ____=____. the given figure is 6−3 =6−3 = 3. ____ − ____=_____. 66 6 6 Fractions - I 21

Example 14: Add: a) 3 + 1 45 23 57 88 b) + c) + 13 13 100 100 c) 48 – 26 3 1 3 +1 4 Solution: a) + = = 125 125 88 8 8 b) 4 + 5 = 4 + 5 = 9 13 13 13 13 c) 23 + 57 = 23 + 57 = 80 100 100 100 100 Example 15: Subtract: a) 8 – 4 b) 33 – 25 99 37 37 Solution: a) 8 – 4 = 4 99 9 b) 33 – 25 = 33 − 25 = 8 37 37 37 37 48 26 48 − 26 22 c) – = = 125 125 125 125 Application In some real-life situations, we use addition or subtraction of like fractions. Let us see a few examples. Example 16: The figure shows some parts of a ribbon coloured in blue and yellow. Find the total part of the ribbon coloured blue and yellow. What part of the ribbon is not coloured? Solution: Total number of parts of the ribbon = 9 Part of the ribbon coloured blue = 2 9 Part of the ribbon coloured yellow = 3 22 9 Total part of the ribbon coloured = 2 + 3 = 2 + 3 = 5 99 9 9 Part of the ribbon that is not coloured is 9 − 5 = 9 − 5 = 4 99 9 9

(Note: This is the same as writing the fraction of the ribbon not coloured from the figure. 4 parts of the 9 parts of the ribbon are not coloured) Example 17: Suman ate a quarter of a chocolate bar on one day and another quarter of Solution: the chocolate on the next day. How much chocolate did Suman eat in all? How much chocolate is remaining? Part of the chocolate eaten by Suman on the first day = 1 4 Part of the chocolate eaten by him on the next day = 1 4 Total chocolate eaten by Suman on both the days = 1 + 1 = 1+1 = 2 44 4 4 He ate 2 chocolate in all. Remaining chocolate = 4 − 2 = 4 − 2 = 2 4 44 4 4 Example 18: Manav painted two-tenths of a strip of chart in one hour and four-tenths of it in the next hour. What part of the strip did he paint in two hours? How much is left unpainted? Solution: Part of the strip of chart painted by Manav in one hour = 2 10 1st hour: Part of the strip painted by him in the next hour = 4 10 2nd hour: Part of the strip painted by him in two hours = 2 + 4 = 2 +4 = 6 10 10 10 10 Part of the strip of chart left without painting = 10 – 6 = 4 10 10 10 [From the figure, the total part of the strip painted = 6 and the part of the 10 strip not painted = 4 .] 10 Fractions - I 23

Higher Order Thinking Skills (H.O.T.S.) Let us see some more examples of addition and subtraction of like fractions. Example 19: Veena ate 5 of a pizza in the morning and 1 in the evening. What part of 88 Solution: the pizza is remaining? Part of the pizza eaten by Veena in the morning = 5 8 Part of the pizza eaten by Veena in the evening = 1 8 To find the remaining part of pizza, add the parts eaten and subtract the sum from the whole. Total part of the pizza eaten = 5 + 1 = 5 +1 = 6 88 8 8 6 86 2 Part of the pizza remaining = 1 – = – = 8 88 8 Drill Time Concept 8.1: Equivalent Fractions 1) Shade the regions to show equivalent fractions. a) 1 and 2  2 4  24

b) 1 and 2   5 10  2) Write four equivalent fractions for each of the following fractions. a) 1 b) 4 c) 3 d) 4 2 7 10 11 Concept 8.2: Identify and Compare Like Fractions 3) Identify like and unlike fractions from the following. a) 2 ,2 , 1,5 ,2 ,7 ,6 ,2 b) 7 , 4 , 4 , 2 , 4 , 2 , 3 , 69 83286889 9 5 9 9 7 4 4 c) 6 , 5 , 5 , 4 , 8 , 7 , 9 , 2 d) 3 , 4 , 1 , 3 , 1 , 4 14 14 17 17 17 14 17 14 5 5 5 7 9 11 4) Arrange the following fractions in the ascending order. a) 3 , 1 , 7 , 4 b) 3 , 2 , 9 , 5 11 11 11 11 13 13 13 13 c) 1 , 3 , 4 , 2 d) 1 , 8 , 7 , 9 7777 14 14 14 14 5) Arrange the following fractions in descending order. a) 1 , 8 , 7 , 4 b) 3 , 6 ,10 , 8 9999 17 17 17 17 c) 7 , 9 , 2 ,13 d) 1 , 7 , 8 , 3 21 21 21 21 20 20 20 20 Concept 8.3: Add and Subtract Like Fractions 6) Add: a) 2 + 5 b) 3 + 16 c) 9 + 4 d) 8 + 4 e) 1 + 2 77 11 11 55 13 13 17 17 Fractions - I 25

7) Subtract: a) 15 − 7 b) 9 − 5 c) 11 − 3 d) 7 − 4 e) 13 − 12 66 88 40 40 45 45 30 30 8) Word problems a) L eena paints three-sixths of a cardboard and Rani paints half of similar cardboard. Who has painted a smaller area? b) Colour each figure to represent the given fraction and compare them. 57 88 c) Ajit ate 1 of a cake in the morning and 2 of it in the evening. What part of the cake 55 is remaining? 26

Chapter Fractions - II 9 Let Us Learn About • finding fractions of a number. • p roblems based on finding fractions. • p roper, improper and mixed fractions. • c onverting improper to mixed fractions and vice versa. Concept 9.1: Fraction of a Number Think Jasleen’s father told her that he spends two-thirds of his salary per month and saves the rest. Jasleen calculated the amount her father saves from his salary of ` 25,000 per month. How do you think Jasleen could calculate her father’s savings per month? Recall In Class 3, we have learnt how to find the fraction of a collection. To find the fraction of a collection, we find the number of each type of object in the total collection. Let us answer these to recall the concept. a) A half of a dozen bananas = _______________ bananas b) A quarter of 16 books = _______________ books c) A third of 9 balloons = _______________ balloons 27

d) A half of 20 apples = _______________ apples e) A quarter of 8 pencils = _______________ pencils & Remembering and Understanding To find the fraction of a number, we multiply the number by the fraction. Let us now learn to find the fraction of a number. Suppose there are 20 shells in a bowl. Vani wants to take 1 of them. So, she divides the shells 5 into 5 (the number in the denominator) equal groups and takes 1 group (the number in the numerator). This gives 5 groups with 4 shells in each group. So, 1 of 20 is 4. 5 Vani’s sister Rani wants to take 3 of the shells. So, she divides 10 the shells into 10 (the number in the denominator) equal groups, and takes 3 groups (the number in the numerator) of them. This gives 2 shells in each group. Hence, Rani takes 6 shells. Therefore, 3 of 20 is 6. 10 We write 1 of 20 as 1 × 20 = 20 = 4. 5 55 Similarly, 3 of 20 = 3 × 20 = 6. 10 10 Example 1: Find the following: 1 a) 2 of a metre (in cm) b) 10 of a kilogram (in g) 5 Solution: a) 2 of a metre = 2 × 1 m = 2 × 100 cm = 2 × 100 cm = 200 cm = 40 cm 5 55 55 b)  1 of a kilogram = 1 × 1 kg = 1 × 1000 g = 1000 g = 100 g 10 10 10 10 Example 2: Find the following: a) 2 of an hour (in minutes) b) 1 of a day (in hours) Solution: 3 4 a) 2 2 ×1h= 2 × 60 min = 2 × 60 = 120 = 40 min of an hour = 3 3 3 33 b) 1 of a day = 1 × 1 day = 1 × 24 h = 1 × 24 h = 24 hrs = 6 h 4 44 4 28

Application Let us now see some real-life examples in which we find the fraction of a number. Example 3: Ravi has ` 120 with him. He gave two-thirds of it to his sister. How much money is left with Ravi? Solution: Amount Ravi has = ` 120 Amount Ravi gave his sister = 2 of ` 120 = 2 × ` 120 = 2 × ` 40 = ` 80 33 Difference in the amounts = ` 120 – ` 80 = ` 40 Therefore, ` 40 is left with Ravi. Example 4: Reema completed one-tenth of a distance of 2 kilometres. How much distance (in metres) has she covered? Solution: The total distance to be covered by Reema = 2 km We know that 1 km = 1000 m. So, 2 km = 2000 m. The distance covered by Reema = 1 of 2 kilometres = 1 x 2000 m = 200 m Example 5: 10 10 Therefore, Reema has covered 200 metres of the distance. A school auditorium has 2500 chairs. On the annual day, 4 of the auditorium 5 was occupied. How many chairs were occupied? Solution: Total number of chairs in the auditorium = 2500 4 Fraction of chairs occupied = 5 4 4×2500 10000 Number of chairs occupied = × 2500 = = 5 55 Therefore, 2000 chairs were occupied in the auditorium. Higher Order Thinking Skills (H.O.T.S.) Let us now see some more examples where we have to find the fraction of a number. Example 6: Venu paints three-sixths of a cardboard and Raj paints a third of it. If the cardboard has an area of 144 sq.cm, what area of the cardboard did each of them paint? Fractions - II 29

Solution: Fraction of the cardboard painted by Venu = 3 6 Fraction of the cardboard painted by Raj = 1 3 Area of the cardboard = 144 sq. cm 3 Example 7: Area of the cardboard painted by Venu = × 144 sq.cm 6 Solution: =3 × 144 sq.cm = 432 sq.cm = 72 sq.cm 66 Area of the cardboard painted by Raj = 1 × 144 sq.cm 3 =1× 144 sq.cm = 144 sq.cm = 48 sq.cm 33 Therefore, Venu painted 72 sq.cm of the cardboard and Raj painted 48 sq.cm of the cardboard. Find if 2 of 154 and 4 of 49 are equal to each other or one of them is greater 11 7 than the other. To find if the fractions of the numbers are equal, we first find their values and compare them. 2 of 154 = 2 × 154 = 2 × 154 = 308 = 28 11 11 11 11 4 of 49 = 4 × 49 = 4 × 49 = 196 = 28 77 77 Therefore, 2 of 154 = 4 of 49. 11 7 Concept 9.2: Conversions of Fractions Think Jasleen knew about fractions in which the numerators were less than their denominators. She wondered if there could be some fractions in which the numerators are greater than their denominators. Do you know of such fractions? 30

Recall In the previous chapter, we have learnt about addition and subtraction of like fractions. Recall that the sum of two like fractions is a like fraction. Let us answer these to recall the concept. a) 2 + 1 = ______ 41 5 5 b) 7 + 7 = ______ c) 1 + 5 = ______ d) 3 + 1 = _______ 11 11 22 e) 1 + 3 = ______ f) 2 + 1 = _______ 88 99 & Remembering and Understanding Consider 1 + 5 = 6 . Here, the sum of two like fractions is a like fraction with its numerator less 888 than its denominator. Such fractions are called proper fractions. Sometimes ,it is possible that we get the sum with its numerator greater than the denominator. For example, 7 + 5 = 12 . Here, the sum of two like fractions is a like fraction with its 88 8 numerator greater than its denominator. Such fractions are called improper fractions. Note: In some cases, the sum of the numerators of the like fractions may be equal to the denominator. Then, the fraction is said to be an improper fraction. For example, 3 + 4 = 7 , 3 + 5 = 8 and so on. 7 7 78 8 8 Fractions such as 7 , 8 and so on can also be written as a whole, that is 1. 78 12 8 + 4 . This has a whole We can write 8 as the sum of like fractions as 88 8 and a proper  8  = 14 . Such fractions are called mixed fractions. fraction  4  . That is, 12 =1+ 4 8  8  8 8 A mixed fraction is also called a mixed number. For example, in the mixed fraction 12 3 , 12 is the whole and 3 is the proper fraction. 88 Fractions - II 31

In short, we can say that, Proper fractions – Fractions having the numerators less than the denominators. Improper fractions – Fractions having the numerators greater than the denominators. Mixed fractions – Fractions having whole numbers and proper fractions. Example 8: List out proper fractions, improper fractions and mixed fractions from the following: Solution: 13 ,15 7 , 11 , 37 , 9 , 65 13 , 143 , 75 3 ,107 27 , 72 , 68 2 , 29 , 50 23 , 69 , 53 18 9 34 6 14 17 98 4 49 59 5 32 35 32 30 From the given fractions, Proper fractions: 13 , 11 , 9 , 29 18 34 14 32 Improper fractions: 37 , 143 , 72 , 69 , 53 6 98 59 32 30 Mixed fractions: 15 7 , 65 13 , 75 3 , 107 27 , 68 2 , 50 23 9 17 4 49 5 35 We usually write fractions as proper or mixed fractions. So, we need to learn to convert improper fractions to mixed fractions and mixed fractions to improper fractions. Conversion of improper fractions to mixed fractions Let us understand the conversion of improper fractions to mixed fractions by solving a few examples. Example 9: Convert 37 to its mixed fraction form. Solution: 6 To convert improper fractions into mixed fractions, follow these steps. Solved Solve these Steps 37 143 72 69 53 6 98 59 32 30 Step 1: Divide the numerator 6 by the denominator. )6 37 − 36 1 32

Solved Solve these 37 Steps 6 143 72 69 53 30 98 59 32 Step 2: Write the quotient as The mixed the whole. The remainder is fraction form of the numerator of the proper fraction and the divisor is its 37 is 6 1 . denominator. This gives the 66 required mixed fraction. Conversion of mixed fractions to improper fractions Let us understand the conversion of mixed fractions into improper fractions by solving a few examples. Example 10: Convert 15 7 into its improper fraction. 9 Solution: To convert mixed fractions into improper fractions, follow these steps. Solved Solve these Steps 15 7 65 13 75 3 107 27 9 17 4 49 Step 1: Multiply the whole by the 15 × 9 = 135 denominator. Step 2: Add the numerator of the proper 135 + 7 = 142 fraction to the product in Step 1. Step 3: Write the sum as the denominator The improper of the proper fraction. fraction form of This given the required improper fraction. 15 7 is 142 9 9. Application Let us now see a few real-life examples involving conversions of fractions. Example 11: Rohan wants to arrange 60 books in his shelf. If only 13 books can be put in a rack, how many racks will be filled by the books? Give your answer as a mixed fraction and as an improper fraction. Fractions - II 33

Solution: Number of books Rohan wants to arrange = 60 Number of books that can be arranged on each rack = 13 Example 12: Number of racks that are filled = 60 ÷ 13 = 4 8 13 Solution: Improper fraction equivalent to 4 8 = 60 13 13 On a science fair day, a group of students prepared 12 1 litres of orange 2 juice. Express the number of litres of orange juice as an improper fraction. Number of litres of orange juice made = 12 1 2 Improper fraction equivalent to 12 1 = 12 × 2 +1 = 25 2 2 2 Higher Order Thinking Skills (H.O.T.S.) Conversion of fractions is done when we need to add and subtract fractions. In the previous chapter, we have already learnt addition and subtraction of like (proper) fractions. Let us see a few examples that involve addition and subtraction of improper and mixed fractions. Example 13: Add: a) 42 + 35 b) 50 23 + 16 Solution: 25 25 35 35 a) 42 + 35 25 25 T o add the given like improper fractions, we add their numerators and write the sum on the same denominator. Therefore, 42 + 35 = 42 + 35 = 77 25 25 25 25 W e usually write fractions as proper or mixed fractions. So, we convert the sum into a mixed fraction by dividing the numerator by the denominator. 77 = 3 2 (77 ÷ 25 gives the quotient as 3 and remainder as 2.) 25 25 Therefore, the sum of the given fractions is 3 2 . 25 34

b) 50 23 + 16 35 35 T o add the given fractions, we have to convert the mixed fraction into improper fraction. So, 50 23 = (50×35)+23 =11777530 + 23 =1773 35 35 35 35 35 T hen add their numerators and write the sum as the numerator. Therefore, 50 23 + 16 = 1773 + 16 = 1773 + 16 = 1789 . 35 35 35 35 35 35 Convert the improper fraction into a mixed fraction. 1789 = 51 4 (1789 ÷ 35 gives the quotient as 51 and the remainder as 4.) 35 35 Therefore, the sum of the given fractions is 51 4 . 35 Example 14: Subtract: a) 342 - 135 b) 34 17 - 37 Solution: 25 25 42 42 a) 342 - 135 25 25 To subtract the given improper fractions, we subtract their numerators. We then write the difference as the numerator. Therefore, 342 - 135 = 342 −135 = 207 25 25 25 25 A s we usually write fractions as proper or mixed fractions, we convert the difference into a mixed fraction. 207 = 8 7 (207 ÷ 25 the quotient as 8 and the remainder as 7.) 25 25 Therefore, the difference of the given fractions is 8 7 . 25 b) 34 17 - 37 42 42 T o subtract the given fractions, we first convert the mixed fraction into an improper fraction. So, 34 17 = 34 × 42 + 17 = 1445 42 42 42 T hen subtract their numerators and write the difference as the numerator. Fractions - II 35

Therefore, 34 17 − 37 = 1445 − 37 = 1445 − 37 = 1408 42 42 42 42 42 42 Again convert the improper fraction into a mixed fraction. 11440485 = 33 22 (1408 ÷ 42 the quotient as 33 and the remainder as 22.) 4422 42 Therefore, the difference of the given fractions is 33 22 . 42 Drill Time Concept 9.1: Fraction of a Number 1) Find the following: a) 1 of 20 b) 3 of 24 c) 3 of 20 d) 4 of 12 e) 2 of 18 2 4563 Concept 9.2: Conversions of Fractions 2) Convert the following improper fractions to mixed fractions. a) 35 b) 121 c) 93 d) 100 e) 115 4 12 12 26 20 3) Convert the following mixed fractions to improper fractions. a) 15 6 b) 23 2 c) 40 4 d) 125 9 Traei)n40M35 y Brain 8 3 5 10 4) Word Problems a) A t Sudhir’s birthday party, there are 19 sandwiches to be shared equally among 13 children. What part of the sandwiches will each child get? Give your answer as a mixed fraction. b) I bought 2 1 litres of paint but used only 3 litres. How much paint is left with me? 22 Give your answer as an improper fraction. 36





EVS-I (SCIENCE) TERM 2

Contents 4Class 9 Birds������������������������������������������������������������������������������������������������������������������������������� 1 10 Animal Behaviour��������������������������������������������������������������������������������������������������������� 7 Inside the Lab – B�������������������������������������������������������������������������������������������������������������� 12 Activity B1: Soil’s Capacity to Hold Water Activity B2: Simple Water Filter 11 Food Storage�������������������������������������������������������������������������������������������������������������� 14 12 Building Materials������������������������������������������������������������������������������������������������������� 19 13 Types of Cloth������������������������������������������������������������������������������������������������������������� 24

Lesson Birds 9 Let Us Learn About R birds and their body parts. u beaks, claws and sounds of birds. a birds that travel. h birdwatching. Think Aman’s teacher showed him the given pictures. She asked him to identify the bird. Aman quickly gave the correct answer. How did Aman spot the difference between a dog and a bird? Remembering What makes birds look different from other animals? Birds have wings and feathers. They have a pair of wings and a tail covered with feathers. In most kinds of birds, the feathers help them to fly. Feathers are soft hair present all over the body including the wings and tail. They are of different colour, and they form different patterns. 1

peacock parrot pheasant ostrich Some birds cannot fly. For example, a penguin spends most of its life in the sea. It does not use its wings to fly. It uses them to swim. Birds like the ostrich cannot fly. All birds have beaks. They do not have teeth. They penguin have two feet with claws. Claws are long, curved nails present on the feet of birds. Birds have ear holes instead of ears. Understanding Birds’ beaks are very important. They help the birds gather food and sometimes to rip, tear, or crush the food. A beak can act as an extra hand, such as when parrots use their beak for climbing. Birds use their beaks for building nests, and even to tie knots. They are also important for preening (cleaning and combing feathers with beaks), which is making sure all of the bird’s feathers are in their proper place. Birds use their beaks to feed their young ones and also to protect them from their enemies. The shapes of beaks and claws of birds are based on their food habits and the place they live. Food of the birds includes nectar, fruits, plants, seeds, meat and various small insects and worms. Some birds also eat other birds. TYPES OF BEAKS Look at the picture of the duck and the pigeon. Can you spot the difference between the types of beaks? Discuss with your friends. Let us see the different types of beaks and their function. 1) Broad, flat beak: Ducks and swans have broad and flat beaks like a spoon. There are tiny holes on either side of the beaks. 2

When these birds find their food in water, they spoon up the muddy water along with their food. The water flows out from the holes in the beaks leaving the insects, worms and water plants behind. The ducks and swans eat them. 2) Strong, curved beak: Parrots have strong, duck pigeon curved beaks. Such beaks help them to crack open nuts or seeds and scoop out the pulp of fruits with the help of the curve of their beaks. 3) Short, hard, pointed beak: Birds like sparrows have short, hard and parrot pointed beaks. They pick up seeds and worms easily and crush them with their beaks to eat. Pigeons and peacocks also have similar types of beaks. 4) Long, chisel-like beak: Woodpeckers have long, chisel-like beaks to tap the bark of a tree. They make holes in tree-trunks in search of insects. Their long, sticky tongues pull out insects and worms from the holes to eat them. 5) Long, broad, pointed beak: Kingfishers have long, broad and sparrow pointed beaks. The beak is used to pick up fish from the water. 6) Sharp, hooked, strong beak: Eagles and hawks have sharp, hooked and strong beaks to easily tear the flesh of their prey. They eat rats, lizards, snakes, frogs, rabbits and even small birds. 7) Thin, long, pointed beak: The beaks of birds like hummingbirds are thin, long and pointed. They help to suck nectar from flowers. A hummingbird does not sit on a flower when feeding. It hovers above the flower like a helicopter and dips its long beak into the flower. woodpecker kingfisher eagle hummingbird TYPES OF FEET We have seen how birds have different types of beaks based on their food habits. In the same way, birds have different types of feet. Birds use their feet for climbing, protecting, holding food, swimming and so on. Birds 3

Look at the different types of feet. Can you guess the function of different feet? sparrow crane hen woodpecker eagle emu duck Let us see the different types of feet. 1) Three toes in front and one toe at the back: Some birds have feet to hold branches or wires. The sparrow clamps its toes around a branch so that it does not fall off. 2) Long and thin feet: Some birds stay in water. The heron and crane have long and thin feet that help them to walk and swim in ponds and catch small water animals. 3) Two toes in front and two toes at back: Birds like woodpecker and parrot have feet that are helpful in climbing trees. 4) Powerful curved talons: Eagle, vulture and hawk have talons to catch and hold their prey firmly. 5) Webbed feet: Ducks and penguins use their feet to paddle through the water. 6) Three forward toes: Birds like emu have three toes facing forward. These toes help them to run fast. SOUNDS OF BIRDS Have you heard birds making sound during sunrise and sunset? A rooster makes sounds during the sunrise. Birds make a variety of sounds to talk to other birds. Here are some of them: 1) Sharp, loud sounds are used to warn other birds of danger. 2) Young birds make different types of sound to call their parents. These are like crying sounds. 4

3) When birds travel in groups or when they want to signal one another, they use a different type of sound. 4) Some birds sing. Songs are musical sounds that have many purposes. Birds use songs to attract other birds. They use songs to prevent other birds from entering their area or nest. Application BIRDS THAT TRAVEL the Siberian crane Birds travel from one place to another to avoid extreme weather conditions. But the changing environment affects this movement of birds. For example, the Siberian cranes once used to travel in the winter from the cold Siberia to India in large numbers. But now we do not see much of these birds. This is because of the illegal hunting and pollution of water bodies. BIRDS THAT ARE LOST Some birds like the dodo and passenger pigeon vanished due to bad weather condition, or human activities. The population of some birds like the red- headed vulture and the sparrow is also decreasing. They are about to vanish. the red-headed vulture sparrow Amazing Facts Ostriches have the largest eyes of all land animals. Their eyes are bigger than their brains! eye of an ostrich Birds 5

Higher Order Thinking Skills (H.O.T.S.) birdwatching Birdwatching is observing birds in their natural homes and environment. It can be done with naked eyes or with the help of binoculars. Birdwatching is a hobby for many people. Collect the information about what things you will need for birdwatching. 6

Lesson Animal Behaviour 10 Let Us Learn About R behaviour and physical features of animals. u benefits of different behaviour and physical features. a similarities in animal and human behaviour. H animal behaviour based on senses. Think Mona wonders why an elephant has a long trunk and a fish has fins. Can you guess? Remembering The animals around us differ in their behaviours and physical features. VARIATIONS IN ANIMAL BEHAVIOUR 1) Groups: Some animals live in groups. They have leaders for their groups. The deer, horses, wild dogs, bison, elephants and wolves are some such animals. Some groups, like a pride of lions, has a male as the leader. Some groups, like a clan of Hyenas, have a female as their leader. Deer have a separate group for males and a separate group for females and baby deer. Some birds and fish also live and travel in groups. 7

Animals that live in groups herd of bison herd of elephants herd of deer herd of horses a shoal of fish a flock of birds 2) Alone: Animals like the tiger, leopard and bear do not have groups. They live alone most of their lives. Animals that live alone tiger leopard bear 3) Area marking: Animals protect the area they live in. They mark their area. Dogs urinate to mark their area. Leopards mark by rubbing themselves against the plants in that area. 4) Moving to another place: Some birds and animals such as the Siberian cranes, monarch butterflies, salmon fish do not live in the same area throughout the year. They go from one place to another. Siberian crane monarch butterfly salmon fish 8

5) Sleep: Some animals sleep continuously for many days or months. Bears, bats and ground squirrels are a few such animals. Bears sleep throughout the winter season. Crocodiles sleep during the summer season. VARIATIONS IN PHYSICAL FEATURES bats ground squirrel Animals also have differences in their body parts. Let us look at the same. 1) Ears: Different animals have different shape and size of ears. The type of sounds they can hear also differs. Animals like tigers and lions have ears facing forward. Animals like rabbit and deer have ears which can be moved around. 2) Hair: Different types of hair patterns are seen ears of a tiger ears of a deer in animals. Some animals have long and thick hair, while some others have thin hair. For example, elephants have thin hair, while bears have a thick layer of hair covering their body. 3) Nose: Different types of noses are trunk of an elephant strong tail of a kangaroo found in animals. Elephants have a long nose developed into a trunk. 4) Tails: Different types of tails are found in animals. Kangaroos have long and strong tails. Understanding We have learnt that birds have different types of beaks, feet, feathers and wings. It is due to different food habits and habitats. We have discussed different animal behaviour and some physical features. Why do they have such behaviour and physical features? BENEFITS OF DIFFERENT ANIMAL BEHAVIOUR 1) By living in groups, animals can protect themselves better from their enemies. Their young ones are better looked after. They can look for food and shelter together. In a group, the animal which is strong and powerful is the leader. Other animals follow it. For example, elephant, bison and deer. Animal Behaviour 9

2) Area marking prevents an animal from entering into another animal’s area. The food available in an area may not be enough for more than one animal to survive. In such cases, area marking helps the animals to survive better. 3) Some behaviours help animals to live in the tough weather and adjust to changes in the availability of food. For example, moving from one place to another, sleeping for a long time and so on. BENEFITS OF Different PHYSICAL FEATURES Let us see how the physical features help animals. 1) In animals like tigers and lions, the ears facing forward help to focus on the prey they hunt. In animals like rabbit and deer, the ears which move around help them to know the direction of their enemies. 2) Hair protect the animals from cold weather. The type of hair in animals depend on the climate of the place. For example, animals living in a cold region have thicker hair than those in a warm region. For the animals like fish that always live in water, their body is covered with scales instead of hair. Also, the shape of their body is such that they can swim easily. Feathers of birds cover and protect their body. 3) The trunk of elephants helps to pick up food and put it into the mouth. It also helps to take up enough water for drinking and bathing. 4) The tails of animals have different uses. For example, monkeys have long tails which help in holding on to branches and jumping from one tree to another. The tails of cats and kangaroos help them to hop and balance. Application We, humans, are social animals. Let us try to find out similarities between us and other animals. 1) Shelter: Animals find caves or build nests for their protection. Like animals, humans also build houses for protection from tough weather and harmful animals. shelters of animals house of humans 10

2) Living in a group: Many animals live together in groups and follow the rules of the group. We also live in small or large groups in the form of family, community or society. Like the animals, we also follow certain rules within our groups. Amazing Facts Animals like the chameleon can change their colour to match with the environment! chameleon Higher Order Thinking Skills (H.O.T.S.) Like us, animals can also smell, see, hear, touch and feel. Some senses of animals are stronger than ours. 1) A dog can hear sounds that we cannot hear. Bats can make and hear sounds which we cannot hear. It helps them while flying. As animals have a sharper sense of hearing, any loud noise can be harmful to them. For example, the sound of crackers affects them a lot. 2) Animals’ sense of smell is also many times stronger than us. The strong sense of smell helps them to protect themselves from enemies. For example, a rabbit gets the smell of its enemy even when it is far away. Animals can find food easily due to a strong sense of smell. You must have seen the expertise of ants and houseflies in finding food. 3) Animals like cats have night vision which helps them to hunt in the dark. Find out more about such senses of animals. Animal Behaviour 11

Inside the Lab – B Make sure you do these activities only with the help of a teacher or an adult. Activity B1: Soil’s Capacity to Hold Water You will need: four empty glass jars, four filter papers, four empty plastic bottles, four different types of soil You need to: 1) cut the empty plastic bottles into half to use the top part as funnels. (Teacher should help the students while cutting.) 2) place funnels on the mouth of the glass jars. 3) fold the filter papers in cone shape, and place them inside the plastic funnels as shown in the picture. 4) fill the plastic funnels with soil as shown in the picture. Fill different types of soil in each funnels. 5) slowly add 200 mℓ of water in each funnel. 6) find out how much water was retained by the soil by looking at the amount of water falling into the glass jars. 7) We will observe that different types of soils have different capacity to hold water. Activity B2: Simple Water Filter Let us now make a simple water filter. You will need: a large plastic bottle, a container, cotton cloth, gravel, sand, muddy water You need to: 1) make about 8–10 holes in the bottom of the large, empty plastic bottle. 12

2) cut off the top of the bottle evenly. (Teacher should help muddy water the students while cutting.) water bottle 3) spread the cotton cloth in the bottom covering all the sand holes. gravel cotton cloth 4) add a layer of gravel. clean water container 5) fill the bottle with sand. simple water filter 6) pour your muddy water through the homemade filter. 7) retrieve the water in another container placed under the filter. 8) look at the water that comes out of the filter. It should be clear. If not, you may have to pass the water through the filter more than once. Note: Now you have made a water filter but the water you get may not be safe to drink. The water may still contain harmful bacteria that your filter did not remove. To get water safe enough to drink, you also need to purify it. Inside the Lab – B 13

Lesson Food Storage 11 Let Us Learn About r food spoilage. u methods to store and preserve food. a benefits of storing food. h food storage during travel. Think Farha’s father cooked biryani for dinner. After dinner, he father smelling the biryani kept the leftover biryani in the kitchen cupboard. Next day, before giving the biryani to Farha, he smelled it. Then he said, “This is spoilt now. Do not eat this. You will fall sick.” What happened to the biryani? Why can’t Farha eat it? Remembering When Farha’s father opened the lid of the cooker, there was a bad smell. He also saw some yellow things on the biryani rice. Can you guess what happened to the biryani? The biryani is spoilt. When food becomes harmful for our health, we say it is spoilt. We should not eat spoilt food. We throw away the spoilt food. Food spoilage means the nutrition from food is lost. This food gets wasted. 14

spoilt food items REASONS FOR FOOD SPOILAGE The food spoils due to the presence of microorganisms. These microorganisms grow faster in a hot climate. Example: fungi, bacteria and so on • Fungi which grow on food are of different sizes. We can see some of them with our eyes and some we cannot. • We cannot see bacteria with our eyes. IDENTIFYING SPOILT FOOD How did Farha’s father know that the biryani was spoilt? The colour, smell, look and touch of the food changes when spoilt. Spot the difference between the two bananas. Some food items that we buy from the market have the date by which the food will be spoilt. It may be given as: • use before, or fresh and spoilt banana • best before, or • expiry date We must always check this date before buying any food item. Think and write how many days the following food items will take to spoil: 1) cooked Maggi: __________________________________ 2) bread: __________________________________ 3) kurkure: __________________________________ Some food items get spoilt in few hours. Some food items gets spoilt in months. Cooked food items (like roti, curry, dal and so on) get spoilt faster than packaged food items (like biscuits, chips and so on). Food Storage 15

Understanding In olden days, people used natural methods to store and preserve food. For example, in cold places, they froze fish and meat on ice. In hotter climates, they dried food in the Sun. Food was stored in cool rivers and caves. frozen fish on ice drying rice grains under the Sun Let us see what we use today. METHODS TO STORE FOOD We need to store all types of food items to use them later. Storing food for later use is called food storage. It is important to store food properly to avoid the wastage of food. Think and write where we store the following food items. 1) milk: ______________________________________________________________________________ 2) dals: _ ______________________________________________________________________________ 3) apples: ____________________________________________________________________________ 4) onion: ________________________________________________________________________________ 5) leafy vegetables : ____________________________________________________________________ Different types of food items are stored in different places. Some in the refrigerator, some in a cool and dry place, some in dry food containers and so on. dry food in containers different food items stored in a fridge 16