9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2

Cross-multiplying, we get 39 5 15 T he cross products are 5 × 9 = 45 and 3 × 15 = 45. Since the cross products are equal; the given fractions are equivalent. b) 1 and 2 36 Cross-multiplying, we get 12 36 T he cross products are 1 × 6 = 6 and 3 × 2 = 6. Since the cross products are equal, the given fractions are equivalent. Example 2: Check if these fractions are equivalent. a) 1 and 2 b) 3 and 9 4 10 9 18 S olution: a) 1 and 2 4 10 Cross-multiplying, we get 12 4 10 T he cross products are 1 × 10 = 10 and 4 × 2 = 8. Since the cross products are not equal (10 ≠ 8), the given fractions are not equivalent. b) 3 and 9 9 18 Cross-multiplying, we get 39 9 18 T he cross products are 3 × 18 = 54 and 9 × 9 = 81. Since the cross products are not equal (54 ≠ 81), the given fractions are not equivalent. Application Let us solve a few examples based on the concept of equivalence of fractions. Example 3: Kiran played for 1 of a day and did his homework for 3 of the day. Did he 5 15 spend the same amount of time for both the activities? Fractions - I 19 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 51 1/7/2019 3:17:26 PM

Solution: If Kiran spent the same amount of time for both the activities, the given fractions must be equivalent. We check the equivalence of fractions by cross-multiplication. 13 5 15 1 × 15 = 5 × 3 = 15 Example 4: As the cross products are equal, the given fractions are equivalent. Solution: Therefore, Kiran spent the same amount of time for both the activities. Clock A shows 2 of an hour and Clock B shows 3 of an hour. Are both the 12 15 clocks showing the same time? If both the clocks are showing the same time, the given fractions must be equivalent. We check the equivalence of fractions by cross-multiplication. 23 12 15 2 × 15 = 30; 12 × 3 = 36 As the cross products are not equal, the given fractions are not equivalent. Therefore, both the clocks are not showing the same time. Higher Order Thinking Skills (H.O.T.S.) Let us now solve some examples where equivalent fractions are used in real-life situations. Example 5: If the given fractions are equivalent, find the missing numerators in the brackets. Solution: a) 15 = [ ] b) [ ] = 3 25 5 49 7 Given that the fractions are equivalent, we know that their cross products are equal. a) 15 × 5 = 25 × [ ] 3 × 5 × 5 = 25 × [ ] 3 × 25 = 25 × [ ] 3 = [ ] 20 1/7/2019 3:17:26 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 52

Therefore, the missing number in the brackets is 3. b) [ ] × 7 = 49 × 3 [ ] × 7 = 7 × 7 × 3 [ ] × 7 = 7 × 21 [ ] = 21 Therefore, the missing number in the brackets is 21. Example 6: If the given fractions are equivalent, find the missing denominators in the brackets. a) 14 = 7 18 = 9 28 [ ] b) [] 27 Solution: As the fractions are equivalent, their cross products are equal. a) 14 × [ ] = 28 × 7 14 × [ ] = 2 × 14 × 7 14 × [ ] = 14 × 2 × 7 [ ] = 2 × 7 [ ] = 14 Therefore, the missing number in the brackets is 14. b) 18 × 27 = [ ] × 9 9 × 2 × 27 = [ ] × 9 [ ] × 9 = 9 × 54 [ ] = 54 Therefore, the missing number in the brackets is 54. Concept 9.2: Fraction in its Lowest Terms Think Pooja knows the method of finding equivalent fractions by both division and multiplication. She wants to know where she could use the division method of finding equivalent fractions. Do you know where it is used? Fractions - I 21 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 53 1/7/2019 3:17:26 PM

Recall In the chapter on division, we have learnt how to find factors of a number. We also learnt to find the H.C.F. of the given numbers. Let us solve the following to recall the concept of H.C.F. Find the H.C.F. of these numbers. a) 36, 48 b) 26, 65 c) 16, 48 d) 20, 60 e) 11, 44 & Remembering and Understanding We have seen that 1 , 2 , 7 , 10 … are all equivalent fractions. However, the fraction 1 is 3 6 21 30 3 said to be in the lowest terms. It is because its numerator and denominator do not have any common factors other than 1. A fraction can be reduced to its lowest terms using either division or H.C.F. Reducing a fraction using division Example 7: Reduce the following fractions to their lowest terms. a) 36 b) 26 48 65 Solution: a) 36 = 36 ÷ 2 = 18 ÷ 2 = 9 ÷ 3 = 3 48 48 ÷ 2 24 ÷ 2 12 ÷ 3 4 Therefore, when reduced to its lowest terms, 36 becomes 3 . 48 4 b) 26 = 26 ÷13 = 22 65 65 ÷13 55 Therefore, when reduced to its lowest terms, 26 becomes 2 . 65 5 Reducing a fraction using H.C.F. We use the concept of H.C.F. to reduce a fraction to its lowest terms. Example 8: Reduce the following fractions to their lowest terms. a) 36 b) 26 48 65 22 1/7/2019 3:17:26 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 54

Solution: a) Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Common factors of 36 and 48: 1, 2, 3, 4, 6, 12 The H.C.F. of 36 and 48 is 12. 36 = 36 ÷12 = 3 48 48 ÷12 4 Therefore, when reduced to its lowest terms, 36 becomes 3 . 48 4 b) Factors of 26: 1, 2, 13, 26 Factors of 65: 1, 5, 13, 65 Common factors of 26 and 65: 1, 13 The H.C.F. of 26 and 65 is 13. 26 = 26 ÷13 = 2 65 65 ÷13 5 Therefore, when reduced to its lowest terms, 26 becomes 2 . 65 5 Application Let us solve a few real-life examples that involve reducing fractions to their lowest terms. Example 9: Jai ate 4 of a watermelon and Vijay ate 16 of another watermelon of the 16 32 same size. Did they eat the same quantity of watermelon? If not, who ate Solution: more? Fraction of watermelon Jai ate = 4 16 Fraction of watermelon Vijay ate = 16 32 To compare the fractions, we must reduce them to their lowest terms so that we get like fractions. 4 4÷4 1 [H.C.F. of 4 and 16 is 4.] 16 = 16 ÷ 4 = 4 16 = 16 ÷ 8 = 2 [Using division method] 32 32 ÷ 8 4 Clearly, 1 < 2. So, 1 < 2 . 44 Therefore, Vijay ate more. Fractions - I 23 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 55 1/7/2019 3:17:26 PM

Example 10: Suraj and Puja were painting the walls of their room. Suraj painted 21 of the 35 wall in an hour and Puja painted 24 of the wall in the same time. Who is more Solution: efficient? 30 Part of the wall painted by Suraj in an hour = 21 = 3 35 5 (H.C.F. of 21 and 35 is 7.) Example 11: Part of the wall painted by Puja in an hour = 24 = 4 30 5 Solution: (H.C.F. of 24 and 30 is 6.) Clearly, 4 is greater than 3 . 55 Therefore, Puja does more work than Suraj in the same time. So, Puja is more efficient. Malik saves ` 550 from his monthly salary of ` 5500. Akhil saves ` 300 from his monthly salary of ` 4500. What fraction of their salary did each of them save? Fraction of salary saved by Malik = 550 = 550 ÷ 10 = 55 ÷ 55 = 1 5500 5500 ÷ 10 550 ÷ 55 10 Fraction of salary saved by Akhil = 300 = 300 ÷ 100 = 3 ÷ 3 = 1 4500 4500 ÷ 100 45 ÷ 3 15 Therefore, Malik saved 1 of his salary and Akhil saved 1 of his salary. 10 15 Higher Order Thinking Skills (H.O.T.S.) Let us see a few more examples on reducing fractions to their lowest terms. Example 12: A circular disc is divided into equal parts. Some parts of the circular disc are painted in different colours as shown in the figure. Write the fraction of each colour in its lowest terms. Solution: Total number of equal parts on the disc is 16. The number of parts painted yellow is 3. Fraction = Number of parts painted yellow = 3 Total number of equal parts 16 (The numerator and the denominator do not have any common factor other than 1. So, the fraction cannot be reduced any further.) 24 1/7/2019 3:17:26 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 56

The fraction of the disc that is painted white = Number of parts painted white = 6 = 6÷2 = 3 Total number of equal parts 16 16 ÷ 2 8 (H.C.F. of 6 and 16 is 2.) The fraction of the disc that is painted red = Number of parts painted red = 4 = 4 ÷ 4 = 1 Total number of equal parts 16 16 ÷ 4 4 (H.C.F. of 4 and 16 is 4.) The fraction of the disc that is painted blue = Number of parts painted blue = 3 Total number of equal parts 16 (The numerator and the denominator do not have any common factor other than 1. So, the fraction cannot be reduced any further.) Example 13: Meena used 250 g sugar for a pudding of 1000 g. What is the fraction of sugar in the pudding? Solution: Quantity of sugar = 250 g Quantity of pudding = 1000 g Fraction of sugar in the pudding = 250 = 250 ÷ 10 = 25 ÷ 25 = 1 1000 1000 ÷ 10 100 ÷ 25 4 Therefore, sugar forms 1 of the weight of the pudding. 4 Concept 9.3: Compare Unlike Fractions Think Pooja has two circular discs coloured in green, red and white as shown. She wants to know if the parts coloured in red and green are the same. Do you know how Pooja can find it? Fractions - I 25 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 57 1/7/2019 3:17:26 PM

Recall In class 4, we have learnt what like and unlike fractions are. Let us recall the same. Fractions such as 1 , 2 and 3 that have the same denominator are called like fractions. 88 8 Fractions such as 1 , 3 and 3 , that have different denominators are called unlike fractions. 87 11 Let us answer the following to recall like and unlike fractions. Identify the like and unlike fractions from the following: a) 3 , 3 , 1 , 5 , 6 , 1 , 4 b) 2, 1 , 1, 7 5, 4 c) 5 , 4 , 7 , 5 , 11 , 3 7 5 7 7 7 4 11 22 22 12 14 , 15 22 15 15 26 24 15 15 & Remembering and Understanding We know how to compare like fractions. To compare two or more fractions, their denominators should be the same. Let us now learn to compare unlike fractions. Steps to compare unlike fractions: 1) Find the L.C.M. of the denominators of the given unlike fractions. Using L.C.M, convert the given unlike fractions into equivalent fractions having the same denominator. 2) Compare their numerators and find which is greater than the other. The fraction with the greater numerator is greater. Example 14: Compare these unlike fractions. a) 3 , 4 b) 3 , 1 c) 1 , 3 7 11 57 48 26 1/7/2019 3:17:26 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 58

Solution: Solved Solve these Steps 3, 4 3, 1 1, 3 7 11 57 48 Step 1: Write like fractions L.C.M. of 7 and 11 is 77. equivalent to the given So, the equivalent fractions, using the least fractions are common multiple of their 3 = 3 ×11 = 33 and denominators. 7 7 ×11 77 4 = 4 × 7 = 28 . 11 11× 7 77 Step 2: Compare their 33 > 28 numerators and find which is So, 33 > 28 . greater or lesser. 77 77 Thus, 3 > 4 . 7 11 Example 15: Compare these unlike fractions. a) 1 , 2 b) 5 , 1 c) 1 , 6 24 63 4 12 S olution: a) 1 , 2 24 The L.C.M. of 2 and 4 is 4. So, equivalent fraction of 1 = 1×2 = 2 2 2×2 4 Since the numerators are equal, 2 = 2 44 Therefore, the given fractions are equal. b) 5 , 1 63 The L.C.M. of 6 and 3 is 6. So, 1 = 1×2 = 2. 3 3×2 6 Since 5 > 2, 5 > 2 . 66 Therefore, 5 > 1 . 63 Fractions - I 27 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 59 1/7/2019 3:17:26 PM

c) 1 , 6 4 12 The L.C.M. of 4 and 12 is 12. So, 1= 1×3 = 3. 4 4×3 12 Since 3 < 6, 3 < 6 . 12 12 Therefore, 1 < 6 . 4 12 Application Let us see some real-life situations where we compare unlike fractions. Example 16: Esha ate 1 of an apple in the morning and 2 of the apple in the evening. 43 When did she eat a larger part of the apple? Solution: Fraction of the apple Esha ate in the morning = 1 4 Fraction of the apple she ate in the evening = 2 3 To find when she ate a larger part we must compare the two fractions. Step 1: Write like fractions equivalent to 1 and 2 with the least common multiple of 4 4 3 and 3 as their denominator. The least common multiple of 4 and 3 is 12. So, the required like fractions are: Step 2: 1 = 1×3 3 and 2 = 2×4 = 8 4 4×3 = 12 3 3×4 12 Compare the numerators of the equivalent fractions. Example 17: Since 8 > 3, 8 > 3 . 12 12 Hence, 2 > 1 . 34 Clearly, Esha ate the larger part of the apple in the evening. Kumar saves 1 of his salary and Pavan saves 2 of his salary. If they earn the 46 same amount every month, then who saves a lesser amount? 28 1/7/2019 3:17:26 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 60

Solution: To find who saves lesser, we must find the lesser of the given fractions. The L.C.M. of 4 and 6 is 12. Equivalent fractions of 1 and 2 are 3 and 4 . 4 6 12 12 Since 3 < 4, 3 < 4 . 12 12 Hence, 1 < 2 . 46 Therefore, Kumar saves lesser amount than Pavan. Higher Order Thinking Skills (H.O.T.S.) Let us see a few more examples using comparison of unlike fractions. Example 18: Colour each figure to represent the given fraction and compare them. 2 2 9 7 Solution: 2 9 2 7 Clearly, the part of the figure represented by 2 is greater than that 7 represented by 2 . Hence, 2 is greater than 2 . 97 9 Let us try to arrange some unlike fractions in the ascending and descending orders. Example 19: Arrange 2 , 1 , 2 , 3 and 1 in the ascending order. 3254 6 Solution: Write equivalent fractions of the given unlike fractions. The L.C.M. of the denominators 2, 3, 4, 5 and 6 is 60. So, the fractions equivalent to 2 , 1 , 2 , 3 and 1 with the L.C.M. as their 3254 6 denominator will be: Fractions - I 29 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 61 1/7/2019 3:17:26 PM

2 = 2× 20 = 40 1 = 1× 30 = 30 , 2 = 2 ×12 = 24 , 3 = 3 ×15 = 45 3 3× 20 60 , 2 2× 30 60 5 5 ×12 60 4 4 ×15 60 and 1 = 1×10 = 10 . 6 6×10 60 Comparing the numerators, 10 < 24 < 30 < 40 < 45. So, 10 < 24 < 30 < 40 < 45 . 60 60 60 60 60 Therefore, the required ascending order is 1 , 2 , 1 , 2 , 3 . 65234 Example 20: Arrange 2 , 1 , 1 , 5 , and 3 in the descending order. 7 4 8 14 16 Solution: Write equivalent fractions of the given unlike fractions. The L.C.M. of the denominators 7, 4, 8, 14 and 16 is 112. So, the fractions equivalent to 2 , 1 , 1 , 5 , and 3 with the L.C.M. as the 7 4 8 14 16 denominator will be: 2 2×16 32 1 1× 28 28 1 1×14 14 5 5× 8 40 7 = 7×16 = 112 , 4 = 4× 28 = 112 , 8 = 8×14 = 112 , 14 = 14× 8 = 112 and 3 = 3×7 = 21 . 16 16×7 112 Comparing the numerators, 40 > 32 > 28 > 21 > 14. 40 32 28 21 14 So, 112 > 112 > 112 > 112 > 112 . Therefore, the required descending order is 5 , 2 , 1 , 3 , 1 . 14 7 4 16 8 Concept 9.4: Add and Subtract Unlike Fractions Think Pooja has a round cardboard with some of its portions coloured. She knows that the fractions that represent the coloured portions are unlike. She wondered how to find the part of the cardboard that is coloured and how much of it is uncoloured. How do you think Pooja can find that? 30 1/7/2019 3:17:26 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 62

Recall We have already learnt to compare fractions. Let us compare the following to revise the same. a) 5 and 1 b) 3 and 2 c) 1 and 2 d) 4 and 3 e) 1 and 3 77 45 88 24 6 27 27 & Remembering and Understanding Unlike fractions can be added or subtracted by first making the denominators equal and then adding up or subtracting the numerators. Let us understand the addition and subtraction of unlike fractions through some numerical examples. Solve: a) 3 + 1 b) 7 + 2 Example 21: 15 10 13 39 c) 22 + 7 100 10 S olution: a) 3 + 1 = 6 + 3 15 10 30 30 [L.C.M. of 15 and 10 is 30.] 6+3 9 3 = 30 = 30 = 10 [H.C.F. of 9 and 30 is 3.] 7 2 21 2 21+ 2 23 b) 13 + 39 = 39 + 39 = 39 = 39 [L.C.M. of 13 and 39 is 39.] c) 22 + 7 = 22 + 70 22 + 70 92 23 == = 100 10 100 100 100 100 25 [ The L.C.M. of 100 and 10 is 100 and the H.C.F. of 92 and 100 is 4.] Example 22: Solve: a) 8 – 4 b) 17 – 5 c) 14 – 17 9 11 30 24 25 50 Solution: a) 8 –4 88 36 [L.C.M. of 9 and 11 is 99.] = – 9 11 99 99 88 - 36 52 == 99 99 b) 17 – 5 = 68 – 25 [L.C.M. of 24 and 30 is 120.] 30 24 120 120 Fractions - I 31 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 63 1/7/2019 3:17:26 PM

68 - 25 43 == 120 120 c) 14 – 17 = 28 17 [L. C. M. of 25 and 50 is 50.] – 25 50 50 50 28 -17 11 = = 50 50 Application In some real-life situations, we use the addition or subtraction of unlike fractions. Let us solve a few such examples. Example 23: The figure shows the coloured portion of two strips of paper. Find the total part that is coloured in both the strips. What part of the strips is not coloured? Solution: Total number of parts of the first strip = 9 Part of the first strip coloured = 2 9 Total number of parts of the second strip = 7 Part of the second strip coloured = 4 n 7 Total coloured part of the strips = 2 + 4 97 14 36 [L.C.M. of 9 and 7 is 63.] = + 63 63 = 14 + 36 50 = 63 63 50 Part of the strip that is not coloured is 2 - 63 [Since 9 + 7 = 1 + 1 = 2.] 9 7 63 63 50 63 + 63 - 50 126 - 50 76 = + – = == 63 63 63 63 63 63 Example 24: Manasa ate a quarter of a chocolate bar and her sister ate two-thirds of it. How much chocolate did they eat in all? How much chocolate is remaining? 32 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 64 1/7/2019 3:17:26 PM

Solution: Part of the chocolate eaten by Manasa = 1 4 Part of the chocolate eaten by Manasa’s sister = 2 3 Total chocolate eaten by Manasa and her sister = 1 + 2 43 3 + 8 = 3 + 8 = 11 12 12 12 12 [L.C.M. of 4 and 3 is 12.] Therefore, the part of the chocolate eaten by both Manasa and her sister = 11 12 Remaining part of the chocolate = 1 – 11 = 12 – 11 = 12 - 11 = 1 12 12 12 12 12 Higher Order Thinking Skills (H.O.T.S.) Let us see some more examples of addition and subtraction of unlike fractions. Example 25: In a town, 5 of the population were men, 1 were women and 1 were 8 46 children. What part of the population was a) men and women? b) men and children? c) women and children? Solution: Part of the population of the town that was men = 5 8 Part of the population of the town that was women = 1 4 Part of the population of the town that was children = 1 6 Part of the population that was men and women = 5 + 1 = 5 + 2 = 7 8 4 8 8 8 Part of the population that was men and children = 5 + 1 = 15 + 4 = 19 8 6 24 24 24 Part of the population that was women and children = 1 + 1 = 3 + 2 = 5 4 6 12 12 12 Fractions - I 33 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 65 1/7/2019 3:17:26 PM

Example 26: In a school, 1 of the students were from the primary school, 1 were from the 35 middle school and the remaining were from the high school. What fraction of the strength of the school was from the high school? Solution: Strength of the school that was from the primary school = 1 3 Strength of the school that was from the middle school = 1 5 Strength of the school that was from the high school  31 51 =  51+53  185 = = 1 – + 1 – = 1 – 15 -8 = 15 - 8 = 7 15 15 15 15 Therefore, 7 of the total strength were high school students. 15 Drill Time Concept 9.1: Equivalence of Fractions 1) Check if the fractions are equivalent. a) 5 and 5 b) 3 and 14 c) 8 and 24 d) 3 and 9 e) 4 and 5 8 21 21 35 23 46 27 81 25 50 Concept 9.2: Fraction in its Lowest Terms 2) Reduce these fractions using H.C.F. d) 12 e) 12 a) 24 b) 36 c) 42 36 30 48 60 70 d) 6 e) 3 3) Reduce these fractions using division. 24 27 a) 36 b) 42 c) 26 72 84 91 Concept 9.3: Compare Unlike Fractions 4) Compare the following unlike fractions: a) 3 , 2 b) 3 , 4 c) 8 , 7 d) 5 , 3 e) 11, 5 7 14 21 42 9 18 11 7 48 34 1/7/2019 3:17:26 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 66

Concept 9.4: Add and Subtract Unlike Fractions 5) Solve: a) 3 + 5 b) 4 + 3 c) 4 + 1 d) 19 + 5 e) 2 + 6 4 13 14 12 15 10 100 10 16 30 6) Solve: a) 4 – 3 b) 14 – 3 c) 13 – 14 d) 3 – 4 e) 15 – 16 9 11 30 24 30 60 15 30 20 40 7) Word problems a) U sha played the keyboard for 7 of an hour and did her homework for 5 of 30 12 an hour. Did she spend the same amount of time for both the activities? b) William ate 3 of a chocolate bar and Wasim ate 1 of the chocolate. Did they 16 4 eat the same part of the chocolate? Who ate less? c) Mani and Roja were painting a rectangular cardboard each. Mani painted 15 of the cardboard in an hour and Roja painted 18 of the cardboard in the 25 30 same time. Who is more efficient? d) Sudheer saves ` 360 per month from his salary of ` 3600. Hari saves ` 200 per month from his salary of ` 2400. What fraction of their salary did each of them save? e) Pavani used 450 cm of satin ribbon from a bundle of satin ribbon of length 3000 cm. What fraction of the satin ribbon is used? Fractions - I 35 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 67 1/7/2019 3:17:26 PM

Chapter Fractions - II 10 Let Us Learn About • the terms ‘mixed’, ‘proper’ and ‘improper’ fractions. • adding and subtracting mixed fractions. • multiplying and dividing fractions by fractions. • finding the reciprocals of fractions. Concept 10.1: Add and Subtract Mixed Fractions Think Pooja has learnt addition and subtraction of unlike fractions. She has also learnt the conversion of improper fractions to mixed fractions and vice-versa. She was curious to know if she could add and subtract improper fractions and mixed fractions too. How do you think Pooja can add or subtract mixed fractions? Recall We have learnt about the types of fractions. Let us recall them here. 1) A fraction whose numerator is greater than the denominator is called an improper fraction. 2) A fraction whose denominator is greater than the numerator is called a proper fraction. 3) The combination of a whole number and a fraction is called a mixed fraction. 36 1/7/2019 3:17:26 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 68

Let us revise the concept of fractions by solving the following: 13 8 11 5 22 17 a) 6 + 9 b) 7 + 14 c) 15 + 10 8 10 9 23 54 d) 3 – 11 e) 2 – 15 f) 6 – 5 & Remembering and Understanding A mixed fraction can be converted into an improper fraction by multiplying the whole number part by the fraction’s denominator and then adding the product to the numerator. Then we write the result on top of the denominator. The addition and subtraction of mixed fractions are similar to that of unlike fractions. Let us understand the same through the following examples. Example 1: 3 + 3 2 Add: 2 5 7 Solved Solve this Steps 23 + 32 12 1 + 15 1 57 43 Step 1: Convert all the mixed 2 3 = 2 × 5 + 3 = 13 ; fractions into improper fractions. 55 5 3 2 = 3 ×7 + 2 = 23 77 7 Step 2: Find the L.C.M. and add the 2 3 + 3 2 = 13 + 23 improper fractions. 5 75 7 [L.C.M. of 5 and 7 is 35.] = 7 ×13 + 5 × 23 35 = 91+115 = 206 35 35 Fractions - II 37 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 69 1/7/2019 3:17:26 PM

Solved Solve this 12 1 + 15 1 Steps 23 + 32 57 43 Step 3: Find the H.C.F. of the The H.C.F. of 206 and 35 is 1. Solve this numerator and the denominator of So, we cannot reduce the 12 1 from 15 1 the sum. Then reduce the improper fraction any further. fraction to its simplest form. 43 Step 4: Convert the improper fraction 206 31 into a mixed fraction. =5 35 35 Therefore, 2 3 + 3 2 57 = 5 31 . 35 Example 2: Subtract 2 3 from 3 2 57 Steps Solved 2 3 from 3 2 Step 1: Convert all the mixed fractions into improper fractions. 57 3 2 = 3 ×7 + 2 = 23 ; 77 7 2 3 = 2 × 5 + 3 = 13 55 5 Step 2: Find the L.C.M. and 32 -23 = 23 13 subtract the improper fractions. - 7575 [L.C.M. of 5 and 7 is 35] = 5 × 23 − 7 ×13 = 115 − 91 = 24 35 35 35 Step 3: Find the H.C.F. of the The H.C.F. of 24 and 35 is 1. So, we numerator and the denominator cannot reduce the fraction any of the difference. Then reduce further. the proper fraction to its simplest form. 38 1/7/2019 3:17:26 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 70

Steps Solved Solve this 2 3 from 3 2 12 1 from 15 1 57 43 Step 4: If the difference is an 24 is a proper fraction. So, we improper fraction, convert it into 35 a mixed fraction. cannot convert it into a mixed fraction. 2 3 24 Therefore, 3 7 – 2 5 = 35 Application In some real-life situations, we use the addition or subtraction of mixed fractions. Example 3: Ajit ate 5 3 biscuits and Arun ate 8 1 biscuits. How many biscuits did they eat 54 in all? How many biscuits were remaining if the box had 20 biscuits in it? Solution: Total number of biscuits in the box = 20 Number of biscuits eaten by Ajit = 5 3 5 1 Number of biscuits eaten by Arun = 8 4 Total number of biscuits eaten by both Ajit and Arun =53 +81 = 28 + 33 = 112 +165 = 277 = 13 17 5 4 5 4 20 20 20 17 = 20 – 277 = 400 − 277 Number of biscuits remaining = 20 – 13 20 1 20 20 123 3 [L.C.M. of 1 and 20 is 20.] = =6 20 20 Therefore, Ajit and Arun ate 13 17 biscuits and 6 3 biscuits are remaining 20 20 Example 4: Veena covered 34 2 km in 2 hours and 16 1 km in the next hour. If she has to 34 travel a total of 65 3 km, how much more distance must she cover? 5 Fractions - II 39 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 71 1/7/2019 3:17:27 PM

Solution: Total distance to be covered by Veena = 65 3 km 5 Distance covered by her in the first 2 hours = 34 2 km 3 Distance covered by her in the next hour = 16 1 km 4 21 Total distance she travelled = 34 3 km + 16 4 km 104 km + 65 km = 416 +195 km = 611 km = 50 11 km 3 4 12 12 12 Distance yet to be covered = 65 3 km – 50 11 km 5 12 = 328 km – 611 km 5 12 = 3936 − 3055 km [L.C.M. of 5 and 12 is 60.] 60 = 881 km = 14 41 km 60 60 Therefore, the distance Veena has to cover is 14 41 km. 60 Higher Order Thinking Skills (H.O.T.S.) Let us see a few more examples of addition and subtraction of mixed fractions. Example 5: By how much is 41 1 greater than 2 39 ? 65 Solution: 1 – 39 2 = 247 – 197 1235 −1182 The required number = 41 6 5 6 5 = 30 = 53 = 1 23 30 30 Therefore, 41 1 is greater than 39 2 by 1 23 . 6 5 30 Example 6: By how much is 22 3 less than 50 1 ? Solution: 47 The required number = 50 1 – 22 3 = 351 – 91 = 1404 − 637 7 474 28 = 767 = 27 11 28 28 Therefore, 22 3 is less than 50 1 by 27 11 . 4 7 28 40 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 72 1/7/2019 3:17:27 PM

Concept 10.2: Multiply Fractions Think Pooja and each of her 15 friends had a bar of chocolate. Each of them ate 5 of the 12 chocolate. How much of the chocolate did they eat in all? How do you think Pooja can find this? Recall Recall that when we find the fraction of a number, we multiply the number by the fraction. After multiplication, we simplify the product to its lowest terms. Similarly, we can multiply a fraction by another fraction too. • F raction in its lowest terms: A fraction is said to be in its lowest form if its numerator and denominator do not have a common factor other than 1. • R educing or simplifying fractions: Writing fractions such that its numerator and denominator have no common factor other than 1 is called reducing or simplifying the fraction to its lowest terms. • Methods used to reduce a fraction: A fraction can be reduced to its lowest terms using 1) division 2) H.C. F. Let us revise the concept by simplifying the following fractions. a) 12 b) 16 c) 13 27 24 65 d) 17 e) 9 f) 14 23 21 42 & Remembering and Understanding Multiply fractions by whole numbers A whole number can be considered as a fraction with its denominator as 1. Multiplying a fraction by 2-digit or 3-digit numbers is the same as finding the fraction of a number. Fractions - II 41 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 73 1/7/2019 3:17:27 PM

Example 7: Find the following: a) 23 of 90 45 b) 15 of 128 32 Solution: a) 23 of 90 = 23 × 90 = 23 × 90 45 45 45 = 2070 = 46 45 Multiplying the numbers in the numerator and then dividing is tedious. It is especially so when the numbers are large. Therefore, we shall find if any of the numbers in the numerator and the denominator have a common factor. If yes, we take the H.C.F. of the numbers. We then divide the numbers to reduce the fraction to its lowest terms. Hence, 23 of 90 = 23 × 90. Here, 45 and 90 have common factors, 3, 5, 9, 15 45 45 and 45. The H.C.F. of 45 and 90 is 45. So, divide both 45 and 90 by their H.C.F. Therefore, 23 × 90 = 23 × 90 2 [Cancelling using the H.C.F. of the numbers] 45 45 1 = 23 × 2 = 46 b) 15 of 128 = 15 × 128 32 32 The H.C.F of 32 and 128 is 32. Divide 32 and 128 by 32, and simplify the multiplication. 15 × 128 4 = 15 × 4 = 60 32 1 Multiply fractions by fractions Multiplication of two fractions is simple. If a and c are two fractions where b,d  are not equal to zero, b d then a × c = a × c b d b × d Product of numerators Therefore, product of the fractions = Product of denominators 42 1/7/2019 3:17:27 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 74

To multiply mixed number, we change them into improper fractions and then proceed. Multiplying the numbers in the numerator and then dividing is tedious. It is especially so when the numbers are large. Therefore, we shall check if any of the numbers in the numerator and the denominator have a common factor. We then reduce the fractions into their lowest terms and then multiply them. Let us look at an example to understand the concept. Example 8: Solve: 23 × 15 45 46 Solution: Follow these steps to multiply the two fractions. Step 1: Check if the numerator and denominator have any common factors. Observing the given fractions, we see that, a) (23, 45) and (15, 46) do not have any common factors to be reduced. b) (23, 46) and (15, 45) have common factors. Step 2: Find the H.C.F. of the numerator and the denominator that have common factors. The H.C.F. of 23 and 46 is 23. The H.C.F. of 15 and 45 is 15. Step 3: Reduce the numerator and the denominator that have common factors using their H.C.F. 1 23 × 1 = 1×1 = 1 15 3 45 46 2 3 × 2 6 Therefore, 23 × 15 = 1 . Example 9: 45 46 6 Solve: a) 2 × 5 b) 7 × 70 c) 84 × 45 56 35 63 54 60 Solution: a) 12 × 1 = 1× 1 = 1×1 = 1 15 1 3 1× 3 3 5 63 b) 17 × 2 = 1 × 2 = 1× 2 = 2 70 1 35 63 9 1 9 1× 9 9 c) 7 84 5 = 7 × 5 = 7×5 = 7 1 54 6 5 6×5 6 16 6 × 45 60 5 Fractions - II 43 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 75 1/7/2019 3:17:27 PM

Application Let us see some real-life examples where we can use multiplication of fractions. Example 10: Tina had 1 kg of flour. She used 1 of it for a recipe. How many grams of 6 10 flour did she use? Solution: Quantity of flour Tina had = 1 kg 6 Part of the flour used by her for a recipe = 1 of 1 kg 10 6 Quantity of flour used by Tina = 1 of 1 kg = 1 × 1 kg = 1×1 kg 10 6 10 6 10 ×6 = 1 kg = 1 × 1000 g = 16.67 g 60 60 Example 11: Mohan saves one-fourth of his monthly salary of ` 5500. Arjun saves two-fifths of his monthly salary of ` 4500. Who saves more and by how much? Solution: Fraction of salary saved by Mohan = 1 of ` 5500. 4 1 = 4/ × 1375 = ` 1375 5500 1 2 × ` 4500 = 2 × ` 900 = ` 1800 Fraction of salary saved by Arjun = 5 Since ` 1800 is more than ` 1375, Arjun saves more. The difference in savings = ` 1800 – ` 1375 = ` 425 Higher Order Thinking Skills (H.O.T.S.) Let us see a few more examples of multiplication of fractions. Example 12: Swetha cut a big watermelon into two equal parts. Jaya cut a part into 16 equal pieces and ate 4 of them. Vijay cut a part into 32 equal pieces and ate 16 of them. Who ate more watermelon? Solution: Each equal part of the watermelon = 1 2 Fraction of watermelon Jaya ate = 4 of 1 = 4 × 1 = 1 × 1 = 1 16 2 16 2 4 2 8 Fraction of watermelon Vijay ate = 16 of 1 = 16 × 1 = 1 × 1 = 1 32 2 32 2 2 2 4 44 1/7/2019 3:17:27 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 76

Comparing the fractions, we see that 1 < 1 or 1 > 1 . 8 4 48 Therefore, Vijay ate more. Example 13: Multiply the following: a) 3 , 7 , 5 b) 1 , 6 , 11, 4 757 7 7 4 11 Solution: a) 3 × 7 × 5 = 3 7577 [Cancelling the common factors in the numerator and denominator] b) 1 × 6 × 11 × 4 = 1× 6 = 6 7 7 4 11 7 × 7 49 [Cancelling the common factors in the numerator and denominator] Concept 10.3: Reciprocals of Fractions Think A chocolate bar was shared among three boys. Pooja got one-third of it. She ate it in parts over a period of four days. If she ate an equal part every day, how much chocolate did Pooja eat in a day? Do you know how to find it? Recall Let us recall the relation between multiplication and division. Multiplication and division are inverse operations. The equation 3 × 8 = 24 has the inverse relationships: 24 ÷ 3 = 8 and 24 ÷ 8 = 3 Similar relationships exist for division. The equation 45 ÷ 9 = 5 has the inverse relationships. 5 × 9 = 45 and 9 × 5 = 45 Let us revise the concept by finding the inverse relationships of the following statements. a) 3 × 4 =12 b) 21÷ 3 = 7 c) 6 × 3 = 18 d) 42 ÷ 7 = 6 Fractions - II 45 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 77 1/7/2019 3:17:27 PM

& Remembering and Understanding Reciprocal of a fraction A number or a fraction which when multiplied by a given number gives the product as 1 is called the reciprocal or multiplicative inverse of the given number. To find the reciprocal of a fraction, we interchange its numerator and denominator. • The reciprocal of a number is a fraction. For example, the reciprocal of 20 is 1 . 20 • The reciprocal of a unit fraction is a number, For example, the reciprocal of 1 is 7. 7 • The reciprocal of a proper fraction is an improper fraction. It can be left as it is or converted into a mixed fraction, For example, the reciprocal of 3 is 7 or 2 1 . 7 3 3 • The reciprocal of an improper fraction is a proper fraction, For example, the reciprocal of 9 is 5 . 59 • The reciprocal of a mixed fraction is a proper fraction, For example, the reciprocal of 2 3 is 8 . 8 19 Note: 1) The reciprocal of 1 is 1. 2) The reciprocal of 0 does not exist as division by zero is not defined. 3) Numbers such as 4, 6, 9 and so on are converted into improper fractions by writing them as 4 , 6 , 9 before finding their reciprocals. 111 4) F ractions are reduced to their lowest terms (if possible) before finding their reciprocals. Let us find the reciprocals of some fractions. Example 14: Find the reciprocals of these fractions. a) 8 b) 4 c) 3 d) 4 17 19 11 5 Solution: To find the reciprocal of a fraction, we interchange its numerator and denominator. 46 1/7/2019 3:17:27 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 78

The reciprocals of the given fractions are: a) 17 b) 19 c) 11 d) 5 84 3 4 Example 15: Find the multiplicative inverses of these fractions. a) 5 b) 7 5 c) 0 d) 1 1 9 e) 33 3 Solution: To find the multiplicative inverse of a fraction, we interchange its numerator and denominator. The multiplicative inverses of the given fractions are: a) 1 b) 9 c) no multiplicative inverse 5 68 d) 1 e) 3 100 Note: 0 has no reciprocal or multiplicative inverse because we cannot multiply any number by it to get 1. Zero multiplied by any number is zero. Therefore, 0 is the only number that does not have a multiplicative inverse. Application Divide a number by a fraction The division of a number by another means to find the number of divisors present in the 1 dividend. For example, 8 ÷ 4 means to find the number of fours in 8. Similarly, 10 ÷ means to 5 find the number of one-fifths in 10. Let us understand the division by fractions through some examples. Example 16: Divide: a) 15 ÷ 1 b) 75 ÷ 3 3 5 Solution: Follow these steps to divide the given. a) 15 ÷ 1 Step 1: 3 15 Step 2: Write the number as a fraction as 15 = 1 13 Find the reciprocal of the divisor. The reciprocal of 3 is 1 . Step 3: Multiply the dividend with the reciprocal of the divisor. 15 ÷ 1 = 15 × 3 = 45 3 1 1 1 Fractions - II 47 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 79 1/7/2019 3:17:27 PM

Step 4: Reduce the product to its lowest terms. 45 = 45 1 Step 1: Therefore, 15 ÷ 1 = 45. Step 2: 3 Step 3: b) 75 ÷ 3 5 75 Write the number as a fraction as 75 = 1 Find the reciprocal of the divisor. The reciprocal of 3 is 5 . 53 Multiply the dividend with the reciprocal of the divisor. 75 ÷ 3 = 75 × 5 Step 4: 5 13 Reduce the product to its lowest terms. 75 × 5 13 The H.C.F. of 75 and 3 is 3. Cancelling 3 and 75 by 3, we get 25 75 5 1 × 3 = 25 × 5 = 125. 1 Note: To divide a number by a fraction is to multiply it by the reciprocal of the divisor. Divide a fraction by a number The division of a fraction by a number is similar to the division of a number by a fraction. Let us understand the division of fraction by numbers through some examples. 1 Example 17: Solve: ÷ 67 3 Solution: To divide the given, follow these steps: Steps Solved Solve this 1 3 ÷ 54 ÷ 67 5 3 Step 1: Write the number as a 67 fraction. 67 = 1 Step 2: Find the reciprocal of 67 1 the divisor. The reciprocal of 1 is 67 . Step 3: Multiply the dividend 1 11 1 by the reciprocal of the 3 ÷ 67 = 3 × 67 = 3 × 67 divisor. 48 1/7/2019 3:17:27 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 80

Steps Solved Solve this 1 3 Step 4: Reduce the product ÷ 54 to its lowest terms. ÷ 67 5 3 11 = 3 × 67 201 11 Therefore, 3 ÷ 67 = 201 . Divide a fraction by another fraction Division of a fraction by another fraction is similar to the division of a number by a fraction. Let us understand this through some examples. Example 18: Solve: 1 ÷ 1 3 21 Solution: To solve the given sums, follow these steps: Solved Solve this 3 210 Steps 1 ÷ 1 25 ÷ 75 3 21 Step 1: Find the reciprocal of 1 21 the divisor. The reciprocal of 21 is 1 . Step 2: Multiply the dividend by 1 1 1 21 3 ÷ 21 = 3 × 1 the reciprocal of the divisor. Step 3: Reduce the product 1 7 into its lowest terms. × 21 = 7 31 11 Therefore, 3 ÷ 21 = 7. Higher Order Thinking Skills (H.O.T.S.) Let us see some real-life examples using division of fractions. Example 19: Sakshi had 7 apples. She cut them into quarters. How many pieces did she get? Fractions - II 49 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 81 1/7/2019 3:17:27 PM

Solution: To find the number of pieces that Sakshi will get, we must find the number of quarters in 7. That is, we must divide the total number of apples by the size of each piece of apple. Number of quarter pieces = 7 ÷ 1 = 7 × reciprocal of 1 = 7 × 4 = 28 44 Therefore, Sakshi got 28 pieces of apple. Example 20: Nani had 3 of a kilogram of sugar. She poured it equally into 4 bowls. How 5 many grams of sugar is in each bowl? Solution: Total quantity of sugar = 3 kg 5 Number of bowls = 4 Quantity of sugar in each bowl = 3 kg ÷ 4 = 3 kg × reciprocal of 4 55 = 3 kg × 1 3 kg = 3 50 5 4= 20 × 1000 g = 3 × 50 g = 150 g 20 1 Therefore, each bowl contains 150 g of sugar. Example 21: There is 16 litres of orange juice in a bottle. 8 litres of it is poured in each 25 25 glass. How many glasses can be filled? Solution: Total quantity of orange juice = 16 litres 25 Quantity of juice poured in each glass = 8 litres 25 Number of glasses filled with juice 16 litres ÷ 8 litres 25 25 21 16 8 16 × 25 = 2 = 25 × reciprocal of 25 = 25 1 8 1 Therefore, 2 glasses are filled. 50 1/7/2019 3:17:27 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 82

Drill Time Concept 10.1: Add and Subtract Mixed Fractions 1) Solve: a) 3 4 + 2 3 b) 2 1 + 7 2 c) 12 1 + 13 2 d) 10 1 2 75 85 75 + 12 33 b) 10 1 – 5 3 2) Solve: 27 1 – 2 1 c) 7 2 – 4 1 d) 12 3 – 11 2 a) 4 84 89 37 Concept 10.2: Multiply Fractions 3) Multiply fractions by whole numbers. a) 12 × 64 b) 3 × 80 c) 4 × 100 d) 3 × 49 32 8 20 7 4) Multiply fractions by fractions. a) 22 × 26 b) 4 × 16 c) 3 × 51 d) 7 × 45 13 44 12 24 17 21 15 49 Concept 10.3: Reciprocals of Fractions 5) Find the reciprocal of the following: a) 27 b) 2 1 d) 50 53 c) 5 23 2 d) 1 by 1 7 49 6) Divide: a) 16 by 1 b) 14 by 2 c) 1 by 3 4 7 42 Fractions - II 51 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 83 1/7/2019 3:17:27 PM

EVS−I (Science) Contents 5Class 6 Plants and Environment������������������������������������������������������������������������������������� 1 7 Food for Animals������������������������������������������������������������������������������������������������� 6 8 Food Production���������������������������������������������������������������������������������������������� 10 9 Forests as Shelter��������������������������������������������������������������������������������������������� 15 Inside the Lab – B��������������������������������������������������������������������������������������������������� 19 Activity B1: Seed Germination Activity B2: Food Web NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 84 1/7/2019 3:17:27 PM

Lesson Plants and Environment 6 Let Us Learn About r habitats and habits of plants. u adaptations of plants. a protection of plant environments. h sacred groves. Think Seema planted a lotus plant in her garden and watered it. But it drooped down and dried up within a few days. What can be the reason for this? Remembering Plants can be found almost all over the Earth. They grow on land as well as in water. These places are called their habitats. Let us learn more about the habitats of plants. TERRESTRIAL The plants that grow on land are known as terrestrial plants. They grow in PLANTS different areas like mountains, plains, deserts, swampy areas, coastal areas and so on. plants on mountains plants in plains plants in deserts plants in swampy areas plants in coastal areas 1 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 85 1/7/2019 3:17:27 PM

AQUATIC PLANTS Plants that grow in water are called aquatic plants. They are of three kinds – floating, fixed and underwater plants. Floating plants: These plants are found floating freely on water. water lettuce They are not attached to the bottom of the water body. lotus For example, water lettuce, water hyacinth and so on. Fixed plants: These plants have roots that are fixed to the soil at the bottom of the water body. Their leaves and flowers float on the surface of the water to get oxygen from the air and sunlight. They have broad and wax coated leaves. This wax coating prevents the leaves from rotting due to water. For example, lotus, water lily and so on. Underwater plants: These plants grow completely under the water. They take in carbon dioxide from the water. For example, seagrass, tape grass and so on. seagrass Now, let us learn about some habits of plants. Plants also differ according to their food habits. Plants that make food on their own: Most green plants make their own food. They absorb water and nutrients from the soil with the help of roots. Leaves produce food by combining carbon dioxide and water using energy from sunlight. Plants which depend on other plants: Some plants such as the cuscuta plant cuscuta and sandalwood tree absorb water and nutrients from the roots of other plants. Such plants that depend on other plants for their food are called parasitic plants. Plants that eat small insects: Some plants trap small insects and digest pitcher plant them. Such plants are called insectivorous plants. For example, pitcher plant, Venus flytrap and so on. Understanding Plants grow on land and in water. They have different food habits. Due to these differences, the plants have different features. The body features and special characteristics that help the plants to live successfully in a particular environment are called their adaptations. 2 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 86 1/7/2019 3:17:27 PM

ADAPTATIONS OF TERRESTRIAL PLANTS leaves of a mountain plant Mountain plants: They are tall, straight and conical. They have narrow needle-shaped leaves. The conical conical shape shape does not allow the snow to remain on their of mountain leaves. If the trees in cold places are not conical in plants shape, snow will collect on the branches. Due to the weight of the snow the branches will break. Plants in plains: They have many branches that spread out. These branches help them to absorb maximum sunlight. branched stem of a tree Desert plants: They have fleshy green stems that store water. Their leaves are reduced to spines to prevent water loss. They have extensive roots. stem of a desert plant Plants in swampy areas: Swampy areas have very sticky and clayey breathing roots soil. So, it is difficult for plants to grow because air cannot reach the roots. Hence, the plants in swampy areas have breathing roots. Such roots come out of the soil for oxygen and sunlight. Breathing roots are roots in the air that help plants to breathe. Plants in coastal areas: These plants have to adjust stem of a leaves of a to strong winds and heavy rainfall. Coconut trees coconut tree coconut tree are mainly found in coastal areas. They have sturdy, flexible stems and thick leaves with many long strips air pockets to overcome strong winds. waxy leaves ADAPTATIONS OF AQUATIC PLANTS Floating Plants: Their leaves and stems are light and spongy due to waxy leaves and the presence of air pockets. Air gets filled in these pockets. It helps them to float on water. Fixed plants: Their leaves are broad. The upper surfaces of the leaves of floating and fixed plants have a waxy layer. This waxy coating prevents the leaves from rotting due to water. Underwater plants: They have narrow and slender leaves. narrow leaves They breathe inside water. Plants and Environment 3 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 87 1/7/2019 3:17:27 PM

Adaptation of Plants According to Food Habits Plants which produce plants Parasitic plants food have green that have special roots. leaves and a well produce Using these roots, developed root food they absorb the system. Leaves are food and water positioned in such a from other plants. cuscuta way that they receive Cuscuta is one maximum sunlight. such plant. insect on the rim of the Insectivorous plants have special structures flap pitcher to trap and digest insects. For example, the rim pitcher plant has a pitcher (pot-like structure) pitcher insect with a flap. The flap produces nectar that trapped attracts insects. The rim of the pitcher is parts of inside the slippery. So the insects slip inside. The pitcher a pitcher pitcher is deep. Moreover, the inside wall is difficult to climb. So the insects drown and dissolve in the liquid present inside the pitcher. Application Plants benefit from their environment. Environment provides all the necessary support to the plants. How do plants support their environment? In the process of photosynthesis, plants: • take in carbon dioxide gas from the air. • release oxygen. • trap the energy of the Sun (light energy). • trap nutrients from the soil. Roots hold the soil firmly which helps to: • prevent soil erosion. • conserve water. Plants support wildlife by providing shelter. 4 1/7/2019 3:17:27 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 88

How do human activities affect the environment? • D ue to human activities, the natural environment of plants is being destroyed. Humans cut down trees for firewood, timber, medicinal purposes and many more. This has destroyed the natural habitats of plants and animals. • Some plants we see around have been introduced in our country from lantana distant places. Some such introduced plants spread rapidly destroying the environment of other local plants by competing for soil, water, nutrients and sunlight. For example, lantana What measures are being taken by the government? Due to the cutting of trees, some trees have disappeared talipot palm soap nut tree from the Earth. Some trees may disappear if we don’t protect them. So, they are given protection by the government. Example: sandalwood tree, Malabar mahogany, talipot palms, soap nut tree. Amazing Facts The General Sherman Redwood tree in California is about 2300–2700 years old. Higher Order Thinking Skills (H.O.T.S.) Why do we celebrate Vanamahotsava? It is a yearly tree-planting movement in India. It began in 1950. It means the ‘festival of trees’. It is celebrated to create awareness about forest conservation and planting trees. Another practice has also been sacred groves followed since olden days to conserve trees. Some small forest areas are worshipped and protected by different communities. These areas are called sacred groves. Find out more about sacred groves. Plants and Environment 5 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 89 1/7/2019 3:17:27 PM

Lesson Food for Animals 7 Let Us Learn About r herbivores, carnivores and omnivores. u body adaptations of animals to suit their eating habits. a food chain and food web. h how some animals may disappear from the Earth. Think Saleena was eating lunch. She found a squirrel on a tree near the window. She wondered where it got its food from. Do you know how animals find food? Remembering Animals cannot make their food. So, they eat plant parts or other animals that they find in their surroundings. For example, a squirrel finds its food from the surroundings. It collects fruits and nuts from different plants. It may eat some insects too. Have you seen a squirrel collecting groundnuts a squirrel eating termites squirrels eating termites? 6 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 90 1/7/2019 3:17:27 PM

What does a cow eat? Does it eat termites like the squirrel? No. It eats grass, fruits or vegetables. Animals around us differ in their eating habits. They are of three types based on their eating habits. 1) Herbivores (‘herb’ means ‘a plant’, and ‘vore’ means ‘eat’): These are animals which eat only plant parts as their food. Cows, rabbits, deer are a few examples of herbivores. a cow eating grass 2) Carnivores (‘carni’ means ‘flesh’, and ‘vore’ means ‘eat’): These animals eat other animals as their food. For example, the lion, tiger, leopard and so on. 3) Omnivores (‘omni’ means ‘all’, and ‘vore’ means ‘eat’): These animals eat both plants and animals as their food. For example, human, bear, crow, squirrel and so on. herbivores carnivores omnivores Understanding Now, let us learn how animals find food themselves ants have a sharp from their surroundings. sense of smell If we happened to spill some sugar on the floor, within minutes, it would be surrounded by ants. How do they find it? They can smell it. If we sit outside the house or school to have some food, a crow may fly down and take away our food. Food for Animals 7 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 91 1/7/2019 3:17:27 PM

Birds can see things from far away. So, they notice the food on our plate even when they fly high in the sky, or sit on a tree far away from us. Animals find their food with the help of their senses. Their eagles spot their prey senses are far stronger than ours. Can we smell the sugar kept from far away in a container inside the cupboard? No. But, ants can. This strong sense of smell helps them to find their food. In the same way, birds can find food with the help of their sharp eyes. Have you seen a cat waving its ear, when we make a scratching sound on the table or ground? They have a sharp sense of hearing. This helps them to find their prey. Do you remember reading about birds and beaks and that the cats have a sharp sense shapes of beaks are suitable for the food they eat? Similarly, have of hearing you ever observed the teeth of a cow? Are they different from that of a dog? Cows have flat teeth. But dogs and cats have sharp, pointed teeth. Why are they different? It is because the food they eat is different. a dog has sharp teeth Cows eat grass. They need flat teeth to grind the plant parts. Dogs and cats eat flesh. They need sharp teeth to tear the flesh. A rabbit has strong front teeth. These help the rabbit to bite food like carrots easily. Some animals use their tongue to sense the prey as well as to catch them. For example, frogs and lizards. Snakes have many senses that help them to find their food. They strong front teeth sense the movement and smell of their prey. help a rabbit to bite a frog uses its tongue to catch the prey a snake uses its sense of smell and movement Application What does an eagle eat? It eats small animals like rats. What do the rats eat? They eat fruits and seeds of plants. From where do these plants get their food? They make their food using sunlight, carbon dioxide, water and nutrients. 8 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 92 1/7/2019 3:17:28 PM

In this way, plants and animals are linked to each other by eating and being eaten. This is called a food chain. a food chain food web Food chains are also connected to each other. For example, plants can be eaten by a deer or a rabbit. The deer can be eaten by not only a lion but also a tiger. The plants can be eaten by a mouse. The mouse can be eaten by a large bird. Such connected food chains form a food web. Amazing Facts The largest carnivore on Earth is the South Atlantic elephant seal. It usually weighs 3,500 kg. South Atlantic elephant seal Higher Order Thinking Skills (H.O.T.S.) All animals need food to live. What will happen if they do not get enough food from the surroundings? Some of them may die. Their number will decrease in that area. If the food in the surroundings became more scarce, their number will decrease further. In this way, some animals may disappear from the surface of the Earth. Many animals have disappeared from the Earth in this way. Some animals are in danger now. Only a few of their kind are left. The Asiatic lion, Bengal tiger, red panda, snow leopard are few animals whose number has decreased. Asiatic lion Bengal tiger red panda snow leopard Food for Animals 9 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 93 1/7/2019 3:17:28 PM

Lesson Food Production 8 Let Us Learn About R farms. U how farmers grow food plants. A the journey of food from the farms to our homes. H growing plants without harming the environment. Think Arvind enjoys eating mangoes, and his favourite vegetable is spinach. What are your favourite fruits and vegetables? Have you ever thought about where these food items come from and how they reach your house? Remembering We buy fruits, vegetables, grains, pulses and so on from the market. We also buy milk, meat and fish. We know that all these food items come either from plants or animals. Where are all these plants and animals grown? Who takes care of them? Let us find out. In villages, you must have seen open fields where some plants are grown. You may have seen some people working in those fields. There may have also been some animals like goats, 10 1/7/2019 3:17:28 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 94

cows, buffaloes and so on. These are farms. A farm is a piece of land used to grow crops and raise animals. People grow different types of useful plants on farms. In some farms, animals that give eggs, milk and meat are also grown. Growing useful plants and raising livestock on a farm is called farming. The people who do these activities are called farmers. farming What are the different types of plants and animals farmers grow on their farms? They grow plants which give us food like vegetables, fruits, cereals, pulses, oilseeds and spices. They also grow sugar cane, tea plant, coffee plant, rubber tree and so on. The animals which are reared on farms include birds like chickens and ducks, cows, buffaloes, goats, pigs and so on. Some farmers rear fish, prawns and so on. Understanding How does a farmer grow plants on his or her farm? Let us find out. 1 First, the farmer has to decide which crops to grow. You know that plants grow from the seeds. So, to grow plants, the farmer needs seeds of these plants. He or she may use the seeds already stored or may buy them from some other people. 2 We have learnt that seed germination needs air, water, sunlight and nutrients from the soil. Once the seeds are ready, the farmer prepares the land to sow these seeds. The soil is cut, lifted, turned over and crushed. This is done to make sure that the soil becomes loose and airy. This help the seeds to get more air and sunlight to germinate. A plough is used to prepare the soil. preparing the soil using animals and machines Farmer may use the plough with the help of animals such as oxen and buffaloes. They may also use machines such as a tractor for this purpose. 3 Plants need nutrients from the soil to grow. So, some nutrient-rich materials are mixed with the soil. Food Production 11 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 95 1/7/2019 3:17:28 PM

4 Then, the seeds are put in the soil and sowing covered with a loose layer of soil. This is sowing. 5 After sowing, the field is watered to help the seeds to germinate. In a few days, small plantlets growing plantlets will grow from the seeds. from seeds 6 They water the plants regularly with the help of water channels made in the fields. They may use sprinklers too. To grow some plants, the entire field needs to be flooded with water. field flooded field watered water channels with water using sprinklers in a farm 7 Farmers remove grass or any other unwanted plants which may grow in the field. 8 Once the plants reach a certain stage of growth, some more nutrient-rich materials may be added to the soil to help the plants grow. 9 Fully grown plants give rise to flowers and fruits. Then, the useful parts of the plants are collected from them. This is called harvesting. In some plants, the fruits are harvested. In other plants, parts such as the stem, leaves, flowers or seeds are harvested. Harvesting is done by people or with the help of machines. While harvesting, some unwanted plant parts may also come along. These are removed, and the required parts of the plant are cleaned up to be used as food. harvesting 12 1/7/2019 3:17:28 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 96

Application The food harvested from farms needs to be stored in a safe place. Otherwise, they will get spoilt. From the farms, they are carried to their storage places. These storage places are called godowns. These godowns are kept dry and airy. godowns They are also kept free from insects and animals like rats that eat the food items. From these godowns, food is transported to the main markets. From the main market, this reaches the local markets. We buy this food from the local market for our use. Amazing Facts Some of the first food plants to be grown by humans were wheat and barley. Although the method used to grow them has changed, we still grow the same plants as we did around 10,000 years ago! barley wheat Higher Order Thinking Skills (H.O.T.S.) On farms, farmers grow so many plants. They may grow more than one set of plants in a year. They will repeat this practice year after year. If the same types of plants grow in the soil for many years, some soil nutrients may get completely used up. Some nutrients, which are not used by that type of plant, may pile up in the soil. Moreover, the farmers use some chemicals to increase the growth of plants. They also use chemicals to kill harmful plants and insects on the farm. These chemicals will kill even Food Production 13 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 97 1/7/2019 3:17:28 PM

the useful organisms in the soil like earthworms. In these ways, farmlands may change into wastelands over the course of time. Some plants need a lot of water to grow. So growing such plants in huge numbers may lead to water shortage in that area. So, it is important to grow plants without harming the environment. How can we do that? 1) Some farmers do not use chemicals on their farms. They use plant and animal made materials to increase plant growth and reduce the harmful insects. For example, they use animal waste like cow dung, ash and plant waste like fallen leaves of trees to add nutrients to the soil. They use manure made of all these things. Farmers spray juice of the leaves of some plants like the neem to kill insects. 2) Another practice is to grow different plants in the same field one after the other. For example, in rice fields, after the harvesting of rice, they will grow vegetables like peas, cucumbers, pumpkins and so on. This helps to keep the nutrients in soil at a proper level. 3) In areas where there is less water, choosing plants that need less water will be helpful. 14 1/7/2019 3:17:28 PM NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 98

Lesson Forests as Shelter 9 Let Us Learn About R different types of forests. U life in the forests. A the uses of forests to living things. H the need to protect the forest cover of the Earth. Think One day Samarth found a beautiful bird’s picture in one of the magazines his father bought for him. His dad told him that the bird could not be found in cities. It lived only in forests. Also, he promised to take him to a forest someday. Do you know what a forest is? Remembering forest with cone shaped trees When we travel to different places, we may see some lands that are covered with many trees and plants. These trees are not grown by people. They just grow on their own. These are forests. Forests are lands with many trees. There are different types of forests on the Earth. For example, forests found in cold mountains have cone shaped trees with needle-like leaves. Forests which grow in warm areas with high rainfall have trees with broad leaves. NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 99 15 1/7/2019 3:17:28 PM

Forests which get rain throughout the year evergreen rainforest forest which changes remain green always. We call them evergreen colour rainforests. But, in some other forests, during the autumn season, the colour of the leaves changes to yellow, orange and red and they fall off. Then, the trees grow new leaves. Understanding Have you ever visited a forest? What are the things we can find inside a forest? Let us read what Samarth found when his father took him to a forest. “Once we entered the forest, the air felt cool and fresh. We could hear the chirping of different birds and the sound of beetles. There was beetle no proper road to walk. The guide in front of us guided us through a monkeys on a tree narrow way between the bushes. When I looked up, I could not see the sky properly. The branches branches of trees were spread forming a cover overhead. covering the sky I could find many types of birds on the trees. There was a group of monkeys on the branches of a huge tree. They were eating some berries. On one of the branches, there was a huge beehive. Suddenly I heard a rustling sound from the ground. I berries beehive could see a snake crawling fast. It disappeared in the bushes. The ground was covered with leaves and animal droppings. It was spongy to walk. Using a stick, I removed some layers of leaves which covered the ground. Below them, I could find dark coloured soil. It was loose. I could find some earthworms, a snail and some other insects in it. There were huge termite mounds here and there. crawling snake forest soil Different types of ants and some other insects were on the ground and tree trunks. One big spider was weaving a web on a bush. Some tree trunks were covered with a spongy green growth. My mother said that they were small plants which grew ground covered termite mound only in moist places. Along with them, there were some with leaves plants with palm tree like leaves. 16 NR_BGM_9789386663504 MAPLE G05 INTEGRATED TEXTBOOK TERM 2_Text.pdf 100 1/7/2019 3:17:28 PM