202110217-TRIUMPH-STUDENT-WORKBOOK-MATHEMATICS-G06-PART1

5. [AS5] 9 + (–4) + 3 = 8 is represented on the number line as . (A) (B) (C) 98 (D)None of these Short Answer Type Questions 6(i) [AS1] a) Add the integers: 10, (–13), 11. b) Add: (–215), 100, (–50). c) Find the sum of –68, –100 and 200. d) Find –10 + 23 + (–12). (ii) [AS1] a) Find the value of 53 + (–26) + (–28). b) Add: 3958, –3959 c) Add: –729, –7098, 729, –2 d) Add: –4004, –999 e) Find the sum: 1393 + (–407) + (–872) + 690 f) Find the sum: 703 + (–3) + (–1) + 1 + (–400) + 0 7(i) [AS1] Add the following integers. a) 8, ( –5) b) –3, 9 EXERCISE 6.3. ADDITION OF INTEGERS

(ii) [AS1] Find the value of the following. a) 6 + (–10) + 12 + (–4) b) (–11) + 9 + (–7) + 13 8 [AS4] Neeraj travelled 25 km north and Amit travelled 89 km south from the same point. Find the distance between the final destination of the two. Long Answer Type Questions 9 [AS5] Find the value of the following using the number line: (i) –2 + (–3) + (–5) (ii) (–8) + (–9) + (+17) 10 [AS5] Find the value of the following using the number line: (i) –3 + 8 – 6 (ii) –6 + (–2) + 5 EXERCISE 6.3. ADDITION OF INTEGERS 99

EXERCISE 6.4 SUBTRACTION OF INTEGERS 6.4.1 Key Concepts i. When two negative integers are added, we get a negative integer as the sum. ii. Subtracting one integer from another is the same as adding its additive inverse to the other. 6.4.2 Additional Questions Objective Questions 1. [AS1] 8 – 3 = . (A) 5 (C) 11 (B) –5 (D) –11 2. [AS1] –8 –(–7) = . (A) –15 (B) 1 (C) –1 (D)None of these 3. [AS1] –8 + 7 – 3 = . (B) 18 (D) –4 (A) 4 (B) –6 (C) –18 . (D) –80 . 4. [AS1] 25 + (–13) –(–12) – 30 = (B) –24 (A) 6 (D) –62 (C) 80 5. [AS1] –38 + 21 –(–17) + 24 = (A) 24 (C) 62 EXERCISE 6.4. SUBTRACTION OF INTEGERS 100

6. [AS2] The pair(s) of integers that have 9 as a difference is/are . (A) 19,10 (B) –19,–10 (C)19, –10 (D)Both (A) and (B) 7. [AS2] The number that must be added to 18 to get –34 is . (A) 52 (B) –52 (C) 34 (D) 96 8. [AS2] The number that must be subtracted from –23 to get –70 is . (A) 48 (B) 52 (C) 34 (D) 96 9. [AS2] If x is a negative integer such that −x = 5 then x = . (A) 5 (B) –4 (C) –5 (D) –9 10. [AS4] In a quiz show, team A scored –30, 20, 5 and team B scored 10, 0, –20 in three successive rounds. The team that scored more is . (A) Team A (B) Team B (C) Both (D)None of these 11. [AS4] At the beginning of a day, Ravi had Rs.120. He gave Rs.70 to his friend. The amount left with him is . (A) Rs. 50 (B) Rs. 30 (C)Rs. 40 (D)Rs. 70 12. [AS4] One evening in Shimla, the temperature was 1◦C. At midnight it became 4◦C colder. The temperature at midnight is . (A) −8◦C (B) 5 ◦C (C) −5◦C (D)-3 ◦C EXERCISE 6.4. SUBTRACTION OF INTEGERS 101

Very Short Answer Type Questions 13 [AS1] Fill in the blanks. (i) –30 + (–30) = . (ii) 38 – (–24) = . (iii) –20 + = –32. (iv) The difference when (–6) is subtracted from (–15) is Short Answer Type Questions 14(i) [AS1] Subtract: a) 30, 7 b) –20, –7 (ii) [AS1] Simplify: a) 47 –(12) –(23) –(–6) b) 35 –9 –(–8) –17 15 [AS4] John has to climb 65 steps of the stairs to reach a temple. He climbed 27 steps. How many steps does he have to climb to reach the temple? 16(i) [AS5] Subtract 4 from 7 using the number line. (ii) [AS5] Simplify 15 – (4) – (3) using the number line. Long Answer Type Questions 102 17 [AS1] Simplify the following: (i) (–21) + (–22) + (–21) (ii) –80 + (40) + (–30) + (6) + (–5) (iii) The sum of two integers is –396. If one of them is 64, find the other. (iv) Subtract the sum of 998 and –486 from the sum of –290 and 732. EXERCISE 6.4. SUBTRACTION OF INTEGERS

18 [AS1] Calculate: 1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + .......... + 19 − 20 19 [AS5] Using the number line simplify the following: 15 + (–6) –7 –3 + 8 –(–4) EXERCISE 6.4. SUBTRACTION OF INTEGERS 103

CHAPTER 7 FRACTIONS AND DECIMALS EXERCISE 7.1 TYPES OF FRACTIONS 7.1.1 Key Concepts i. Fraction: A fraction means a part of a group or of a whole. For example,35 is a fraction. Here, 3 is called the numerator and 5 is called the denominator. ii. Kinds of fractions: Proper fraction: A fraction is said to be a proper fraction if its numerator is less than its denominator. Ex: 2 , 5 etc. 7 9 Improper fraction: A fraction is said to be an improper fraction if its numerator is greater than or equal to its denominator. Ex: 7 , 9 , 6 etc. 2 5 6 Mixed fraction: An improper fraction can be written as a combination of a whole and a part. Such a fraction is called a mixed fraction. Ex: 4 3 , 2 1 , 7 5 etc. 5 3 6 23 3 3 1 1 5 5 5 = 4 5 = 4 + 5 ; 2 3 = 2 + 3 ; 7 6 = 7 + 6 Mixed fraction = (whole) + (part) . 7.1.2 Additional Questions Objective Questions 1. [AS3] A number representing a part of is called a fraction. (A) A number (B) An integer (C)A whole (D)A fraction 2. [AS3] A fraction with denominator greater than numerator is called fraction. (A) An equivalent (B) A proper (C)An improper (D)A like EXERCISE 7.1. TYPES OF FRACTIONS 104

3. [AS3] Fractions with the same denominator are called fractions. (A) Llike (B) Unlike (C) Equivalent (D) Proper 4. [AS3] A fraction with its numerator greater than its denominator is called fraction. (A) A proper (B) An improper (C)A like (D)An unlike 5. [AS3] 6 and 6 are fractions. 13 11 (A) Like (B) Unlike (C) Equivalent (D) Improper 6 [AS5] Choose the correct answer. (i) To represent 2 on a number line, each division is sub–divided into equal parts. 5 (A) 1 (B) 2 (C) 5 (D) 10 [AS5] Answer the following questions in one sentence. (ii) Show 7 on a number line. 10 (iii) Show the fractions −3 , 6 and 13 on a number line. 11 11 11 (iv) Represent 3 on a number line. 5 (v) Represent 3 on a number line. 10 Short Answer Type Questions 7(i) [AS1] Convert the given mixed fractions into improper fractions. a) 2 3 b) 5 8 5 15 (ii) [AS1] Convert the following mixed fractions into improper fractions. (i) 6 3 (ii) 3 5 (iii) 51 2 10 11 3 EXERCISE 7.1. TYPES OF FRACTIONS 105

8(i) [AS1] Write each improper fraction as a mixed fraction. a) 63 b) 101 c) 209 10 9 12 (ii) [AS1] Write these improper fractions as mixed fractions. a) 48 b) 236 11 19 9 [AS1] Express these improper fractions as mixed fractions. (i) 15 (ii) 25 (iii) 32 (iv) 85 13 12 18 16 10(i) [AS1] Express these mixed fractions as improper fractions. a) 2 7 b) 7 4 9 13 (ii) [AS1] Express each of the following improper fractions as a mixed fraction. a) 23 b) 37 c) 50 5 6 7 11(i) [AS3] Identify the numerators and denominators of the following fractions: a) 12 b) −9 31 17 (ii) [AS3] Write fractions as indicated. a) Numerator: 4, Denominator: 7 b) Numerator:18, Denominator: 25 c) Numerator: (2)(–7), Denominator: (–3)(–5) 12(i) [AS3] Identify proper fractions from the following. 100 , 125 , 3 , 2 , 51 93 80 14 9 25 (ii) [AS3] Identify improper fractions from the following. 3 , 51 , 13 , 83 , 102 , 96 8 12 25 20 35 45 13(i) [AS3] Classify the following fractions as improper or mixed: 1 2 , 6 , 2 5 , 8 , 12 , 3 2 3 5 8 3 5 9 EXERCISE 7.1. TYPES OF FRACTIONS 106

14(i) [AS4] The length of femur, the longest bone in the human body is 101 cm. Express this length as 2 a mixed fraction. (ii) [AS4] Sujith bought 15 3 kg of wheat. How is the weight of wheat expressed as an improper 4 fraction? 15(i) [AS5] Write the fraction for the shaded part in the following figures. a) b) c) (ii) [AS5] Write the shaded parts of the following figures as fractions. a) b) c) EXERCISE 7.1. TYPES OF FRACTIONS 107

16(i) [AS5] Write the fractions for the shaded part in the following figures. a) b) (ii) [AS5] Draw circles, divide them into parts and shade them as per the given fractions. a) 2 1 b) 5 1 c) 1 2 3 4 3 Long Answer Type Questions 17 [AS3] Define the following: (i) Equivalent fractions (ii) Like fractions (iii) Unlike fractions (iv) Mixed fractions 18 [AS5] Write improper fractions to represent the shaded parts of the following figures. (i) (ii) (iii) (iv) (v) EXERCISE 7.1. TYPES OF FRACTIONS 108

19 [AS5] Divide the following figures into parts and shade them as per the fractions given. (i) 3 1 6 (ii) 2 3 8 (iii) 4 1 4 (iv) 1 5 8 (v) 2 2 5 EXERCISE 7.1. TYPES OF FRACTIONS 109

20 [AS5] Colour the Indian flag and write what fraction of the Indian flag the following colours are. (i) White (ii) Orange (iii) Green (iv) White and Green 21 [AS5] Show the following fractions on a number line. 2 , 0 , 4 , 6 , 13 , 4 2 5 5 5 5 5 5 22 [AS5] Represent the following like fractions on a number line. 1 2 , 1 1 , 1 5 , 1 3 , 1 9 10 10 10 10 10 23 [AS5] Represent 2 2 on a number line. 5 EXERCISE 7.1. TYPES OF FRACTIONS 110

24 [AS5] Write mixed fractions for the shaded parts of the following figures. (i) (ii) (iii) (iv) (v) EXERCISE 7.1. TYPES OF FRACTIONS 111

EXERCISE 7.2 EQUIVALENT FRACTIONS 7.2.1 Key Concepts i. A fraction is said to be in the standard form (or lowest form) if its numerator and denominator have no common factor except 1. ii. Equivalent fractions of a given fraction can be obtained by multiplying or dividing both the numerator and the denominator by the same number. 7.2.2 Additional Questions Objective Questions 1. [AS1] A fraction which is equivalent to 2 is . 3 (A) 4 (B) 4 7 6 (C) 5 (D) 6 7 3 2. [AS4] Four pizzas are to be shared equally among 5 children. The share of each child is . (A) 5 (B) 1 4 4 (C) 1 (D) 4 5 5 3. [AS1] The fraction which is not equivalent to 2 is . 3 8 14 (A) 12 (B) 21 (C) 4 (D) 10 9 15 4. [AS1] 24 reduced to its simplest form is . 60 21 6 (A) 30 (B) 15 (C) 3 (D) 2 5 5 EXERCISE 7.2. EQUIVALENT FRACTIONS 112

5. [AS4] An astronaut who weighs 86 kg on the Earth would weigh 14 1 kg on moon. The weight of 3 the astronaut on the moon written as an improper fraction is . (A) 14 kg (B) 14 kg 3 6 (C) 43 kg (D) 43 kg 6 3 6. [AS4] If 5 is equivalent to x , then x = . 12 3 (A) 5 (B) 4 4 5 (C) 5 (D) 3 3 5 7. [AS2] If a = 4 , then the value of 6a + 4b is . b3 6a − 5b (B) 3 (D) 5 (A) –1 (C) 4 8. [AS2] If 3 is equivalent to x , then the value of x is . 4 28 (A) 6 (C) 8 (B) 21 (D) 9 9. [AS2] If 45 is equivalent to 3, then the value of x is . 60 x (B) 6 (A) 3 (C) 4 (D) 9 Short Answer Type Questions 10 [AS1] Convert the following set of unlike fractions into a set of like fractions. 1 , 1 , 5 , 4 3 2 6 5 11 [AS1] Find the value of ‘p’ in each pair so that the fractions are like fractions. (i) 2 , 3 5 p (ii) 25 , 32 70 p (iii) 18 , 15 36 p EXERCISE 7.2. EQUIVALENT FRACTIONS 113

12 (i) [AS3] Write like fractions that are proper fractions for the following. a) 1 , , , , b) 5 , , , , c) 3 , ,,, 6 5 7 (ii) [AS3] Write like fractions that are improper fractions for the following. a) 8 , , , , b) 12 , , , , 5 7 13 (i) [AS3] Write like fractions that are mixed fractions for the following. a) 1 3 ,,, 5 b) 418 , , , (ii) [AS3] Identify the sets of like fractions among the following. 5 , 3 , 1 , 12 , 8 , 6 , 7 12 5 8 15 12 12 12 14 [AS5] Represent the set of like fractions pictorially: 3 , 5 , 6 , 7 , 4 , 8 8 8 8 8 8 8 Long Answer Type Questions 15 [AS1] Write the standard form of each of the following fractions. (i) 12 (ii) 25 (iii) 55 (iv) 12 (v) 18 15 120 255 80 360 16 [AS1] Convert these fractions into standard form. (i) 56 (ii) 27 (iii) 16 (iv) 14 (v) 36 70 72 40 35 63 EXERCISE 7.2. EQUIVALENT FRACTIONS 114

EXERCISE 7.3 ORDERING , ADDITION AND SUBTRACTION OF FRACTIONS 7.3.1 Key Concepts i. Comparing like fractions: Since the denominators are the same, greater the numerator, greater is the fraction. For example, 5 = 5 , 5 < 7 < 9 10 10 10 10 10 ii. Comparing unlike fractions: To compare unlike fractions, we have to convert them into equivalent like fractions first. Then compare the like fractions. iii. Addition and Subtraction of unlike fractions: To add or subtract unlike fractions, we need to convert them into equivalent fractions with the same denominators. Then add or subtract. iv. Addition of mixed fractions: One way is to convert them into improper fractions and add. The other is to add the whole number parts and fractional parts separately, and write their sum. 7.3.2 Additional Questions Objective Questions 1. [AS3] The fraction that is less than 4 is . 3 (A) 5 (B) 2 3 3 (C) 1 1 (D) 7 3 3 2. [AS3] The fraction that is greater than 2 is . 6 1 2 (A) 3 (B) 3 (C) 1 (D) 2 4 7 3. [AS1] 1 + 7 = . 5 5 2 8 (A) 5 (B) 10 (C) 8 (D) 17 5 5 4. [AS1] 7 + 2 = . 8 4 (A) 9 (B) 11 12 8 (C) 9 (D) 11 8 4 EXERCISE 7.3. ORDERING , ADDITION AND SUBTRACTION OF FRACTIONS 115

5. [AS1] 11 − 7 = . 5 10 (A) 4 (B) 1 5 30 (C) 2 (D) 3 30 2 Very Short Answer Type Questions 6 [AS1] Answer the following questions in one sentence. (i) Subtract: 85 − 39 (ii) Subtract: 2 1 4 −2 55 (iii) Add: 3+7 22 22 Short Answer Type Questions 7(i) [AS1] Find the sum: 4 + 3 + 2 11 11 11 (ii) [AS1] Solve: a) 5 + ? + 1 = 10 b) 715 + 2 1 + 1 3 12 12 5 5 12 ? 8(i) [AS1] a) Subtract 2 from 7 . b) Subtract 6 2 from 11 4 . 9 9 7 7 (ii) [AS1] Simplify: a) 5 − = 2 8 8 b) 4 1 − 3 2 = 6 9 9 [AS1] Simplify: (i) 3 + = 6 7 7 (ii) 4 2 − 3 1 = 5 5 EXERCISE 7.3. ORDERING , ADDITION AND SUBTRACTION OF FRACTIONS 116

10 [AS2] Compare the following fractions. (i) 2 5 ii) 11 11 iii) 27 43 3 3 9 9 31 31 11(i) [AS2] Which is greater: 3 or 4 ? 5 7 (ii) [AS2] Which is smaller: 12 or 11 ? 17 15 Long Answer Type Questions 12 [AS1] Add: (i) 3 + 2 + 5 5 7 35 (ii) 8 + 4 + 12 25 15 50 (iii) 1 + 2 + 4 5 10 20 13 [AS1] Arrange the following fractions in ascending order: 2 , 34, 7 , 75 , 4 3 9 5 14 [AS1] Arrange the following fractions in descending order: 15 [AS1] Add: (i) 8 + 3 + 1 + 5 8 8 9 9 (ii) 1 2 + 2 1 + 1 2 + 1 3 15 15 5 5 (iii) 12 + 11 + 9 + 1 5 5 4 4 16 [AS1] Simplify: (i) 2 3 + 1 3 − 3 2 5 10 15 (ii) 1 + 3 − 1 6 8 4 (iii) 7 + 1 − = 1 12 12 2 17 [AS1] (i) Simplify:7 2 + 1 1 + 4 7 3 4 12 (ii) 2 3 + 6 15 − 3 5 = 5 + 8 16 8 (iii) 99 1 + 99 3 + 99 5 − 99 2 . 7 7 7 7 EXERCISE 7.3. ORDERING , ADDITION AND SUBTRACTION OF FRACTIONS 117

18 [AS2] Fill the boxes with an appropriate sign (<, = or >). (i) 1 1 (ii) 2 3 (iii) 3 2 (iv) 3 2 2 5 4 6 5 3 4 8 19 [AS4] A school wants to make a new playground by cleaning up an abandoned plot that is shaped like a rectangle.They give the job of planning the playground to a group of students. The students decide to give 1 of the playground for basket ball court and 38of the ground for soccer field. How 4 much is left for swing and other play equipment? 20 [AS5] Write these fractions appropriately as additions or subtractions: (i) (ii) (iii) EXERCISE 7.3. ORDERING , ADDITION AND SUBTRACTION OF FRACTIONS 118

EXERCISE 7.4 PLACE VALUES IN A DECIMAL NUMBER AND ORDERING OF DECIMALS 7.4.1 Key Concepts i. In a decimal number, the dot represents the decimal point and it comes between the ones place and the tenths place. ii. Every fraction with denominator 10 and its multiple can be written in decimal notation and vice–versa. iii. One block divided into 100 equal parts means each part is 1 (one–hundredth) of a unit. It 100 can be written as 0.01 in decimal notation. 7.4.2 Additional Questions Objective Questions . 1. [AS3] The digit in the tens place of the decimal number 3267.58 is (A) 8 (B) 6 (C) 7 (D) 3 2. [AS3] The digit in the tenths place of the decimal number 826.48 is . (A) 8 (B) 6 (C) 4 32 (D) 2 3. [AS3] 3.2 (B) < (A) > (D)> or = (C) = 4. [AS3] 7.6 7.66 (A) > (B) < (C) = (D) < or = EXERCISE 7.4. PLACE VALUES IN A DECIMAL NUMBER AND ORDERING O. . . 119

5. [AS3] 0.2 0.02 (A) > (C) = (B) < (D) < or = Very Short Answer Type Questions 6 [AS3] Answer the following questions in one sentence. (i) Write the place value of the underlined digit: 23.1 5 6 (ii) Write the place value of the underlined digit: 5.0 8 (iii) Write the place value of the underlined digit: 12. 8 7 (iv) Write the place value of the underlined digit: 0.6 1 (v) Write the place value of the underlined digit: 156.92 3 7 [AS3] Answer the following questions in one sentence. (i) Write the decimal number for 3 tenths and 9 hundredths. (ii) Write the decimal number for 898 thousandths. (iii) Write the decimal number for 6 ones 5 tenths 9 hundredths 8 thousandths. (iv) Write the decimal number for one hundred twenty five thousandths. (v) Write the decimal number for two hundred sixty five and forty six ten thousandths. Short Answer Type Questions 8(i) [AS3] Rewrite in ascending order. a) 0.04, 1.04, 0.14, 1.14 b) 9.09, 0.9, 1.1, 7 (ii) [AS3] Find the greater in each pair. a) 0.2 or 0.4 b) 70.08 or 70.7 c) 6.6 or 6.58 EXERCISE 7.4. PLACE VALUES IN A DECIMAL NUMBER AND ORDERING O. . . 120

9(i) [AS3] Rewrite in descending order. a) 8.6, 8.59, 8.09, 8.8 b) 6.8, 8.66, 8.06, 8.68 (ii) [AS3] Write the following decimals in descending order. a) 5.893, 5.983, 5.903, 5.938 b) 0.786 , 0.706, 0.760, 0.768, 0.756 c) 0.1007, 0.0071, 0.0710, 0.0171 Long Answer Type Questions 10 [AS2] Convert the following fractions to decimals: (i) 15 (ii) 512 (iii) 28 (iv) 498 (v) 39 1000 100 100 10000 10 11 [AS4] Write the fractions for the following decimals: 0.009, 23.15, 0.817, 100.001, 0.16. 12 [AS4] Jamila is working out a problem involving 1 . She needs to enter this fraction into a calculator. 4 1 How would she enter 4 as a decimal on the calculator? EXERCISE 7.4. PLACE VALUES IN A DECIMAL NUMBER AND ORDERING O. . . 121

EXERCISE 7.5 ADDITION AND SUBTRACTION OF DECIMAL FRACTIONS 7.5.1 Key Concepts i. To add or subtract two decimals numbers, first write them one below the other such that their decimals points are exactly one below the other, and all the corresponding digits are also one below the other. Then add or subtract. 7.5.2 Additional Questions Objective Questions 1. [AS4] The normal body temperature is 98.6◦F. Ravi’s temperature rose by 3.5◦F. Ravi’s temperature is . (A) 101.1◦F (B) 102.1◦F (C) 95.1◦ F (D) 100.1◦ F 2. [AS1] 5206 m – 2.015 km expressed in km is . (A) 31.91 km (B) 3.191 km (C)0.3155 km (D)315.5 km 3. [AS1] The value of 4 + 4.44 + 44.4 + 4.04 + 444 is . (A) 500.88 (B) 577.2 (C) 495.22 . (D)472. 88 4. [AS1] 1 + 0.1 + 0.01 + 0.001 = (B) 1.011 (A) 1.001 (C) 1.003 (D) 1.111 EXERCISE 7.5. ADDITION AND SUBTRACTION OF DECIMAL FRACTIONS 122

5. [AS1] 8932 cm is greater than 9685 mm by . (B) 79.635 cm (A) 796.35 cm (D)79625 cm (C)7963.5 cm Very Short Answer Type Questions 6 [AS1] Answer the following questions in one sentence. (i) Add: 0.07 + 0.42 (ii) Subtract: 7.61 − 5.13 Short Answer Type Questions 7 [AS1] Find the sum of the following decimals. (i) 14.01 + 1.1 + 1.98 (ii) 2.3 + 18.94 (iii) 2.57 + 3.75 8 [AS1] Subtract: (i) 25.11 – 3.80 (ii) 9.85 – 0.61 9(i) [AS1] a) Find the value of 28.796 –13.42 – 2.555. b) What should be added to 39.587 to get 80.375? (ii) [AS1] a) Subtract the sum of 2.832 and 8.56 from sum of 13.95 and 1.008. b) Find the difference between 8.125 and 0.8125. 10 (i) [AS4] Shamim sent three packets by post. One weighed 879 g 54 mg, the second weighed 98 g 653 mg and the third weighed 2856 mg. Find the total weight of the packets. (ii) [AS4] An empty box weighs 1 kg 240 g. When filled with oranges it weighs 19 kg. What is the weight of the oranges? EXERCISE 7.5. ADDITION AND SUBTRACTION OF DECIMAL FRACTIONS 123

Long Answer Type Questions 11 [AS1] (i) Take out 19.38 and 56.025 from 200.111. (ii) What should be subtracted from 82.120 to get 21.859? EXERCISE 7.5. ADDITION AND SUBTRACTION OF DECIMAL FRACTIONS 124

CHAPTER 8 DATA HANDLING EXERCISE 8.1 RECORDING AND ORGANIZh{pvu OF DATA 8.1.1 Key Concepts i. Data is a collection of numbers gathered to give some information. ii. To quickly get a particular information from a given data, it can be arranged in a tabular form using tally marks. 8.1.2 Additional Questions Objective Questions 1. [AS3] A collection of information is called . (A) Information (B) Data (C)Frequency (D)Tally marks 2. [AS3] The number of times a particular value occurs in the data is called its . (A) Frequency (B) Data (C)Information (D)Range 3. [AS3] If represents 10 books, then represents books. (A) 3 (B) 40 (C) 100 (D) 1000 EXERCISE 8.1. RECORDING AND ORGANIZATION OF DATA 125

4. [AS3] The representation of data using pictures or symbols is called a (A) Histogram (B) Bargraph (C) Pictograph (D)Frequency table 5. [AS3] The width of the bars in a bar graph for all bars. (A) Remains the same (B) Is different (C)Increases from left to right (D)Decreases from left to right Long Answer Type Questions 6 [AS5] The following observations show the number of children present for daily sports practice during the month of August. Arrange the data as a frequency distribution. 35 40 40 38 40 40 36 34 40 40 38 37 40 35 38 39 40 38 40 37 35 34 35 36 37 38 35 40 35 38 7 [AS5] The weight (in g) of 36 oranges picked at random from a basket are as follows. 65 73 68 73 71 66 70 72 66 72 70 65 73 65 65 70 71 67 68 69 68 67 70 69 68 67 69 67 72 70 70 67 68 67 73 70 Arrange the data in a suitable frequency distribution. EXERCISE 8.1. RECORDING AND ORGANIZATION OF DATA 126

EXERCISE 8.2 REPRESENTATION OF DATA 8.2.1 Key Concepts i. Data that has been organized and presented in frequency distribution tables can also be presented using pictographs and bar graphs. ii. A pictograph represents data in the form of pictures, objects or parts of objects. It can be drawn using symbols to represent a certain number of items or things. 8.2.2 Additional Questions Objective Questions 1. [AS3] If represents 90 trees, then represents trees. (A) 30 (B) 40 (C) 20 (D)None of these 2. [AS3] The number represented by is ________. (A) 4 (B) 5 (C) 6 (D)None of these EXERCISE 8.2. REPRESENTATION OF DATA 127

3. [AS5] The pictograph shows the capacity of 4 containers. The container that has a capacity of 1 litre is ______. 2 Bottle Flask Mug Glass Key: represents 100 ml (A) Bottle (B) Flask (C) Mug (D) Glass 4. [AS3] If the symbol represents 150 trees, then the number of trees represented by is _______. (A) 600 (B) 700 (C) 750 (D) 500 EXERCISE 8.2. REPRESENTATION OF DATA 128

5. [AS5] If represents 15 students, the group of symbols that represents 90 students is ______. (A) (B) (C) (D) Long Answer Type Questions 6 [AS5] The table shows the number of TV sets sold at Diwakar’s store. Make a pictograph by using pictures. Month Sales January 20 February 40 March 25 April 30 7 [AS5] The table given shows the number of students playing four different games: Games Football Hockey Cricket Badminton No. of 200 140 100 50 students Present this information as a pictograph. EXERCISE 8.2. REPRESENTATION OF DATA 129

8 [AS5] The pictograph shows the pocket money that six pupils get each week. represents 5 rupees (Rs. 5). Study the pictograph and answer the questions that follow. Rani – Sunder – Keerthana – Sravani – Sita ram – Ramakanth – (i) Who gets exactly Rs. 45? (ii) How much money did they get altogether? (iii) Who gets the maximum pocket money? (iv) Who gets the minimum pocket money and how much? (v) How many students got equal money? EXERCISE 8.2. REPRESENTATION OF DATA 130

9 [AS5] The pictograph shows the money spent by six pupils on buying notebooks. Radha Satish John Nirmala Rashid Vinay Using the given pictograph, answer the following questions. (i) Without counting, find the pupil who spent the least amount on buying notebooks. (ii) How much money did they spend altogether? (iii) Who spent exactly Rs. 40? (iv) How much money did Nirmala spend? (v) Who spent the maximum amount? EXERCISE 8.2. REPRESENTATION OF DATA 131

10 [AS5] The librarian of a school prepared a record of the number of library books borrowed by students on each day of a week. Then she made the pictograph given to show this information. Number of library books borrowed Monday – Tuesday – Wednesday – Thursday – Friday – Each represents 25 books. Using the given pictograph, answer the following questions. (i) On which day were the least number of books borrowed and how many? (ii) On which day were the maximum number of books borrowed and how many? (iii) How many books were borrowed on Tuesday? (iv) Altogether how many books were borrowed on the first three days of the week? (v) How many books in all were borrowed during the week? EXERCISE 8.2. REPRESENTATION OF DATA 132

EXERCISE 8.3 BAR GRAPH 8.3.1 Key Concepts i. Data can be represented by means of a bar diagram or a bar graph. ii. In a bar graph, bars of uniform width are drawn horizontally or vertically with equal spacing between them. iii. The length of each bar corresponds to the respective frequency. 8.3.2 Additional Questions Objective Questions Using the given bar graph, choose the correct option in the questions given. 1. [AS5] Cars of _______colour is the least common among the cars parked. (A) Black (B) White (C)Red (D)Grey 2. [AS5] The colours of the same number of cars parked are _______. (A) Black and Grey (B) White and Black (C)White and Red (D)Grey and White EXERCISE 8.3. BAR GRAPH 133

3. [AS5] The total number of cars in the parking lot is ________. (A) 20 (B) 35 (C)50 (D)40 4. [AS5] The fraction of the number of red cars to that of white cars is _______. (A) 5 (B) 2 2 5 (C) 3 (D) 1 1 3 5. [AS5] The colour of the cars that are the maximum in number is _______. (A) Black (B) White (C)Red (D)Grey Very Short Answer Type Questions . 6 [AS3] Fill in the blanks. (i) In a pictograph, if represents 20 apples, then represents (ii) If each represents 3 flowers, then represents . . (iii) The symbol represents . (iv) The tally mark representation for ‘10’ is . (v) In a bargraph, the height of a bar represents its EXERCISE 8.3. BAR GRAPH 134

Long Answer Type Questions 7 [AS5] The number of passengers arriving into a city during six months of a year is given. Drawa horizontal bar graph to represent the data taking 1 cm for every 5000 passengers. Month No. of passengers July 40,000 Aug 80,000 Sep 60,000 Oct 40,000 Nov 50,000 Dec 20,000 8 [AS5] The number of votes obtained by five contestants for the post of class representative in a 6thclass election is as given. Draw a vertical bar graph for the data. Student Shanker Joseph Pallavi Santosh Anoop Votes 15 25 20 10 30 obtained 9 [AS5] Survey of the favourite ice–cream flavour of 23 boys is as given. Represent it as a bar graph. –crIceeam Vanilla Chocolate Almond Pista Others 6 5 2 8 2 Favourite ice–cream of boys EXERCISE 8.3. BAR GRAPH 135

10 [AS5] The following table shows the marks secured by Sumit in the annual examination. English Maths Hindi Sanskrit Science Social 50 40 60 70 50 55 Draw a vertical bar graph to show the given information. EXERCISE 8.3. BAR GRAPH 136

CHAPTER 9 INTRODUCTION TO ALGEBRA EXERCISE 9.1 PATTERNS – MAKING RULES 9.1.1 Key Concepts i. Patterns follow a specific rule. By observing the pattern, we can extend it further. For example, if we need 3 match sticks to make a triangle, then we need (2 × 3) = 6 match sticks to make 2 triangles, (3 × 3) = 9 match sticks to make 3 triangles and so on. Continuing similarly, we can extend the pattern. Here, n × 3 gives the number of match sticks needed to form ’n’ number of triangles in the pattern. 9.1.2 Additional Questions Objective Questions 1. [AS3] One centimetre equals 0.3937 inches. The expression which gives the number of inches in x centimetres is _________. (A) 0.3937 − x (B) 0.3937 + x (C) 0.3937 x (D)0.3937 ÷ x 2. [AS3] The verbal expression that does not represent a − 8 is ________. (A) 8 less than a (B) a decreased by 8 (C)Take away 8 from a (D) a subtracted from 8 3. [AS1] The value of the expression 3ab, for a = 4 and b = 2 is _______. (A) 24 (B) 12 (C) 8 (D) 6 EXERCISE 9.1. PATTERNS – MAKING RULES 137

4. [AS1] The value of a2 + 2a − 3 for a = 2 is _______. (A) 11 (B) 6 (C) 5 (D) 4 5. [AS1] The expression that is not equal to 18 is ________. (A) 2t, for t = 9 (B) t – 5, for t = 23 (C) 3t + 3, for t = 5 (D) 9t ÷ 3, for t = 5 Short Answer Type Questions 6(i) [AS1] If a = 6 and x = 2, find the values of: a + 6x b) 2ax + 7x − 10 4ax − 3a − 2 a) 5a − 3x (ii) [AS1] Evaluate: a) pq(p + 3) + r f or p = 2, q = 3 and r = 1 b) 12p(q – r) for p = 1, q = 4, r = 2 c) 1 – x + y for x = − 2, y = − 7 7 [AS3] Write the algebraic expressions for: (i) Four times the sum of y and seven (ii) 25 decreased by four times ‘e’ (iii) Take away the product of 15 and t from 60 8 [AS4] The score of Manisha in mathematics is 25 more than two–thirds of her score in science. If she scored x marks in science, determine her score in mathematics. 9(i) [AS5] Find the rule which gives the number of match sticks required to make the following letters: a) T b) N (ii) [AS5] Observe the following pattern: How many line segments does each such shape contain? 138 EXERCISE 9.1. PATTERNS – MAKING RULES

Long Answer Type Questions 10 [AS1] Find the values of the following expressions for a = 4 and b = 2. (i) a + b (ii) a – b (iii) ab (iv) a b (v) 3ab (vi) a + 5b (vii) 3ab – 4b + 5 (viii) 5a − 2b 4ab − 8 11 [AS3] Write the algebraic expressions: (i) Radhika has 3 books more than twice the books with Rakesh. Write the relationship using the letter y. (ii) The cost of one pen is Rs. 7. What is the rule to find the cost of ‘n’ pens? (iii) The cost of 9 books is Rs. 23. Find the rule to buy 'n' books where n < 9 and then find the price of one book. (iv) Venu says that he has two books less than what Laxmi has. Write the relationship using the letter x. (v) A teacher distributes 6 pencils per student. How many pencils are needed for a given number of students? (Use ‘z’ for the number of students.) 12 [AS3] (i) How many weeks are there in ‘d’ days? Write an algebraic expression for it. (ii) A man has 350 watches. He sells ‘w’ watches everyday. Write an algebraic expression to show the number of watches he would be left with after ‘t’ weeks. EXERCISE 9.1. PATTERNS – MAKING RULES 139

13 [AS4] (i) Raja is 10 years older than Ravi. If Ravi’s age is x years, what is Raja’s age? (ii) A ball and a kite cost Rs. 65. If the ball costs Rs. b, what is the cost of the kite? 14 [AS4] (i) Each boy eats 5 toffees. How many toffees do ‘n’ boys eat? (ii) Sandy scores 8 marks in long answer type questions. For short answer questions, 2 marks are given for each correct answer. What is Sandy’s total score if she answers x short answer questions correctly? EXERCISE 9.1. PATTERNS – MAKING RULES 140

EXERCISE 9.2 EXPRESSIONS WITH VARIABLES 9.2.1 Key Concepts i. A variable takes different values. Its value is not fixed. ii. We may use any letter a, b, m, n, p, q, x, y, z etc. to represent a variable. iii. A variable allows us to express relations in any practical situation. iv. Variables are numbers, although their value is not fixed. We can do operations on them just as in the case of fixed numbers. v. We can form expressions with variables using different operations. Some examples are 2 - m, x 3s + 1, 8p, 3 etc. 9.2.2 Additional Questions Objective Questions 1. [AS3] ‘a’ increased by twice ‘b’ is written as______. (A) a + 2b (B) 2(a + b) (C)b + 2a (D)a + b 2. [AS3] “3 times the difference of 30 and c” is written as________. (A) 3(30) − c (B) 3(30 − c) (C)30 − 3c (D)3c –30 3. [AS3] “70 increased by the quotient of x and y” can be written as__________. (A) 70 − x (B) 70 × x y y (C) 70 + x (D) 70 ÷ x y y 4. [AS3] “3p + 5” can be written as________. (B) 5 more than 3 times p (A) 5 times product of 3 and p (D)5 times 3 times 3 and p (C)5 less than product of 3 and p EXERCISE 9.2. EXPRESSIONS WITH VARIABLES 141

5. [AS3] 6n –1 can be written as_________. (B) One less than six times ‘n’ (A) One and six times ‘n’ (D)One time six times ‘n’ (C)One more than six times ‘n’ Short Answer Type Questions 6 [AS3] 'n' represents any integer. Write the expression that represents any multiple of 3. 7 [AS3] Represent the numbers in terms of n, where 'n' represents any integer. (i) The square of any multiple of 5. (ii) The cube of any even number. Long Answer Type Questions 8 [AS3] Write each of the following statements as an expression. (i) n is increased by thrice m. (ii) Three times the sum of 30 and C. (iii) 70 decreased by the quotient of y and x. (iv) Length in centimetres that is 4 cm longer than y metres. 9 [AS3] The symbol ‘n’ represents any integer. Write the statement for the following expressions. (i) 3n (ii) 2n + 1 (iii) n − n 3 (iv) 2 n − 8 5 EXERCISE 9.2. EXPRESSIONS WITH VARIABLES 142

EXERCISE 9.3 RULES FROM GEOMETRY AND SIMPLE EQUATIONS 9.3.1 Key Concepts i. Variables allow us to express many common rules of geometry and arithmetic in a general way. ii. An equation is a condition on a variable. Such a condition limits the values the variable can have. iii. An equation has two sides, LHS and RHS on either side of the equality. iv. The LHS of an equation is equal to its RHS only for definite values of the variable in the equation. Such a value of the variable is called the solution of the equation. v. To get the solution of an equation, one of the methods used is the Trial and Error method. 9.3.2 Additional Questions Objective Questions 1. [AS3] 8 less than total number of students x is thirty. The equation that representsthe given statement is ________. (A) 8 − x = 30 (B) 30 − 8 = x (C) x + 30 = 8 (D) x − 8 = 30 2. [AS1] The solution of the equation –6 + a = 12 is_________. (A) –6 (B) 18 (C) 6 (D) –18 3. [AS3] The inverse of “Multiply by –3” is ________. (A) Divide by 3 (B) Multiply by 3 (C)Divide by –3 (D) Multiply by 1 3 EXERCISE 9.3. RULES FROM GEOMETRY AND SIMPLE EQUATIONS 143

4. [AS1] The solution of the equation “The difference between n and 16 is 5” is________. (A) 11 (B) –11 (C) 21 (D) –21 5. [AS1] The equation that does not have m = 42 as a solution is _______. (A) m = 6 (B) m = 1 7 42 (C) m = 13 (D) m = 2 4 21 Very Short Answer Type Questions 6 [AS3] Answer the following questions in one sentence. (i) Write any two simple equations and give their LHS and RHS. (ii) Identify LHS and RHS of the following equation. a + 7 = 12 (iii) Write the LHS and RHS of the equation 2z + 3 = 5z + 10. (iv) Write an equation for the statement ‘5 times a number ‘a’ equals to 20’ and identify its LHS and RHS. (v) Write an equation for the statement ‘14 more than a number ‘n’ equals 20’ and identify its LHS and RHS. Short Answer Type Questions 7(i) [AS1] Find the solution of the equation x – 4 = 2 by trial and error method. (ii) [AS1] Solve the equation 3x − 5 = 7 − x by trial and error method. EXERCISE 9.3. RULES FROM GEOMETRY AND SIMPLE EQUATIONS 144

8(i) [AS1] Complete the patterns given: x 2468 2x + 5 9 29 a 13 6 7 1 58 3a − 2 p 5 10 15 20 25 26 5p + 1 (ii) [AS1] The next term in the sequence 1, 10, 20, 31 is . 9(i) [AS3] a) Find the general rule for the perimeter of a rectangle. Use variables ‘l ’ and ‘b’ for length and breadth of the rectangle respectively. b) Find the general rule for the area of a square by using the variable ‘s’ for the side of a square. c) What is the rule for perimeter of an isosceles triangle? (ii) [AS3] a) Find an expression for the area (A) of a rectangle whose length is 'l' and breadth is 'b'. b) Express the perimeter of a triangle ‘p’ as an expression, when its sides are 'a', 'b' and 'c'. c) The perimeter of a plot is 4a. If it is in the shape of a square, what is its side? Long Answer Type Questions 10 [AS1] Solve the following equations: (i) 2x + 1 = 5 (ii) 3a – 3 = 9 (iii) 5z – 1 = 24 (iv) 2q + 5 = 17 (v) 8b + 6 = 22 EXERCISE 9.3. RULES FROM GEOMETRY AND SIMPLE EQUATIONS 145

11 [AS3] State which of the following are equations. (i) x + 3 = 7 (ii) r + 5 > 8 (iii) 3x – 5 < 2 (iv) 2a – 4 = 3 (v) 3z – 27 > 3 12 [AS3] Write the LHS and RHS of the following equations: (i) x + 5 = 11 (ii) 2p – 6 = 10 (iii) 4a + 1 = 8 (iv) 3z + 9 = 16 (v) 2b – 4 = 8 EXERCISE 9.3. RULES FROM GEOMETRY AND SIMPLE EQUATIONS 146

—— Project Based Questions —— (i) Collect the information about the population details in India from 1950 to 2015. Write the total population of India, male population of India, female population of India in the form of a table and also write these numbers in Indian system and international system using commas. (ii) Prepare a table showing the smallest and the greatest numbers of 2, 3, 4, 5, 6, 7, 8, 9 and 10 digit numbers. Write these numbers using commas in Indian and international systems of numeration and also write these numbers in words. (iii) Define Natural Numbers and Whole Numbers. Check the properties of Whole Numbers under all the four basic operations. Prepare a table to compare the properties of Natural Numbers and Whole Numbers. (iv) Without actually finding the factors of a number, we can find prime numbers between any two numbers with an easy method. This method was given by the Greek Mathematician Eratos- thenes, in the third century BC. Using this method find the prime numbers between 300 and 500 and list all the pairs of twin primes between them. (v) Palindrome is a number which reads the same from both the ends. Every palindrome number with even number of digits in it is divisible by 11. Ex. : 1221. If we reverse the digits in it, we get 1221 only. Hence, 1221 is a palindrome number. 1221 is divisible by 11. Write atleast 10 palindrome numbers with different number of digits such that the minimum of digits is 5, check whether they are divisible by 11 or not and write your conclusion. (vi) A polygon is a simple closed figure bounded by line segments. The points of intersection of the line segments are called vertices. The line segments formed by joining any vertex to another vertex which is not adjacent to it is called a diagonal. Using match sticks prepare the polygons with 3, 4, 5, 6, 7, 8, 9 and 10 sides and name them. Prepare a table with the shape of the polygon, name of the polygon, number of vertices and number of diagonals. PROJECT BASED QUESTIONS 147