202110181-APEX-STUDENT-WORKBOOK-MATHEMATICS-G06-PART1

24 [AS5] Write mixed fractions for the shaded parts of the following figures. (i) (ii) (iii) (iv) (v) EXERCISE 7.1. TYPES OF FRACTIONS 98

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 99

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 (A) 3 (B) 6 (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 100

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 101

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 102

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 from4711 . 9 9 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 103

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 104

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 105

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. . . 106

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. . . 107

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. . . 108

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 109

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 110

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 111

—— 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 112

(vii) Draw the pictures of clocks and describe the position of the hands in a clock according to the conditions given and also mention the time after rotation. a. The hour hand is at 2 and the minute hand starts at 12 and makes 1 of a revolution. 2 1 b. The hour hand is at 5 and the minute hand starts at 2 and makes 2 of a revolution. c. The hour hand is at 7 and the minute hand starts at 5 and makes 1 of a revolution. 4 3 d. The hour hand is at 3 and the minute hand starts at 5 and makes 4 of a revolution. e. Both the hands are at 3 and the minute hand makes 3 1 of a revolution. 3 PROJECT BASED QUESTIONS 113

Additional AS Based Practice Questions Q1 [AS5] Observe the given picture and answer the questions that follow: a) Arrange the people in the picture in increasing order of their heights. b) Arrange the people in decreasing order of their heights. Q2 [AS5] Mohan and Gita went to buy an almirah. There were many almirahs available in the shop with their price tags. a) Arrange their prices in increasing order. 114 b) Arrange their prices in decreasing order. ADDITIONAL AS BASED PRACTICE QUESTIONS

Q3 [AS5] Draw the factor tree for 72. Q4 [AS5] Which of the following correctly represents the factor tree of 60? A) B) C) D) Q5 [AS2] Of the given letters, check and mention which are open or closed figures. ADDITIONAL AS BASED PRACTICE QUESTIONS 115

Q6 [AS2] What is the difference between each of the given figures? Why are they called polygons? Q7 [AS2] Which of the following angles are obtuse? Measure the angles and verify your answer. Q8 [AS2] In the given figure, how many angles are obtuse? Check your estimation by measuring them and also give their measures. ADDITIONAL AS BASED PRACTICE QUESTIONS 116

Q9 [AS5] If 4 match sticks are needed to make one square, then draw a table and using the rule fill in the number of match sticks for making 2 and 3 squares as given in the figure below: ADDITIONAL AS BASED PRACTICE QUESTIONS 117