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Playing with Numbers Elicit Warm-up Help the rabbit reach the carrot! Look at the picture on the right. Help the rabbit by solving the problems given below. Rule: The rabbit can take one step forward every time it gives the correct answer. 1. 4 × 100 + 7 × 10 + 3 × 1 = 2. 10 less than 10 times 51 = 3. 5 × 10,000 + 9 × 10 + 1 × 1= 4. 36,000 + 400 - 100 + 10 = The problems given above involved more than one operation. 1. How did you get the answers without using a place value chart? 2. Which operation did you carry out ﬁrst? My teacher told us to solve a problem that involves more than one operations. I am not able to do it. I need help to understand which operation to perform ﬁrst. Learning Objectives In this chapter, you will learn about: • Simpliﬁcation of brackets- BODMAS rule • Multiples and factors • Types of numbers • Prime factorisation- division and factor tree method • Prime triplets • Divisibility rules • Least common multiple (LCM) and highest common factor (HCF) • Prime Factorisation and Division Method for LCM and HCF • The property: LCM × HCF = Product of two numbers 16 

Chapter Review FLUENCY MULTIPLE CHOICE QUESTIONS 1-3 1. The simpliﬁed form of 14 + 8x4 + 194 ÷ 7 is: a. 84 c. 90 d. 62 2. The smallest factor of every number is: a. 2 b. 4 C. 0 1 3. The number 2 is the smallest prime number and is: a. prime b. odd c. twin prime even 4. The HCF of the coprime numbers 4 and 15 is: a. O C. 2 d. ﬁnite 5. Which of the following numbers is divisible by 3? a. 73 b. 137 54 d. 277 6....... is a perfect number. a. 469 b. 459 496 d. 495 7. 56892341 is divisible by: a. 9 b. 10 C. 11 d. 12 8. If P is the 8th prime number and Q is the 12th prime number, then Q - P is: a. 30 b. 28 18 d. 14 9. A number is always divisible by 90, if: a. it is divisible by both 7 and 45. b. it is divisible by both 8 and 18. c. it is divisible by both 9 and 11. None of these 10. What is the least digit that can be replaced with '#' ', so that the number 90##53 is divisible by 11? a. 3 0 c. 1 d. 2 PROBLEM-SOLVING SUBJECTIVE QUESTIONS 1. Observe the numbers given below. Write the exact divisor of each pair of numbers. a. 1002, 1005 b. 1020, 5000 c. 2100, 7000 2. Observe the grid and answer the following. 1-3 4-7 4-6 (2) (3 (5 (13) 12) 18 19) 2 0 23) 81 29 301 31 3 2 37) 38 39 (43) 47 4 8 501 53) 57 58 59) 6 0 1 61) 6 3 67 68 6 9 7 0 73) 双 79 80 81 8 2 (83) 87 89 1 8 0 32 8-10 7-8 

a. The sum of two odd numbers and one even number is .Cve.A..... b. The product of three odd numbers is Add c. The numbers 17 and 71 are prime numbers. Find such pairs of prime numbers up to 100.13, 3) 17,70 79,97 37,73 3. Complete the following as the sum of odd primes by ﬁlling in the boxes. a. 19+5=24 b. +7 = 18 C. + 3 = 32 d. = 61 4. Evaluate the following using the BODMAS rule. b. 19-5 + 6x4 - 25 ÷ 25 c. 6 x (36÷ 9) - 4 + 9 5. Write the smallest possible digit in the blank so that the number formed is divisible by 8. a. 9.0.16 b. 1021.6. c. 99.0.216 6. The same digit goes into the ﬁrst place and the last place of the 8-digit number given below and is divisible by 2. Find the smallest such digit. 2 431209.2.. 7. The number 764 * 52 is completely divisible by 11. What digit does * stand for? 8 8. A 6-digit number is divisible by 5 as it has 0 in its ones place. That number is also divisible by 9, as the sum of its digits is 9. So, the number must also be divisible by 45. a. What is the prime factorisation of 45? b. Determine the smallest 6-digit number which is divisible by 45. 900000 REASONING 9 10 11-12 9. Which smallest digit will you add to 31290876 to make it divisible by the numbers 5, 8 and 10? What are the last two digits? 0. Three water tankers contain 5000 litres, 8000 litres and 10,000 litres of water, respectively. Find the maximum capacity of a container that can measure the water of all the three tankers when used an exact number of times. Explain how you arrived at your answer. 1. What is the meaning of the following statements? Explain each statement in one line. a. Sum of the digits = 1 + 5 + 1 + 5 = 12, which is divisible by 3. b. Sum of the digits = 5 + 3 + 6 = 14, which is not divisible by 3. c. 11 and 13 are coprime. 12. In a colony, there are 62 blocks of ﬂats. The blocks are numbered from 1 to 62. A van stops at every sixth block, while a bus stops at every tenth block. According to Meera, if the van and the bus both start from the entrance of the colony, they will meet at the 6th, 10th, 18th and 60th blocks. a. Do you agree with Meera? b. What would be the answer according to you? ANALYSIS & CREATING 13 14 13. Think of situations where playing with numbers is used. Make up a story for numbers. 14. Place the numbers 2, 3, 5 and 7 in four boxes in such a way that the statement answer to the problem is 16 and the boxes are connected with the signs x, + and - 33

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