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1. From the list below, pick out the number or numbers that satisfies the conditions stated in each part. 13, 22, 27, 35, 8, 12, 19, 72, 48, 36, 25. ( i ). Multiples of 7 = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77…..}. From the list the only multiple of 7 is 35. (ii).

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  1. 1. From the list below, pick out the number or numbers that satisfies the conditions stated in each part. 13, 22, 27, 35, 8, 12, 19, 72, 48, 36, 25 (i) Multiples of 7 = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77…..} From the list the only multiple of 7 is 35. (ii) Factors of 36 = {1, 2, 3, 4, 6, 9, 12, 18, 36} From the list the factors of 36 are 12 and 36. (iii) Square numbers = {1, 4, 9, 16, 25, 36, 49, 64, 81….} From the list the square numbers are 36 and 25.

  2. 1. From the list below, pick out the number or numbers that satisfies the conditions stated in each part. 13, 22, 27, 35, 8, 12, 19, 72, 48, 36, 25 (iv) Prime numbers = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41….} From the list the prime numbers are 13 and 19.

  3. 2. (i) What are the prime factors of: (a) = 24 × 33 432 (b) 522 = 2 × 32 × 29 (ii) Hence, or otherwise, find the Highest Common Factor of 432 and 522. Common factors are 2 and 32. HCF = 2 × 32 = 18

  4. 3. Show that is an integer and find its value.

  5. 4. Jan ate of her lunch while walking to school and another at break time. What fraction of her lunch did she have left to eat at lunchtime? LCM = 12 left to eat.

  6. 5. Calculate of 98 and express your answer as a fraction of 56.

  7. 6. In a group of 20 students, three have red hair. In the school, there are 600 students. How many would you estimate have red hair?

  8. 7. Write 720 as a product of its prime factors. 720 = 24 × 32 × 5

  9. 8. Find the highest common factor of 60 and 96. Factors of 60 = 22 × 3 × 5 Factors of 96 = 25 × 3 Common factors = 22 and 3 HCF = 22 × 3 = 12

  10. 9. Find the lowest common multiple (LCM) of 24 and 36. Prime factors of 24 = 23 × 3 Prime factors of 36 = 22 × 32 Highest powers of the common factors are 23 and 32 LCM = 23 × 32 = 72

  11. 10. James thinks of two numbers. He says ‘The highest common factor (HCF) of my two numbers is 3, the lowest common multiple (LCM) of my two numbers is 45.’ Write down two numbers that James could be thinking of. 9 and 15 3 and 45 Prime factors of 3 = 3 Prime factors of 9 = 32 Prime factors of 45 = 32 × 5 Prime factors of 15 = 3 × 5 HCF = 3 HCF = 3 LCM = 32 × 5 = 45 LCM = 32 × 5 = 45

  12. 11. Which one of the following is not a rational number? Explain your answer. (i) (ii) 3∙142 (iii) (iv) π π : It can’t be expressed in the form

  13. 12. Arrange the following in order from smallest to largest. (i) (ii) (iii) 1∙6 (iv) (1∙19)2 = 0·6666… 1∙6 = 1∙6 (1∙19)2 = 1∙4161 = 1·4142… So arranging from smallest to largest we get:

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