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Numbers

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Published in: Mathematics
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Types of number Ordering The four operations

Divya J / Dubai

15 years of teaching experience

Qualification: CAIE and Pearson Examiner for IGCSE an AS Levels, Masters in Mathematics

Teaches: SAT, ACT, Maths, IGCSE/AS/AL, Physics, Biology, Chemistry, Mathematics

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  1. .- 01 Lecture No Mathematics Numbers Today's Targets O Types of number Ordering O The four operations
  2. Different types of numbers Natural numbers Integers Rational numbers Irrational numbers Real numbers Prime numbers Reciprocal Square numbers Cube numbers Factors Prime factors Highest common factor Least Common Multiples
  3. Ordering numbers The following symbols have a specific meaning in mathematics: = is equal to is not equal to is greater than > 2 is greater than or equal to is less than is less than or equal to
  4. The Four Operations Calculations involving more than one operation (+, —, x and 4). First Second Third Fourth B DM AS Brackets Indices Division and/or Multiplication, working from left to right. Addition and/or Subtraction, working from left to right.
  5. Question Here is a set of numbers: {-4 Which of these numbers are: (a) Natural numbers? (b) Square numbers? (c) Negative integers? (d) Prime numbers? (e) Multiples of two? (f) Factors of 80? , -1, o, 3, 4, 6, 9, 15, 16, 19, 20).
  6. Question (a) Use a factor tree to express 400 as a product of prime factors.
  7. Question (b) Use the division method to express 1080 as a product of prime factors.
  8. Question (c) Use your answers to find: The LCM of 400 and 1080.
  9. Question (ii) Use your answers to find: The HCF of 400 and 1080.
  10. Question (c) Use your answers to find:
  11. Question (c) Use your answers to find: (iv) Whether 1080 is a cube number, how can you tell?
  12. Question For each of the numbers shown below, state whether it is rational or irrational: (a) 1.3 (b) 0.6 (d) (g) -22 5 0.625
  13. Question For each of the numbers shown below, state whether it is rational or irrational: (a) (e) (b) (0
  14. Question Write the following decimals in order of magnitude, starting with the smallest: 6.0 0.6 0.66 0.606 0.06 6.6 6.606
  15. Question Evaluate the followingwithout a calculator: (i) 3.6 — 8.74+9 (ii) 0.72 x 0.04 (iii) 0.592 + 0.8 0.55 x 0.81 (iv) 4.5
  16. Question Simplify: (ii) (iii) 6x2+4x5 4 x (100 - 15) (5+6) x
  17. [S19, 21, Q 12] 29 27 28 30 31 32 From the list of numbers, write down 33 (b) a multiple of 7, a cube number, a prime number,
  18. [W18, 22, Q 23] (a) Write 56 as a product of its prime factors. [2]
  19. [W18, 22, Q 23] (b) Find the lowest common multiple (LCM) of 56 and 42. [2]
  20. [W14, 23, Q 2] Write the following in order of size, smallest first. 0.34 Answer 0.62 0.73 [2]
  21. [Wu, 22, Q 1] Insert one pair of brackets only to make the following statement correct. 6+5 x 10-8=16
  22. • • • • • • • Revision An integer is a positive or negative whole number or zero, e.g., 2, —3, ... A prime number is divisible only by itself and by 1, e.g., 2, 3, 5, 7, 11, 13, ... The multiples of 12 are 12, 24, 36, 48, The factors of 12 are 1, 2, 3, 4, 6, 12. A square number is the result of multiplying a number by itself, e.g„ 5 x 5 = 25, so 25 is a square number. A cube number is the result of multiplying a number by itself. Indices are used as a neat way of writing products. 24=2 35 243
  23. Revision • Indices are used as a neat way of writing products. 35 243 [2 to the power 4] [3 to the power 5] • The reciprocal of a number is the result of dividing 1 by that number. The reciprocal of 4 is —, [In index form, this is written as 4-11 In general, the reciprocal ofn is—. This can be written as n 1.
  24. Revision A rational number is any number which can be expressed as a fraction. An irrational number cannot be expressed as a fraction. Examples of irrational numbers include:
  25. Revision Whole numbers, Fractions, Recurring decimals, Terminating decimals. + The square root of any number other than square numbers. + A decimal which does not repeat or terminate (e.g., Tt).
  26. Revision 1-2 1- 6 (Addition) - -5 (Subtraction) This is erroneous. The correct value is 3. If we have a string of these two operations, we call it a sum and we should work from left to right: 1-2+3 -4+5=-1+3-4+5
  27. Revision Similarly, division is no more important than multiplication. If we have a string of these two operations, we call it a product and we will work from left to right again: 1+2x3+4x5=o.5x3+4x5 = 0.375 x 5 = 1.875

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