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INTEGERS

INTEGERS. By: NIKMATUL HUSNA. o C. 60. Read the temperature on the thermometer as it changes. 50. 40. 30. 20. 20 0 C. 10. 0. -10. -20. -30. o C. 60. Read the temperature on the thermometer as it changes. 50. 40. 30. 20. -10 0 C. 10. 0. -10. -20. -30. 30m. Sea level.

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INTEGERS

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  1. INTEGERS By: NIKMATUL HUSNA

  2. oC 60 Read the temperature on the thermometer as it changes. 50 40 30 20 200C 10 0 -10 -20 -30

  3. oC 60 Read the temperature on the thermometer as it changes. 50 40 30 20 -100C 10 0 -10 -20 -30

  4. 30m Sea level 30 m 20m 10m 0m -10m -20m -30m 25 m 20 m 15m Estimate the height above or below sea level of the following points: 6 m 5 m -5 m -10m -15 m -25 m -25 m -30 m

  5. The Integers Consist of: • Negative Numbers • Zero • Positive Numbers

  6. 1 -1 2 -2 3 -3 4 -4 5 -5 NUMBER LINE 0

  7. Arithmetic operation By: NIKMATUL HUSNA

  8. 1 -1 2 -2 3 -3 4 -4 5 -5 0 Positive in the right and negative in the left Plus = forward , minus= backward

  9. 1 -1 2 -2 3 -3 4 -4 5 -5 0 Calculate2 + 3 2 3 So, 2 + 3 = 5

  10. 1 -1 2 -2 3 -3 4 -4 5 -5 0 Calculate2 + (–3) 2 3 So, 2 + (– 3) = –1

  11. 1 -1 2 -2 3 -3 4 -4 5 -5 0 Calculate–2 + 3 –2 3 So, –2 + 3 = 1

  12. 1 -1 2 -2 3 -3 4 -4 5 -5 0 Calculate–2 +(–3) –2 3 So, –2 + (– 3) = – 5

  13. 1 -1 2 -2 3 -3 4 -4 5 -5 0 Calculate2 – 3 2 3 So, 2 – 3 = -1

  14. 1 -1 2 -2 3 -3 4 -4 5 -5 0 Calculate2 – (-3) 2 3 So, 2 – (- 3) = 5

  15. 1 -1 2 -2 3 -3 4 -4 5 -5 0 Calculate-2 – 3 –2 3 So, -2 – 3 = -5

  16. 1 -1 2 -2 3 -3 4 -4 5 -5 0 Calculate-2 – (-3) –2 3 So, -2 – (- 3) = - 1

  17. ADDITION • Same Sign 125 + 234 = 359 - 58 + (-72) = -130 • Different Sign 75 + (-90) = - 15 (-63) + 125 = 62

  18. The Properties of Addition: • Commutative Law a + b = b + a 7 + 4 = 11 and 4 +7 =11 • Associative Law (a+b)+c = a+(b+c) (5+(-3))+8 = 10 and 5+((-3)+8) = 10

  19. 3. Identity Element The identity of addition in integers is 0 a + 0 = 0 + a = a 5+ 0 = 0 + 5 = 5 4. Closure Law if a and b are the integers, then a + b is also the integers. 3 + 5 = 8 3, 5, 8 are integers

  20. 5. Inverse of Addition if a + b = 0, then b is called the inverse of a 3 + (-3) = 0

  21. SUBTRACTION The Properties of Subtraction only: Closure Law If a and b are integers, a-b is also integers.

  22. 8 – 3 = 5 8 + (-3) = 5 If a and b are the integers, then a – b = a + (-b)

  23. Change Into Addition • a – b = • a – (-b) = • - a – (-b) = • - a – b =

  24. 30 x 5 = … -3 x 41 = … 21 x (-4) = … (-50) x (-4) = … 15 x (-7) = … Multiplication Calculate this example :

  25. The Properties of Multiplication • Closure Law • Commutative, Associative and Distributive Law. • Identity Element The identity of multiplication in integers is 1 1 x a = a x 1= a

  26. Distributive Law 3 x (-2 + 4) = 6 (3 x (-2)) + (3 x 4) = 6 a x (b + c) = (a x b) + (a x c)

  27. Calculate this example : 3 : 3 = 28 : (-7) = -35 : 5 = 40 : (-8) = -72 : (-9) = Division

  28. Division is inverse of multiplication 24 : 3 = 8 And 3 x 8 = 24 a, b and c with b factor of c and b ≠ 0 a : b = c  a = b x c

  29. TASK : 1. 45 + 56 × 48 – 216 : 9 = 2. 15.762 : 37 – 512 + 96 × 72 = 3. 19 × 27 + 5.205 : 15 – 269 = 4. (–9) – 6 × (–72) : 16 – 20 = 5. (8.742 – 9.756) × 36 : (4.356 – 4.360) =

  30. 6. 168 : ((17 – 24) × (–19 + 15)) = 7. 24 × (240 : ((–36 + 40) × (–23 + 17)) = 8. 360 : (15 + ((27 – 32) × (–9 + 16))) = 9. 420 : (–7) + 70 – 30 × (–8) + 15 = 10. 13 × (140 : (–7)) + (–2) × 19 =

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