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Introduction to integers

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Introduction to integers

  1. 1. Introduction to Integers
  2. 2. Integers Defined…• An integer (pronounced IN-tuh-jer) o is a whole number o Is not a fraction. o Is a number that can be positive, negative, or zero. opposite integers-6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 negative integers positive integers
  3. 3. Four real life situations in which integers can be used.• Spending and earning money• Rising and falling temperatures• Stock market gains and losses• Gaining or losing metres in an NRL game.-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 Note: A positive integer does not have to have a + sign. For example, +3 and 3 are the same.
  4. 4. Multiplying Integers
  5. 5. Dividing Integers
  6. 6. Adding and Subtracting with IntegersUsing a number line you add by moving to the right.e.g. -2+3 = 1 (As shown on the diagram below).
  7. 7. Subtracting IntegersSimilarly, when you are subtracting integers, you areMoving the arrow to the left. No matter where you start on the number line, you always move to the left. E.g. (-5) – 2 = -7
  8. 8. Adding and Subtracting IntegersSome different, slightly more difficult examples•3+(-7) becomes 3 – 7 = -4•-5 + (-2) becomes -5 – 2 = -7•5-(-3) becomes 5 + 3 = 8•-6-(-3) becomes -6 + 3 = -3
  9. 9. • The Problem: The highest elevation in Northern Lookout is Snow Peak, which is 15 237 metres above sea level. The lowest elevation is Tree Valley, which is 368 metres below sea level. What is the distance from the top of Snow Peak to the bottom of Tree Valley?
  10. 10. SolutionWe can represent each elevation as an integer: Elevation Integer 15 237 metres above +15 237 sea level Sea level 0 368 metres below -368 sea levelThe distance from the top of Snow Peak tothe bottom of Tree Valley is the same as thedistance from +15 237 to -368 on the numberline. We add the distance from +15 237 to 0,and the distance from 0 to -368, for a total of15 605 metres.
  11. 11. • Integers are the set of whole numbers and their opposites• Whole numbers larger than zero are called positive integers; whole numbers less than zero are called negative integers• The integer zero is neither positive nor negative.• Two integers are opposites if they are the same distance away from zero, but on opposite sides of the number line.• Positive integers may be written with or without a sign.

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