Introduction To Integers
- 1. Integers – What exactly are they?? Mrs. Young
- 2. Problem: The highest elevation in North America is Mt. McKinley, which is 20,320 feet above sea level. The lowest elevation is Death Valley, which is 282 feet below sea level. How would we write these two elevations using integers?
- 3. Solution: We could solve the problem above using integers. Integers are the set of positive whole numbers and their opposites (negative whole numbers). Note that fractions and decimals are not included in this definition --- ONLY whole numbers! The number line can be used to represent the set of integers. Look carefully at the number line below and the definitions that follow.
- 4. Definitions -The number line goes on forever in both directions. This is indicated by the arrows. -Whole numbers greater than zero are called positive integers . These numbers are to the right of zero on the number line. -Whole numbers less than zero are called negative integers . These numbers are to the left of zero on the number line. -The integer zero is neutral. It is neither positive nor negative. - The sign of an integer is either positive ( + ) or negative ( - ), except zero, which has no sign.
- 5. Definitions continued Two integers are opposites if they are each the same distance away from zero, but on opposite sides of the number line. One will have a positive sign, the other a negative sign. In the number line above, + 3 and - 3 are labeled as opposites. Let's revisit the problem from the beginning of this slide show to solve it.
- 6. Problem: The highest elevation in North America is Mt. McKinley, which is 20,320 feet above sea level. The lowest elevation is Death Valley, which is 282 feet below sea level. How would we write these two elevations using integers?
- 7. Solution: We can represent each elevation as an integer: Let’s try it!!! Elevation Integer 20,320 feet above sea level + 20,320 sea level 0 282 feet below sea level - 282
- 8. Example 1: Write an integer to represent each situation: 10 degrees above zero a loss of 16 dollars a gain of 5 points 8 steps backward
- 9. Example 2: Name 4 real life situations in which integers can be used: Spending and earning money Rising and falling temperatures Gaining and losing yards in a football game Stock market gains and losses
- 10. NOTE: A positive integer does not have to have a + sign in front of it. For example, + 3 and 3 are interchangeable (the same).
- 11. Example 3: Name the opposite of each integer: - 12 + 21 - 17 + 9
- 12. Summary Integers are the set of whole numbers and their opposites. Whole numbers greater than zero are called positive integers; whole numbers less than zero are called negative integers. The integer zero is neither positive nor negative, and has no sign. Two integers are opposites if they are each the same distance away from zero, but on opposite sides of the number line. A positive integer may be written with or without a sign.