Introduction to Integers The Pluses and Minuses of Life

Integers Defined… Integers are the set of whole numbers and their opposites Integers are positive and negative numbers The number line goes on forever in both directions and is indicated by arrows Whole numbers greater than zero are called positive integers and these numbers are to the right of zero on the number line opposite integers -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 negative integers positive integers

Integers Defined… Whole numbers less than zero are called negative integers and these numbers are to the left of zero on the number line. The integer zero is neither positive nor negative The sign of an integer is either positive (+) or negative (-), except zero, which has no sign. Opposite Integers: when two numbers are the same distance away from zero, on opposite sides of the number line, one will have a positive sign, the other a negative sign.

Write an integer to represent each situation: 15degrees above zero +15 a loss of 11 dollars -11 a gain of 8 points +8 3 steps backward -3 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10

Name the opposite of each integer. -11 +11 +27 -27 -14 +14 +4 -4 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10

Name 4 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 yards in a football 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.

The Problem: The highest elevation in Northern Lookout is Snow Peak, which is 15 237 feet above sea level. The lowest elevation is Tree Valley, which is 368 feet below sea level. What is the distance from the top of Snow Peak to the bottom of Tree Valley?

Solution We can represent each elevation as an integer: Elevation   Elevation Integer 15 237 feet above sea level +15 237 Sea level 368 feet below sea level -368 The distance from the top of Snow Peak to the bottom of Tree Valley is the same as the distance from +15 237 to -368 on the number line. We add the distance from +15 237 to 0, and the distance from 0 to -368, for a total of 15 605 feet.

Points to Remember: 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.