Integers and Absolute Value
- 1. Objectives: Graph and compare integers Find the absolute value of a number Integers and Absolute Value
- 2. Number Sets Real Numbers (all numbers- negative, positive, fractions, decimals…) … -3, -2.5, -2, -1, - ½ , 0, 1, 2.3, 3, … INTEGERS (positive and negative numbers) …-3, -2, -1, 0, 1, 2, 3… Whole Numbers (positive numbers) 0, 1, 2, 3, 4, 5… Natural Numbers (counting numbers) 1,2,3,4,5,6…
- 3. Identify the Number Sets Identify all of the number sets the number belongs to. Example: 6 6 is a natural, whole, integer, and real number ! ------------------------------------------------------------- -9 ½ 0 25 -2.5
- 4. Integers Integers are all of the positive and negative whole numbers . There are no fractions or decimals that are integers. … .. -3, -2, -1, 0, 1, 2, 3 … -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Negative Direction Positive Direction
- 5. Graphing Integers on a Number Line Graph an integer by drawing a dot at the point that represents the integer. Example: -6, -2, and 3 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
- 6. Order Integers from Least to Greatest You need to know which numbers are bigger or smaller than others, so we need to order them from least to greatest. Example: Order the integers -4, 0, 5, -2, 3, -3 from least to greatest. The order is -4, -3, -2, 0, 3, 5. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
- 7. Order Integers from least to greatest Order the integers 4,-2,-5,0,2,-1 from least to greatest. Order the integers 3,4,-2,-5,1,-7 from least to greatest. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
- 8. Absolute Value Absolute value of a number is the DISTANCE to ZERO. Distance cannot be negative, so the absolute value cannot be negative. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
- 9. Absolute Value Evaluate the absolute value: Ask yourself, how far is the number from zero? | -4 | = | 3 | = | -9 | = | 8 | = -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
- 10. Opposites Two numbers that have the same ABSOLUTE VALUE , but different signs are called OPPOSITES. Example -6 and 6 are opposites because both are 6 units away from zero. | -6 | = 6 and | 6 | = 6 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
- 11. Opposites What is the opposite? -10 -35 12 100 10 35 -12 -100
- 12. Using Absolute Value in Real Life The graph shows the position of a diver relative to sea level. Use absolute value to find the diver’s distance from the surface.