2.1 Integers and Absolute Value

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Presentation transcript:

2.1 Integers and Absolute Value Objectives: Compare integers. Find the absolute value of a number

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 … Negative Direction Positive Direction -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Graphing Integers on a number line Draw 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 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Graphing Integers on a number line Graph -7, 0, and 5 Graph -4, -1, and 1 -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

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

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

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

Absolute Value Evaluate the absolute value: Ask yourself, how far is the number from zero? | -4 | = | 3 | = | -9 | = | 8 - 3 | + = -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Absolute Value Evaluate the absolute value: Ask yourself, how far is the number from zero? | 12 ÷ -4 | = | 3 ● 15 | = | -9 + 1 | - │1 + 2│ = | 8 - 3 | + │20 - 20│= -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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

Opposites What is the opposite? -10 -35 12 100 1 X

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.