Understanding Integers and Absolute Value Concepts
This content covers the definitions and examples of integers, integers on a number line, opposites of numbers, absolute value, and real-life applications related to freezing points. Explore the concept of integers, their representation on a number line, absolute value calculations, and practical scenarios involving freezing points of substances.
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Presentation Transcript
Define Integer Definition of Integer: X The set of whole numbers, their opposites and zero. Examples of Integer: {...-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7...}
Integers on a Number Line Negative Numbers Positive Numbers Zero -5 -4 -3 -2 -1 1 2 0 3 4 5 Numbers to the left of zero are less than zero Numbers to the right of zero are greater than zero Zero is neither positive or negative
Opposites The numbers -4 and 4 are shown on the number line. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Both numbers are 4 units from 0, but 4 is to the right of 0 and -4 is to the left of zero. The numbers -4 and 4 are opposites. Opposites are two numbers which are the same distance from zero.
Absolute Value of Numbers The absolute value is the distance a number is from zero on the number line, regardless of direction. Distance and absolute value are always non-negative (positive or zero). - 10 -9 -8 -7 -6 -5 -4 -3 - 2 -1 0 1 2 3 4 5 6 7 8 9 10 What is the distance from 0 to 5? 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 - 1 0 1 2 3 4 - 10 -2 What is the distance from 0 to -5?
Absolute value is symbolized by two vertical bars |4| This is read, "the absolute value of 4" 9 1 8 - 10 - 9 - 8 - 7 -6 -5 - 4 - 3 - 2 -1 0 1 2 3 4 5 6 7 0 What is the | 4 | ?
Real life application The freezing point is the temperature at which a liquid becomes a solid. a. Which substance in the table has the lowest freezing point? b. Is the freezing point of mercury or butter closer to the freezing point of water, 0 C?
Is the freezing point of airplane fuel or candle wax closer to the freezing point of water? Explain your reasoning.
