Integers and Absolute Value Define Integer Definition of

Integers and Absolute Value

Define Integer Definition of Integer: 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. . . } X

Integers on a Number Line Negative Numbers -5 -4 -3 Numbers to the left of zero are less than zero Positive Numbers Zero -2 -1 0 1 Zero is neither positive or negative 2 3 4 5 Numbers to the right of zero are greater than zero

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? -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?

Absolute value is symbolized by two vertical bars |4| 10 9 8 This is read, "the absolute value of 4" 7 -6 -5 -4 3 -2 -1 0 1 2 3 4 What is the | 4 | ? 5 6 7 8 9 1 0

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.