Integers and Absolute Value #37

Vocabulary Positive numbers are greater than 0. They may be written with a positive sign (+), but they are usually written without it. 2 Negative numbers are less than 0. They are always written with a negative sign (–). Ex:-2 Integers is a member of a set of whole numbers and their opposites. Ex:…-3,-2,-1,0,1,2,3,4… Absolute Value is the distance of a number from zero on a number line; shown by I I. Ex: I-5I=5

You can graph positive and negative numbers on a number line. On a number line, opposites are the same distance from 0 but on different sides of 0. Integers are the set of all whole numbers and their opposites. Opposites –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 Negative Integers Positive Integers 0 is neither negative nor positive. 3

|<--3 units--> | <--3 units-->| The absolute value of an integer is its distance from 0 on a number line. The symbol for absolute value is ||. |–3| = 3 |3| = 3 |<--3 units--> | <--3 units-->| –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 Absolute values are never negative. Opposite integers have the same absolute value. |0| = 0 4

Identifying Positive and Negative Numbers in the Real World Name a positive or negative number to represent each situation. A. a jet climbing to an altitude of 20,000 feet B. taking $15 out of the bank C. 7 degrees below zero 5

Name a positive or negative number to represent each situation. Example 1 Name a positive or negative number to represent each situation. A. 300 feet below sea level B. a hiker hiking to an altitude of 4,000 feet C. spending $34 6

Example 2: Graphing Integers Graph each integer and its opposite on a number line. A. +2 –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 B. –5 –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 7

Additional Example 2 Continued Graph each integer and its opposite on a number line. C. +1 –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 8

Additional Example 3: Finding Absolute Value Use a number line to find the absolute value of each integer. A. |–2| –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 9

Additional Example 3: Finding Absolute Value Continued Use a number line to find the absolute value of each integer. B. |8| –1 0 1 2 3 4 5 6 7 8 9 10

Additional Example 3: Finding Absolute Value Continued Use a number line to find the absolute value of each integer. A. |6| –1 0 1 2 3 4 5 6 7 8 9 11

Additional Example 3: Finding Absolute Value Continued Use a number line to find the absolute value of each integer. B. |–4| –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 12