Integers in Real-World Situations 11-1 Integers in Real-World Situations Course 1 Warm Up Problem of the Day Lesson Presentation

Vocabulary positive number negative number opposites integer

Positive numbers are greater than 0 Positive numbers are greater than 0. They may be written with a positive sign (+), but they are usually written without it. Negative numbers are less than 0. They are always written with a negative sign (–).

Additional Example 1: 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 Positive numbers can represent climbing or rising. +20,000 Negative numbers can represent taking out or withdrawing. –15

Additional Example 1: Identifying Positive and Negative Numbers in the Real World Name a positive or negative number to represent each situation. C. 7 degrees below zero Negative numbers can represent values below or less than a certain value. –7

Check It Out: 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 Negative numbers can represent values below or less than a certain value. –300 Positive numbers can represent climbing or rising. +4,000

Check It Out: Example 1 Name a positive or negative number to represent each situation. C. spending $34 Negative numbers can represent losses or decreases. –34

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.

The set of whole numbers includes zero and the counting numbers. {0, 1, 2, 3, 4, …} Remember!

Additional Example 2: Graphing Integers Graph each integer and its opposite on a number line. A. +2 –2 is the same distance from 0 as +2. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 B. –5 +5 is the same distance from 0 as –5. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

Additional Example 2: Graphing Integers Graph each integer and its opposite on a number line. C. +1 –1 is the same distance from 0 as +1. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

Graph each integer and its opposite on a number line. Check It Out: Example 2 Graph each integer and its opposite on a number line. A. +3 –3 is the same distance from 0 as +3. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 B. –4 +4 is the same distance from 0 as –4. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

Graph each integer and its opposite on a number line. Check It Out: Example 2 Graph each integer and its opposite on a number line. C. 0 Zero is its own opposite. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

Lesson Quiz Name a positive or negative number to represent each situation. 1. saving $15 2. 12 feet below sea level 3. What is the opposite of –6? 5. When the Swanton Bulldogs football team passed the football, they gained 25 yards. Write an integer to represent this situation. +15 –12 6 +25

–2 is to the left of 1 on the number line. Check It Out: Example 1 Use the number line to compare each pair of integers. Write < or >. A. –2 1 B. 2 –3 C. –3 –4 –5 –4 –3 –2 –1 0 1 2 3 4 5 –2 < 1 –2 is to the left of 1 on the number line. 2 > –3 2 is to the right of –3 on the number line. –3 > –4 –3 is to the right of –4 on the number line.

Additional Example 2: Ordering Integers Order the integers in each set from least to greatest. A. –2, 3, –1 B. 4, –3, –5, 2 Graph the integers on the same number line. –3 –2 –1 0 1 2 3 Then read the numbers from left to right: –2, –1, 3. Graph the integers on the same number line. –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 Then read the numbers from left to right: –5, –3, 2, 4.

Lesson Quiz Order the integers in each set from least to greatest. 1. –3, 7, 4 2. –11, 2, 5, –15 Compare. Write <, >, or =. 3. –3 -4 4. –12 –10 5. A location in Carlsbad Caverns is 752 ft below sea level, and another location is 910 ft below sea level. Which location is closer to sea level? –3, 4, 7 –15, –11, 2, 5 > < the location at –752 feet