Introduction to Integers

What is a Positive Number? Positive number – a number greater than zero. 1 2 3 4 5 6

What is a Negative Number? Negative number – a number less than zero. -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

Are these numbers on the same or opposite sides of zero? If two numbers have the same sign, they are on the same side of zero. If two numbers have the opposite signs, they are on the opposite sides of zero. -3 and -4.5 2 3 and 1.3 -6 and 2

What are Opposite Numbers? Opposite Numbers – numbers that are the same distance from zero in the opposite direction -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

Opposites Continued… Example 1: The opposite of 7 is -7. 9 Example 3: -9 and ___ are opposites. What is the sum of a number and its opposite? 0.

What is an Integer? Integers – Integers are all the whole numbers and all of their opposites on the number line including zero. Example: 0, 1, 2, 3, 4 … Example: -1, -2, -3, -4 …

What is a Rational Number? Rational Numbers – Numbers that can be expressed as one integer divided by another non-zero integer. Examples: 3 4 , −7 8 , 3 −1 , and 0.75

What is the Absolute Value of a number? Absolute Value – The distance a number is from 0 on a number line. Example 1: The absolute value of 3 or of –3 is 3. -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 Example 2: Using Symbols 5 =____ 𝑜𝑟 −5 =___ 5 5

Negative Numbers Are Used to Measure Temperature Example: The temperature in Antarctica was 34 degrees below 0 or -34°C. ZERO: In this case, zero represents the freezing point, 0° C.

Negative Numbers Are Used to Measure Under Sea Level 30 Example: The diver dove 20 feet below sea level. OR -20 feet 20 10 -10 -20 -30 ZERO: In this case, zero represents that you are standing at the surface of the ocean. -40 -50

Negative Numbers Are Used to Show Debt Let’s say your parents bought a car but had to get a loan from the bank for $5,000. How can we represent the amount of money your parents have as an integer? -5,000 ZERO: In this case, zero represents that you no longer owe any money for the car.

Integers Are Used to Measure Movement Example: Mary and George walked into an apartment building and went to the elevator. They needed to go to the sixth floor to visit their cousin. How can we represent the number of floors they ascended? +6 ZERO: In this case, zero represents the ground floor where Mary and George walked into the elevator.

Writing Positive Numbers If you don’t see a negative or positive sign in front of a number it is positive. +9 and 9 represent the same number

Real-Life Situations Write an integer to represent each situation below. (Don’t use labels) You gain 10 yards on the football field. You owe your brother $25. You lose 5 pounds on a diet. You earn $30 mowing lawns.

Real-Life Situations Write a real-life situation to represent the integers below. Be creative! - 45 24 - 56 66