Integers Absolute Value What is an integer Integers

Integers & Absolute Value

What is an integer?

Integers are the set of all whole numbers and their opposites.

Okay…but what does that mean?

Integers Negative numbers are numbers to the left or below zero and are less than zero.

Integers The numbers – 1, -2, 3, … are called negative integers. The number negative 3 is written – 3.

Integers Positive numbers are numbers to the right of zero and are more than zero.

Integers The numbers 1, 2, 3, … are called positive integers. The number positive 4 is written +4 or 4.

Integers Zero is neither negative nor positive.

Opposites are two numbers that are the same distance from zero

Let’s look at some examples of opposites! • -4 and +4 • -2 and +2 • -5 and +5

But what about zero? What is the opposite of 0?

0 Zero is neither positive or negative

Integers can also represent situations

Here are some examples: • Sarah went up four steps • +4 • The temperature is twelve below zero. • -12 • The elevation of the mountain is 52, 000 feet • +52, 000

And a few more… • The football team lost 8 yards • -8 • Anne gained 10 pounds • +10 • Tara spent $20 of • -$20 her checking account.

Representing a situation with an integer: (see notes) Example: Dry ice is solid carbon dioxide, which freezes at about 109 degrees below zero Fahrenheit. Use an integer to represent this situation. Step 1: Identify key words: below and zero Step 2: Write the integer: -109

You try: The lowest elevation in New Orleans, LA, is 8 feet below sea level. Use an integer to represent this elevation. -8

More (not on notes)… • The stock market showed a gain of 212 points today • +212 • Death Valley, California is 282 feet below sea level • -282 • The elevator went down two floors. • -2

Identifying Opposite Remember opposites are two numbers that are the same distance from zero. Example: Write the opposite of 3 So, the opposite of 3 is -3.

You Try: 1. Write the opposite of -5 • 5 2. Write the opposite of -100 • 100 3. Write the opposite of 1, 999 • -1, 999 4. Write the opposite of 209 • -209

Now let’s talk about Absolute Value

Absolute Value is… The distance a number is from zero on the number line.

So… • The symbol for absolute value of a number, n, is | | • Opposites have the same absolute value. • **Remember, drop the bars, drop the sign—that’s your answer every time!!!! 4

Unless… • The negative sign is OUTSIDE of the absolute value bars. = -4

Example: Find |-4| = 4 Find |2|= You Try: 2 4. ) Find |-5| +|-3| = 1. ) Find |-1| = 1 2. ) Find |7|= 7 3. ) Find |-9|= 9 8 5. ) Find |7| - |-4|= 3 6. ) Find |-1| + |-1|= 2

Comparing and Ordering Integers You can use a NUMBER LINE to compare integers. As you move left on a number line the numbers become LESS.

Comparing and Ordering Integers As you move to the RIGHT on a number line the numbers become GREATER.

Example: Compare -6 -4 You Try: 1. ) Compare 5 -3 2. ) Compare -12 3. ) Compare 2 4. ) Compare -20 9 4 -1

Example: Ordering Integers Order the scores on the scoreboard from least to greatest: You can use a number line to help you. In order from least to greatest these scores are: -400, -200, 100, 300. Tigers Bulldogs Lions Spartans -200 300 -400 100

You Try: 1. Order these scores from least to greatest: -25, 100, -50, and 75 -50, -25, 75, 100 2. In golf, a negative score is called “under par. ” List the golf scores -1, +2, -3, and +4 from least to greatest. -3, -1, 2, 4

Time to practice! Let’s go!!