Integers and Absolute Value • Vocabulary, Graphing, and Inequalities

1. Unit 1 Chapter 2-1 Integers and Absolute Value

2. Vocabulary: • Integers – set of whole numbers and their opposites • Opposites – numbers that are the same distance from zero on a number line, but on opposite sides of zero • Negative number – is a number less than zero Number to left of the Numbers to the right of zero are less than zero zero are greater than zero -5 -4 -3 -2 -1 0 1 2 3 4 5 Zero is neither positive or negative

3. Write integers for each situation Ex 1: 500 feet below sea level The integer is -500 Ex 2: A temperature increase of 12º The integer is +12 Ex 3: A loss of $550 The integer is -550

4. Graph of a point with a coordinate -3 Graph of a point with a coordinate 2 To graph integers, locate the points named by the integers on a number line. The number that corresponds to a point is called the coordinate of that point. -4 -3 -2 -1 0 1 2 3 4 • Remember, the increments between each integer on your number line needs to be spaced out evenly. -3 < 2 OR 2 > -3 Read as -3 is less than 2 OR 2 is greater than -3 Any mathematical sentence containing < > is called an inequality. An inequality compares numbers or quantities

5. Let’s practice Use the symbols < > to compare to make the sentence true. Ex 1: 5 - 4 Ex 2: 7 - 10 Ex 3: -1 1

6. Let’s check our answers Use the symbols < > to compare to make the sentence true. Ex 1: 5 > - 4 Ex 2: 7 > - 10 Ex 3: -1 <1

7. Absolute Value Absolute Value is the distance from zero on a number line. Note: Absolute value of a non-zero number is ALWAYS positive because distance is always positive. “The absolute value of -4” is written as l-4l. 4 units 4 units -4 -3 -2 -1 0 1 2 3 4 l-4l = 4 and l4l = 4

8. Let’s practice Evaluate: Ex 1: l -8l Ex 2: l9l + l-7l Ex 3: l-5l + l-6l Ex 4: l20-20l

9. Let’s check out answers! Evaluate: Ex 1: l -8l = 8 Ex 2: l9l + l-7l = 9+7= 16 Ex 3: l-5l + l-6l = 5+6= 11 Ex 4: l20-20l = 0