Math 7 (Period 4)

Integers and Absolute Value 3.1

Why are operations with integers so important?

Integers, which include whole numbers and their opposites are used to describe signed quantities such as temperatures above and below 0 º, elevations above and below sea level, and gain and losses in value.

Operations with integers are used in many careers including sports writing and paleontology, for example. For example, sportswriters use integers as they calculate movement on the football field or scores over or under par in a golf game.

Sets of Numbers:
Counting or Natural Numbersà  1, 2, 3, 4, …

Whole Numbers à 0, 1, 2, 3, 4…

Integers à …-4, -3, -2, -1, 0, 1, 2, 3, 4….

Integers include the Natural Numbers and their Opposites AND Zero

The integer 0 is neither negative NOR positive.

Students normally read -3 as “negative 3”

We graphed the negative integers, ZERO, and the positive integers on a number line. When graphing specific integers on a number line, you must place a closed dot on the point that represents the integer. See Page 105 of your textbook looking at Example 1 as well as Example 2.

The Absolute Value of a number is the distance between the number and 0 on a number line. Absolute Value is a DISTANCE concept—and therefore the absolute value of any number CANNOT be negative. Distance cannot be negative!  

Absolute values are written with two vertical bars called absolute value signs.

│7│ = 7   You read this as… “The Absolute Value of 7 is 7”

│-7│ = 7  You read this as… “The Absolute Value of -7 is 7”

│0│ = 0  You read this as… “The Absolute Value of 0 is 0”

Two numbers that have the same absolute value BUT have different signs are called opposites. For example -7 and 7 are opposites.
The negative sign can also be thought of as “the opposite of ” 
Thus “the opposite of 7” and “negative 7” are the same number

We talked about the different temperatures around the country… Buffalo, NY can get really cold and in our book it has an example of -20º We compared that temperature with our 93º temperature that we had only a few days ago.

What is the difference between the two? 93 – (-20) = 113º WOW!