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Integers & Absolute Value
Integers & Absolute Value
Objectives:
To be able to identify, compare, and order positive and negative integers.
To be able to determine the absolute value of numbers and expressions.
Why learn this: To use positive and negative numbers to measure temperature, height (as in above and below sea level), money, and more. We use absolute value to determine the distance from a point, without regard to the direction we are moving from that point.
Vocabulary: Integer - all positive whole numbers, their
opposites, and zero
Opposites - two numbers that are the same distance from zero on the number line, but in opposite directions. Ex. 2, -2
Number Line -
Absolute Value - a number’s distance from zero on the number line (always a positive value).
Integers & Absolute Value
WHERE DO WE SEE INTEGERS IN OUR DAILY LIVES
Money!Temperature!Elevations (height or depth of places in the world)YearsTimeRecipes/Cooking
Integers are EVERYWHERE!
Integers less than zero Integers greater than zeroare negative integers are positive integers
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
negatives are zero is neither positives CAN written with negative nor be written a (-) sign positive with a (+) sign
5 positives Integers greater than zero
4 are written are positive integers 3 with + sign 2 1 zero is neither 0 negative nor -1 positive -2 -3 negatives -4 written with Integers less than zero -5 a - sign are negative integers
Writing Integers in Real-Life SituationsWrite an integer to describe each situationExample 1: an increase of 6 inches
+ 6
Example 2: owe your parents $15
- 15
Example 3: a loss of 7 pounds
- 7
Example 4: earned 5 dollars interest
+ 5
Example 5: a temperature of 9 degrees below zero
- 9
Graphing integers on a Number LineGraph each integer on the number line
Example 1: Graph - 4 on the number line
Example 2: Graph - 8 on the number line
Example 3: Graph + 10 on the number line
Example 4: Graph + 2 on the number line
-10 -8 -6 -4 -2 0 2 4 6 8 10
Graphing integers on a Number LineGraph each integer on the number line
Example 1: Graph - 4 on the number line
Example 2: Graph - 8 on the number line
Example 3: Graph + 10 on the number line
Example 4: Graph + 2 on the number line
-10 -8 -6 -4 -2 0 2 4 6 8 10
Extension The number shows the amounts of money Erica,Jerry, Bob, and Rayhave in their wallets orowe one of their parents.
Who has the most money?Who has the least money? Who owes four dollars?
108
0
642
-10
- 2- 4- 6- 8
Erica
Ray
Bob
Jerry
Quick Practice
Write the opposite of each number.
a)2 b) 4 c) -3 d) -11
a) -2 b) -4 c) 3 d) 11
When graphing integers on a number line, make sure to:•Use at least 3 numbers•Use one number that is less then the number (to the left) and one number that is greater (to the right)•Put a dot to indicate which integer you are graphing
Example: Graph -3 on a number line:
-4 -3 -2
Graphing integers on a Number Line
Comparing Integers
Comparing Integers
Replace the □ with <, >, or = to make the sentence true.
Example 1: - 9 □ 8
- 9 < 8
Example 2: 83 □ 84
83 < 84
Example 3: 5 □ - 5
5 > - 5
Example 4: - 6 □ - 4
- 6 < - 4
Example 5: - 7 □ - 7
- 7 = - 7
Ordering Integers
Order each set of integers from least to greatest.
Example 1: - 162, - 10, - 81, 59 →
- 162, - 81, - 10, 59
Example 2: 9, - 8, 4, - 9 →
- 9, - 8, 4, 9
Example 3: 2, 6, - 2, 0 →
- 2, 0, 2, 6
Example 4: 7, 5, - 1, - 5 →
- 5, - 1, 5, 7
Quick Practice
Which number in the pair is farther away from zero.
a) 4, -5 b) 2, 5 c) -1, -3 d) -12, 11
a) -5 b) 5 c) -3 d) -12
What is absolute value?The distance of some number from zero on the
number line
Absolute Value is ALWAYS positive!
What does absolute value look like?
7 units 7 units
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Integers & Absolute Value
What is absolute value?The distance of some number from zero on the
number line (ALWAYS Positive)
What does absolute value look like?
the absolute
value of 7 | 7 | = 7
the absolute
value of – 7 | – 7 | = 7
Integers & Absolute Value
Absolute Value
Evaluate the expression.
Example 1: | 3 |
3
Example 2: | - 68 |
68
Example 3: | 6 | + | - 9 |
6 + 9
= 15
Example 4: | - 8 | - | - 9 |
8 – 9
= -1
Integers & Absolute Value
Quick Practice
Find each absolute value.
a)l-21l b)l14l c) l-1l d)l21l
a) 21 b)14 c) 1 d)21
Extension Evaluate 6 + | n | if n = - 16.
6 + | n | = 6 + | - 16 |
= 6 + 16
= 22
Integers & Absolute Value
Integers & Absolute Value
Absolute Value in real life!An eyeglass prescription is given as a positive or
negative number. A prescription for a person who is farsighted is positive. A prescription for a person who is nearsighted is negative. The greater absolute value, the stronger the prescription. Which prescription is stronger, -3 or 2?
Step 1: Think about the problem. What information was given and what am I trying to figure out?
Integers & Absolute Value
Absolute Value in real life!An eyeglass prescription is given as a positive or
negative number. A prescription for a person who is farsighted (can’t see near) is positive. A prescription for a person who is nearsighted is negative. The greater absolute value, the stronger the prescription. Which prescription is stronger, -3 or 2?
Step 2: Determine the answer
What is the absolute value of each prescription?
| -3 | | 2 |
3 2
Which prescription is greater?
-3!
Absolute Value in real life!A seagull is flying at an altitude of 107 feet and a shark is swimming at a depth of 112 feet relative to sea level. Which animal is farther from sea level?
Sea level (0 feet)
107 feet
-112 feet
l-4l l-3l>
l12l l-12l=
l-20l l10l>
l-14l l-15l<
l-7l 6>
-5 l-4l<
-15 5<
19 l-19l=
