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.

Integers & Absolute Value 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).

WHERE DO WE SEE INTEGERS IN OUR DAILY LIVES Money! Temperature! Elevations (height or depth of places in the world) Years Time Recipes/Cooking Integers are EVERYWHERE!

Integers less than zero Integers greater than zero are 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 Situations Write an integer to describe each situation Example 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 Line Graph 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 Line Graph 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 Ray have in their wallets or owe one of their parents. Who has the most money? Who has the least money? Who owes four dollars? 10 Ray 8 6 4 Erica 2 - 2 Jerry - 4 - 6 - 8 Bob -10

Quick Practice Write the opposite of each number. 2 b) 4 c) -3 d) -11   2 b) 4 c) -3 d) -11 a) -2 b) -4 c) 3 d) 11

Graphing integers on a Number Line 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

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

Integers & Absolute Value 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 value of – 7 | – 7 | = 7

Integers & 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

Quick Practice Find each absolute value. l-21l b)l14l c) l-1l d)l21l a) 21 b)14 c) 1 d)21

Integers & Absolute Value Extension Evaluate 6 + | n | if n = - 16. 6 + | n | = 6 + | - 16 | = 6 + 16 = 22

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? 107 feet Sea level (0 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 =