operations with integers powerpoint created by: miss henry
TRANSCRIPT
![Page 1: Operations with Integers PowerPoint Created By: Miss Henry](https://reader036.vdocument.in/reader036/viewer/2022062516/56649dc85503460f94abe2cd/html5/thumbnails/1.jpg)
Operations with Integers
PowerPoint
Created By:
Miss Henry
![Page 2: Operations with Integers PowerPoint Created By: Miss Henry](https://reader036.vdocument.in/reader036/viewer/2022062516/56649dc85503460f94abe2cd/html5/thumbnails/2.jpg)
What is an Integer?
• A whole number that is either greater than 0 (positive) or less than 0
(negative)
• Can be visualized on a number line:
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What is a Number Line?
•A line with arrows on both ends that show the integers with slash marks
•Arrows show the line goes to infinity in both directions ( + and -)
•Uses a negative sign (-) with negative numbers but no positive sign (+)
with positive numbers
•Zero is the origin and is neither negative nor positive
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What are Opposites?
•Two integers the same distance from the origin, but on different sides of zero
•Every positive integer has a negative integer an equal distance from the origin
•Example: The opposite of 6 is -6
•Example: The opposite of -2 is 2
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What is Absolute Value?•Distance a number is from zero on a
number line (always a positive number)
•Indicated by two vertical lines | |
•Every number has an absolute value
•Opposites have the same absolute values since they are the same distance from zero
•Example: |-8| = 8 and |8| = 8
•Example: |50| = 50 and |-50| = 50
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What Can We Do to Integers?
•Integers are numbers, so we can add, subtract, multiply, and divide them
•Each operation has different rules to follow
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Adding Rules – Same Signs
•If the integers have the SAME signs: ADD the numbers & keep the same sign!
•Positive + Positive = Positive Answer
•Negative + Negative = Negative Answer
• Examples: -3 + (-10) = ? ? = -13
• 6 + (8) = ? ? = 14
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Adding (Same Signs) - Examples #1. -3 + (-10)
Step 1: 13 Add the #s
Step 2: -13 Keep same sign (Both #s are
negative – Answer is negative!)
#2. 6 + (8)
Step 1: 14 Add the #s
Step 2: 14 Keep same sign (Both #s are positive – Answer is positive!)
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Adding Rules – Different Signs
•If the integers have the DIFFERENT signs: SUBTRACT the numbers & use sign of the
BIGGER number!
•Bigger # is Positive = Positive Answer
•Bigger # is Negative = Negative Answer
• Examples: -13 + (7) = ? ? = -6
• 23 + (-8) = ? ? = 15
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Adding (Different Signs) - Examples #1. -13 + (7)
Step 1: 6 Subtract the #s
Step 2: -6 Use sign of bigger # (Bigger # is negative - Answer is negative!)
#2. 23 + (-8)
Step 1: 15 Subtract the #s
Step 2: 15 Use sign of bigger # (Bigger # is positive - Answer is positive!)
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Subtracting Rules•Put ( ) around second number & its sign
•Change SUBTRACTION sign to an ADDITION sign
•Change sign of 2nd number to its opposite
•Follow the rules for ADDITION:
-SAME signs: Add & keep the same sign -DIFFERENT signs: Subtract &
use sign of bigger # • Examples: -5 – -10 = ? ? = 5• 9 - 23 = ? ? = -14
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Subtracting - Examples #1. -5 – -10 #2.9 - 23
Step 1: -5 – (-10) Insert ( ) 9 – (23)
Step 2: -5 + (-10) Change – to + 9 + (23)
Step 3: -5 + (10) Change 2nd sign 9 + (-23)
Step 4: 5 Follow adding rules -14 d
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Multiplying Rules• Multiply the numbers like usual
•If the integers have the SAME signs: ANSWER will be POSITIVE
•If the integers have DIFFERENT signs: ANSWER will be NEGATIVE
• Examples: -3 · (-5) = ? ? = 15
• -9 · (-10) = ? ? = 90
• -7 · 7 = ? ? = -49
• 6 · -6 = ? ? = -36
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Multiplying - Examples
• #1. -3 · (-5) #2. -9 · (-10)
• 15 Multiply the numbers 90
• 15 Same signs = Positive Answer 90#3. -7 · 7 #4. 6 · -6
49 Multiply the numbers 36
-49 Different signs = Negative Answer -36
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Dividing Rules• Divide the numbers like usual
•If the integers have the SAME signs: ANSWER will be POSITIVE
•If the integers have DIFFERENT signs: ANSWER will be NEGATIVE
• Examples: -33 ÷ (-3) = ? ? = 11
• -90 ÷ (-10) = ? ? = 9
• -20 ÷ 2 = ? ? = -10
• 6 ÷ -6 = ? ? = -1
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Dividing - Examples
• #1. -33 ÷ (-3) #2. -90 ÷ (-10)
• 11 Divide the numbers 9
• 11 Same signs = Positive Answer 9 #3. -20 ÷ 2 #4. 6
÷ -6
10 Divide the numbers 1
-10 Different signs = Negative Answer -1
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Mixed PracticeSolve the following problems:
-9 + - 9
-18
7 · -4
-28
-10 - (-19)
9
-35 ÷ -7
5
15 + -25
-10
-23 - 9
-32
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Review
• Visit the website below for additional information on integers:
http://www.math.com/school/subject1/ lessons/S1U1L10GL.html
• Click on the signs below to review the rules for each operation
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Review
• Visit the website below for additional information on integers:
http://www.math.com/school/subject1/ lessons/S1U1L10GL.html
• Click on the signs below to review the rules for each operation