integers (3)
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Operations with
IntegersPowerPoint
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What is an Integer?
A whole number that is eitheror
Can be visualized on a number line:
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What is a Number Line?
A line with arrows on both ends that showthe 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 numbersZero is the origin and is
negative nor positive
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What are Opposites?
Two integers the same distance from theorigin, 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 numberline (always a positive number)
Indicated by two vertical lines | |
Every number has an absolute value
Opposites have the same absolute valuessince 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 signs: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
-3 + (-10)13 Add the #s
13 Keep same sign (Both #s arenegative
Answer is negative!)
6 + (8)
14 Add the #s
14 Keep same sign (Both #s arepositiveAnswer is positive!)
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Adding Rules Different Signs
If the integers have the signs:the numbers & use sign of the
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-13 + (7)
6 Subtract the #s
-6 Use sign of bigger # (Bigger # isnegative - Answer isnegative!)
23 + (-8)
15 Subtract the #s
15 Use sign of bigger # (Bigger # ispositive - Answer ispositive!)
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Subtracting RulesPut ( ) around second number & its sign
Change sign to ansign
Change sign of 2nd
number to its
Follow the rules for
- signs:Add & keep the same sign- signs: Subtract & use sign of bigger #
Examples: -5 -10= ? ? = 5 9- 23 = ? ? = -14
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Subtracting - Examples-5 -10 9 - 23
-5 (-10) Insert ( ) 9 (23)
-5 + (-10) Changeto + 9 + (23)
-5 + (10) Change 2ndsign 9 + (-23)
5 Follow adding rules -14
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Multiplying Rules
Multiply the numbers like usualIf the integers have the signs:
will be
If the integers have signs:will be
Examples: -3 (-5) = ? ? = 15
-9 (-10) = ? ? = 90
-7 7 = ? ? = -49
6 -6 = ? ? = -36
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Multiplying - Examples
-5) (-4) ((-1) (-20)
# -4 5 (-1) (4 (-6 ) (-3)
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Find the products of the following.
1. -4 (-6) 9. 2 0 (-5) (-100)
2. 8 (-2) 7 10. (-2) (-1) 3 5
3. -7 4 (-3)
4. 6 3 (-9)
5. (-2 ) (-1) 0
6. 5 (-10) (-1)
7. (-2) 5 (-3) (-5)
8. (-1) (-1) (-1) 7
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Dividing Rules Divide the numbers like usual
If the integers have the signs:will be
If the integers have signs:will be
Examples: -33 (-3) = ? ? = 11
-90 (-10) = ? ? = 9
-20 2 = ? ? = -10
6 -6 = ? ? = -1
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Dividing - Examples
-30 (-3) -9 (-3)
-24 8 36 -6
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Find the quotients of the following.
1. (-40) 5 9. 12 (-2) (-3)
2. (-10) (-2) 10. 7 (-7) 1
3. 45 (-9)4. 60 (-10) 2
5. (-20) (-5) (-1)
6. 4 (-1) (-1)
7. (-144) (-12)
8. 100 (-100) (-1)
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Mixed Practice
:-9 + - 9
-18
7 -4
-28
-10 - (-19)
9
-35 -7
5
15 + -25
-10
-23 - 9
-32
T F l
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True or False?
1.All integers are negative.
2.The absolute value of everyinteger is its opposite.
3.Two integers that areopposites have the same
absolute value.
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True or False?
1.The opposite of an integer isalways negative.
2.The absolute value of apositive integer is the integer
3.The absolute value of an
integer is always greater thanthe integer.
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2.The absolute value of aninteger is always positive.
1.A positive and negativeinteger will always add tozero.
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Point are different points on anumberline. Using the following clues, order theintegers for .
D is the least of the integers
Points A and D are the same distance from 0.
Point C is closer to D than it is to B.
Point C is a positive integer
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Make up a puzzle
same as the one givento you about ordering
of integers. Show onepossible solution.
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Review
Visit the website below for additionalinformation on integers:
http://www.math.com/school/subject1/
lessons/S1U1L10GL.html Click on the signs below to review the
rules for each operation
http://www.math.com/school/subject1/lessons/S1U1L10GL.htmlhttp://www.math.com/school/subject1/lessons/S1U1L10GL.htmlhttp://localhost/var/www/apps/conversion/current/tmp/scratch11450/Integers.ppthttp://localhost/var/www/apps/conversion/current/tmp/scratch11450/Integers.ppthttp://localhost/var/www/apps/conversion/current/tmp/scratch11450/Integers.ppthttp://localhost/var/www/apps/conversion/current/tmp/scratch11450/Integers.ppthttp://www.math.com/school/subject1/lessons/S1U1L10GL.htmlhttp://www.math.com/school/subject1/lessons/S1U1L10GL.html