Download - F1 Math C6 Integers1ab
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Operations withIntegers
PowerPoint
Created By: Miss Henry
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What is an Integer?
• A whole number that is either greaterthan 0 (positive) or less than 0
(negative)
• Can be isuali!ed on a number line:
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What is a "umber #ine?
•A line with arrows on both ends thatshow the integers with slash mar$s
•Arrows show the line goes to in%nity in
both dire&tions ' ( and )*
•+ses a negatie sign ')* with negatienumbers but no positie sign '(*
with positie numbers•,ero is the origin and is neither
negatie nor positie
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What are Opposites?
• -wo integers the same distan&e .rom theorigin/ but on di0erent sides o. !ero
•1ery positie integer has a negatie
integer an e2ual distan&e .rom the origin
•13ample: -he opposite o. 4 is
)4•13ample: -he opposite o. )5 is
5
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What is Absolute
6alue?•7istan&e a number is .rom !ero on anumber line 'always a positie number*
•Indi&ated by two erti&al lines 8 8
•1ery number has an absolute alue
•Opposites hae the same absolute aluessin&e they are the same distan&e .rom !ero
•13ample: 8)98 9 and 898 9
•13ample: 8;
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What Can We 7o to Integers?
•Integers are numbers/ so we &an add/subtra&t/ multiply/ and diide them
•1a&h operation has di0erent rules to .ollow
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Adding =ules > ame
igns•I. the integers hae the SAME signs:ADD the numbers @ $eep the same sign
•Positie ( Positie Positie Answer•"egatie ( "egatie "egatie Answer
• 13amples: )3 + (-10) = ? ? = -1
• 6 ( '9* ? ?
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Adding 'ame igns* )
13amples #1. -3 + (-10) Step 1: D Add the #s
Step 2: -D Keep same sign (Both #s arenegative – Answer is negative!)
#2. 6 + (8)
Step 1: Add the #s
Step 2: Keep same sign (Both #s are positive – Answer is positive!)
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Adding =ules > 7i0erent igns
•I. the integers hae the DIFFERE! signs:S"!RA$! the numbers @ use sign o. the
I%%ER number
•Bigger E is Positie Positie Answer
•Bigger E is "egatie "egatie Answer
• 13amples: -13 + (7) = ? ? = -6
• 23 ( ')9* ? ? ;
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Adding '7i0erent igns* )13amples #1. -13 + (7)
Step 1: 4 Subtract the #s
Step 2: )4 Use sign of bigger # (Bigger # isnegative - Answer is negative!)
#2. 5D ( ')9*
Step 1: ; Subtract the #s
Step 2: ; Use sign of bigger # (Bigger # is positive - Answer is positive!)
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ubtra&ting =ules•Put ' * around se&ond number @ its sign
•Change S"!RA$!I& sign to anADDI!I& sign
•Change sign o. 5nd
number to its opposite
•Follow the rules .or ADDI!I&:
)SAME signs: Add @ $eep the same sign)DIFFERE! signs: ubtra&t @
use sign o. bigger E • 13amples: ); > )<
= ? ? =
5
• 9 ) 5D ? ?
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ubtra&ting ) 13amples #1. ); > )< #2.G ) 5D
Step 1: ); > ')'5D*
Step 2: ); ( ')
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Multiplying =ules
• Multiply the numbers li$e usual•I. the integers hae the SAME signs:
AS*ER will be +&SI!I,E
•I. the integers hae DIFFERE! signs:AS*ER will be E%A!I,E
• 13amples: )D · (-5) = ? ? = 15
• -9 · (-10) = ? ? = 90
• -7 ? ? )G
• 6 · -6 = ? ? = -36
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Multiplying ) 13amples
• #1. )D · (-5) #2. -9 · (-10)
• ; &u%tip%' the numbers G<
• ; Same signs ositive Answer G<
#3. ) · 7 #4. 6 · -6
49 &u%tip%' the numbers D4
)G *ifferent signs +egative Answer )D4
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7iiding =ules• 7iide the numbers li$e usual
•I. the integers hae the SAME signs:AS*ER will be +&SI!I,E
•I. the integers hae DIFFERE! signs:AS*ER will be E%A!I,E
• 13amples: )DD ÷ (-3) = ? ? =
11
• -90 ÷ (-10) = ? ? = 9
• -20 J 5 ? ? )<
• ÷ - = = -
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7iiding ) 13amples
• #1. )DD ÷ (-3) #2. -90÷ (-10)
• *ivide the numbers G
• Same signs ositive Answer G #3. )5
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Mi3ed Pra&ti&e
Solve the olloing pro/les:
)G ( )G
)9
)
)59
)< ) ')G*
G
)D; J
);
; (
)5;)<
)5D ) G
)D5
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=eiew
• 6isit the website below .or additionalin.ormation on integers:
http:KKwwwLmathL&omKs&hoolKsube&tK
lessonsK+#
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=eiew
• 6isit the website below .or additionalin.ormation on integers:
http:KKwwwLmathL&omKs&hoolKsube&tK
lessonsK+#