2204919 integer notes
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8/7/2019 2204919 Integer Notes
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IntegersIntegers
For 7For 7thth Grade MathGrade Math& Pre& Pre--AlgebraAlgebra
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What is an Integer?What is an Integer?
An integer is any whole number orits opposite.
Integers are part of a group of numbers called ³real numbers.´
Integers can be positive (+) or
negative (-).
-3, 1, 104, -76 : all these are
integers!
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OK OK ±± so what¶s anso what¶s anopposite?opposite?
An opposite has thesame absolute value
but a different sign.
The opposite of 5 is -5.
The opposite of -7 is 7.
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OK OK ±± so what¶sso what¶sabsolute value?absolute value?
Absolute value tellshow far a number is
from zero.
It tells how ³big´ the
number is withoutconsidering the sign.
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Absolute ValueAbsolute Value
Absolute value isalways positive.always positive.
The symbol for
absolute value istwo vertical linesaround a
number.
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Absolute ValueAbsolute Value
|-5| = 5
|8| = 8
|-13| = 13
(Read: The absolute value of -5 is 5.)
(Read: The absolute value of 8 is 8.)
(Read: The absolute value of -13 is 13.)
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IMPORTANT!!!IMPORTANT!!!If a number does not
have a sign, it is
consideredPOSITIVE.
A number with a plus
sign in front of it isalso consideredpositive.
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Are all numbersAre all numbersintegers?integers?
NO!! Only whole numbers orthe opposite of whole
numbers (negatives).
What can¶t be an integer?
Numbers that havefractions or numbers after
a decimal are not integers.
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These numbers are not integers:
2/3 1.05 5 7/8
2.5 7/9
-- But they are still ³real numbers.´ You can add, subtract, multiply &
divide them, but they are not
integers.
Are all numbersAre all numbersintegers?integers?
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Putting Integers in OrderPutting Integers in Order
Let¶s look at a number line.
-6 -4 -2 0 2 4 6
Numbers get bigger (more
positive) as you go to the right
They get smaller (morenegative) as you go to the left.
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Negativenumbers giveus a way totalk abouthow much
less thanzero
something is.
Why do we even needWhy do we even need
negative numbers?negative numbers?
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Like on Jeopardywhen somebodyhas no money andthen they lose$500. Their scoreis -500.
Or like when it gets
really cold outside,negative numberstell us how farbelow zero it is.
Why do we even needWhy do we even neednegative numbers?negative numbers?
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Other Ways to Use NegativesOther Ways to Use Negatives
Direction (positive for east,negative for west)
Yardage lost in football
Money (negative money is a debt)
Altitude (negative altitude is below
sea level)
Time (negative time is before an
event, positive time is after)
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Using < and >Using < and >
Sometimes we need to use the³greater than´ and ³less
than´ symbols to comparetwo numbers.
If you read the symbols fromleft to right, it¶s easy toremember which symbol iswhich.
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Using < and >Using < and >
If you come to the openend first, say ³greater
than.´
If you come to the pointedend first, say ³less than.´
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Practice with these:
8 > 3 -9 < -7
3 < 8 |4| <|-6|
-7 > -9 |-22|>|18|
Using < and >Using < and >
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Adding IntegersAdding Integers
When two numbers have thesame sign, the sum will also
have the same sign.
Positive + Positive = Positive
Negative + Negative = Negative
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Adding IntegersAdding Integers
8 + 3 = 11 (or +8 + +3 = +11)
-7 + -10 = -17
3 + 19 = 22
-2 + -3 = -5
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Adding integers with differentsigns is a little more
complicated.
You have to figure out whichnumber has the greatest
absolute value.
(That just means which numberis farther from zero.)
Adding IntegersAdding Integers
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Adding IntegersAdding Integers
To add two numbers withdifferent signs, find their
difference (subtract) anduse the sign of the number
that has the largestabsolute value.
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Adding IntegersAdding Integers
-10 + 3 = -7
15 + -4 = 11
8 + -13 = -5
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Subtracting IntegersSubtracting Integers
Instead of subtracting, we
want to always talk aboutadding.
We are going to change all
our subtraction problemsto addition.
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In any subtraction problem:
Change the minus to a plusand change the sign of the
second number.
(We could also just say³add the opposite.´)
Subtracting IntegersSubtracting Integers
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Subtracting IntegersSubtracting Integers
9 - +3 = 9 + -3 = 6
-15 - +6 = -15 + -6 = -21
7 - + 12 = 7 + -12 = -5
-6 - -8 = -6 + 8 = 2
13 - -4 = 13 + 4 = 17
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Multiplying & DividingMultiplying & DividingIntegersIntegers
There are only two kinds of multiplying & dividing
problems:
Integers with the same sign
Integers with differentsigns
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You have been multiplying& dividing numbers with
the same sign for a longtime!
Multiplying or dividing twonumbers with the samesign always makes a . . .
Multiplying & DividingMultiplying & DividingIntegersIntegers
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Multiplying & DividingMultiplying & DividingIntegersIntegers
3 x 8 = 24
-3 x -8 = 24
50 / 2 = 25
-50 / -2 = 25
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There is only one possibilityleft for multiplying &
dividing numbers withdifferent signs.
Multiplying & dividingnumbers with differentsigns always makes a . . .
Multiplying & DividingMultiplying & DividingIntegersIntegers
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