2204919 integer notes

8/7/2019 2204919 Integer Notes

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IntegersIntegers

For 7For 7thth Grade MathGrade Math& Pre& Pre--AlgebraAlgebra



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!



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.



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.



Absolute ValueAbsolute Value

Absolute value isalways positive.always positive.

The symbol for

absolute value istwo vertical linesaround a

number.



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.)



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.



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.



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?



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.



Negativenumbers giveus a way totalk abouthow much

less thanzero

something is.

Why do we even needWhy do we even need

negative numbers?negative numbers?



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?



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)



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.




If you come to the openend first, say ³greater

than.´

If you come to the pointedend first, say ³less than.´



Practice with these:

8 > 3 -9 < -7

3 < 8 |4| <|-6|

-7 > -9 |-22|>|18|




Adding IntegersAdding Integers

When two numbers have thesame sign, the sum will also

have the same sign.

Positive + Positive = Positive

Negative + Negative = Negative




8 + 3 = 11 (or +8 + +3 = +11)

-7 + -10 = -17

3 + 19 = 22

-2 + -3 = -5



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.)





To add two numbers withdifferent signs, find their

difference (subtract) anduse the sign of the number

that has the largestabsolute value.




-10 + 3 = -7

15 + -4 = 11

8 + -13 = -5



Subtracting IntegersSubtracting Integers

Instead of subtracting, we

want to always talk aboutadding.

We are going to change all

our subtraction problemsto addition.



In any subtraction problem:

Change the minus to a plusand change the sign of the

second number.

(We could also just say³add the opposite.´)





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



Multiplying & DividingMultiplying & DividingIntegersIntegers

There are only two kinds of multiplying & dividing

problems:

Integers with the same sign

Integers with differentsigns



You have been multiplying& dividing numbers with

the same sign for a longtime!

Multiplying or dividing twonumbers with the samesign always makes a . . .





3 x 8 = 24

-3 x -8 = 24

50 / 2 = 25

-50 / -2 = 25



There is only one possibilityleft for multiplying &

dividing numbers withdifferent signs.

Multiplying & dividingnumbers with differentsigns always makes a . . .





45 / -9 = -5

-12 x 5 = -60

-5 x 9 = -45

60 / -5 = -12

2204919 integer notes

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