integers positives and negeatives!. describing landscapes when describing landscapes, scientists can...

IntegersPositives and negeatives!

Describing Landscapes

When describing landscapes, Scientists can compare heights of mountains by meters, sometimes miles; but what about describing ocean depths?

Scientists chose sea level as a zero point for integers, and describe heights above it in positive numbers, and numbers below in negative numbers.

Check out the number line!

•Notice how positive and negative 2 are only 2 places away from zero. They are equal distances from zero. Hence, opposites!

•Absolute value is the distance from zero on the number line. How far away is -7 from 0? How far away is 7 from 0?

•Therefore, both -7 and 7 have the same absolute value!

•What else can negative numbers describe?

So how can we compare numbers?

• Recall common symbols:

• <

• =

• >

• Now we have the absolute value symbol: |3|

• Example 1: 3 ______ |-3|

• What is the relationship?

Using your number line

• Absolute value is: the distance from zero. So

|5| = 5

• |-3| = 3

• So |-6| ________ 4

• - |-3| ___________ |-2|

Using absolute value:

Example 1: Adding positive values- add the ab. Values ( 5 +5 = |5| + |5|)

Adding negative numbers : (-5)+ (-9) + (-16)

SHOW

YOUR SIGN

S

Signs of Numbers

• Sum of positive integers is ________

• Sum of negative integers is ________

• Sum of negative and positive number has the sign of the number with greatest absolute value

• Sum of number and opposite is zero

• Examples: page 6, 1 and 2

Examples

• 5 +5

• -8 + (- 2)

• -12 + 6

• 8 + (-13)

• 7 + (-7)

Adding integers with unlike signs

• Method 1: Take the positive number and add the negative number (see number line)

• (6) +(-4) = _____

• Method 2: Subtract the absolute values, and give the result the sign of the greater number.

• -9 +13 = |13| - |-9| = 13 – 9 = 4 and use the sign of the larger number ( in this case, the larger number is…)

• Try 1, 2, 3, 4 right now!

SuBtractingIntegers

Represents -1 ( a negative 1)

MINUS

So (-9) – (-4) = -5

Do examples 1,2,3 on page 9

Number Line Example

Take away- 4

Come on Deep Sea Divers!

Your new teacher just won the lottery, and the whole class is going scuba diving. The oxygen tanks can go 55 feet below sea level. The diving experts suggest that new divers should only go 34 feet below their first time.

What is the distance between the sea level and how deep you go?

If you go to 34 feet, what is the absolute value of the difference between the level of where you go and where an experienced diver goes?(How much deeper is the expert diver?)

Adding/subtracting Integers

• Sum of positive integers is ________

• Sum of negative integers is ________

• Sum of negative and positive number has the sign of the number with greatest absolute value

• Sum of number and opposite is zero

• Example: ( 3) + (3) + (3) + (3) = 3x4=

• (-3) + (-3) + (-3) + (-3) = (-3)x4 =

Rules of Multiplying integers

• +times+ = +

• - times - = +

• - times + = -

• - times 0 = 0

When multiplying many numbers…

• Multiply the numbers, and follow your rules!

• Negative times negative:

• Positive times positive:

• Positive times positive:

• You can also multiply many numbers together!

• -4 x -4 x 3 = (-4 x -4) x 3 =

• Do examples 1, 2, 3, 7, 11

Properties!

Commutative•a +b= b +a ab=ba

Associative(a+b) +c = a + (b+c) (ab)c=a(bc)

IdentityA +0= A ax1=a

Inverse ZEROa+(-a)=0 0xa=0