Math 6High(Period 3)

Adding Integers Using Addition Rules 4.3

Absolute Value of a number--> is its distance from ZERO on a number line. 

The absolute value of a number a is written as  

The absolute value of any number is always positive because absolute value is a distance concept—and distances are always POSITIVE

When Adding  Integers using the following rules:

To add two integers with the same sign, just add them and use their sign.

To add two integers with different signs, subtract the lesser absolute value from the greater absolute value and write the sign of the integer with the greater absolute value.
We called this  “Who Wins?... and   “ By How Much?”   

That is you decide who is the winner (the integer with the greater absolute value) and you take the difference ( subtract the smaller absolute value from the larger absolute value). Use the “winner’s sign.”

Identity Property of Addition: 

The sum of zero and any integer is the integer

0 + (-3) = -3  

Zero is called the ADDITIVE IDENTITY.

The sum of -3 and -5 is negative because

-3 + -5  are both negative  --> they have the same sign

-3+ -5 = -8

But what about

-5 + 3= ?

These are two integers with DIFFERENT SIGNS… Who wins? The negative… by how much?  5-3 = 2 so the solutions is – 5 + 3 = -2

What about 5 + (-3) ?

Again these are two integers with DIFFERENT SIGNS… Who wins? This time the positive… by how much? 5-3 = 2 so the solutions is  5 +(-3) = 2

Here are a number of good strategies to use when adding more than just two integers….

When adding a series of numbers use the commutative and associative properties of addition to group numbers with the same sign.   

• First, always look for ZERO PAIRS  (they cancel each other out)—giving you less work to do!  
• Find the sum of the positive numbers and the sum of the negative numbers. Then add the two sums.

Finding the average of integers is just the same as finding the average of natural numbers. Just remember to use the strategies above to combine positive and negative numbers.
For instance   The daily temperature for one week in Helene Montana in the winter was 5ºC ,    3ºC,      2ºC,     0ºC,     -2ºC,    -3ºC       -4ºC .   

Notice, there are 7 degrees listed for the 7 days—even though one of them was 0ºC.
You need to make sure you use the 7 temperatures.

In this case I would use zero pairs to add 3 + (-3) and 2 + (-2) and I am left with only adding  5 + (-4) = 1 that was easy.... where is my Easy Button? 

Now divide 1 by the number of temperatures we started with-- that was 7 for the 7 days...

1 /7 is 0.142857…. which would round to a very chilly 0.14ºC