Math 7 (Period 4)

Using Rules to Add Integers 3.3

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

-          7 + (-5) = -12

To add two integers with different signs find the absolute values and take the difference. Use the sign of the number with the larger absolute value.

In 7^th grader terms:

Thinkà  Two teams:  the negatives and the positives

Ask yourself.. Who wins?  (that tells you who has the greatest absolute value)..

Stack them with the winner on top and take the difference ( subtract)

Use the sign of the winner!

The two questions to ask yourself ...Who wins? and By how much? 

43 + (-152)

The negatives win here

stack

152

-43

109

The solution must be -109

What if there are several addends? Here is a great strategy to follow:

1) See if there are any additive inverse first. Cross them out  using Inv+

2) Add the positives to the positives

AND

the negatives to the negatives

What properties allow us to do that? C+ and A+

3) Finally add the positive sum to the negative sum…
See “Who wins?” and “By how much?”

We tried this with a string of addends:

+ 3 + (-2) + 17 + 20 + (-3) + (-17)

We noticed that 3 and (-3) were additive inverses as well as

17 and (-17)

We crossed them out and were left with

(-2) + 20

That became easy—The signs were different so we asked ourselves.. “Who wins? and “By how much?”

the positive won.. by 18 so the answer was

+18

Then we tried:

+4 + (-5) + 18 + 3+ 25 + (-18) +(-4) + (-6)

we noticed we could cross out the +4 and the (-4)

as well as the +18 and the *-18)

Those were both additive inverses.

We were left with

+(-5) + 3+ 35 + (-6)

Add the positives 3 + 25 = 28

Add the negatives +(-5)+(-6) = -11

Then take the difference

28 -11 = 17

Much easier than working from left to right. You will make less “silly” mistakes using these strategies!

Adding Integers with variable expressions

Just substitute in for the variable, putting the substituted number into hugs (  )

Then evaluate using the integer rules… Plug & Chug

y + 5  where y = -12

(-12) + 5 = -7