Math 6H ( Period 5)

Adding Integers 3-2

Chapter 3-2 Adding Integers

Integers like 2 and -2 are called opposites

Two integers that are opposites are also called Additive Inverses

ADDITIVE INVERSES:

When the two addends are OPPOSITE SIGNS of the SAME AMOUNT, the sum is ZERO.

I say: Additive Inverses…YAY! Because looking for them, makes the math easier.

Who wins? NO ONE! IT’S A TIE!!!

Additive Inver Property- the sum of any number and its addivitve inverse ( opposite) is ZERO

Adding Integers

The rules:

SAME SIGN: Just add and keep the sign

4 + 5 = 9     and -4 + (-5) = -9

-14 + (-16) = -30

DIFFERENT SIGNS: Don’t add! Take the difference (subtract) and take the sign of the bigger absolute value

 When adding integers with different signs—DON’T ADDà take the difference and use the sign of the larger absolute value!!

I SAY:

WHO WINS? (which number [absolute value] is bigger?)

BY HOW MUCH? (you’ll automatically take the difference)

When you play a game, you know if you won or not

AND

You know how much you either won or loss by!

 ALWAYS “ STACK ‘EM”

-8 + 20

Who won?

The positive team

By how much?

12!

Does it work with same signs?

Yes, because only one team came to play ;)

-8 + (-20)

Who won?

Only the negative came to play so the negatives

By how much?

Since they’re on the same team, just add up the players’ scores

TWO MORE WAYS TO UNDERSTAND ADDING INTEGERS:

1. A positive/ negative sketch

Represent each positive number with the appropriate number of + signs

Represent each negative number with the appropriate number of – signs

Place them on different rows

Box in the number that match and cross them out…they are ADDITIVE INVERSES and equal 0

Whatever is left OUTSIDE the box, is the answer

-3 + 5

 -  -  - 

 +  +  +  +  +

The answer is +2

2. A number line

The positive direction is right

The negative direction is left

Remember: Due to our BFF the Commutative Property of Addition, you can do addition in any order that’s easiest!

-8 + 12 + (-4)

becomes

-8 + (-4) + 12

Then add the first two addends

-12 + 12 = 0

Simplify

w + (-4) + 2 = w + (-2)

7 + a + -7 = a