Combining Integers

Combining Integers

What is an Integer? (No decimals No Fractions)Negative numbers Positive numbersZero

Getting Started9 feet. Correct?First, lets talk about the real world. If you went outside and dug a 10 foot hole and then got your shovel and put 1 foot of dirt back in the hole, how deep would the hole be?

There is Something Strange Here!!We have the following -10 + 1 = -9This is a 10 foot hole. We then add 1 foot of dirt and end up with a 9 foot hole.

The Strange thing is How did you solve it?

This is an addition problem, but to solve it you had to subtract.

-10 + 1 = -9First you need to understand that

You must compare what is in front of the two numbers. The addition sign doesnt tell you what to do.

-10 + 1 = -9The signs are differentWe already know we must subtract to solve this. 10 - 1 9We always keep the sign in front of the bigger number. Thus the answer is -9.In factWe always subtract when the signs are different!!And

Lets Dig Another Hole!11 feet. Correct?If you went outside and dug a 10 foot deep hole and then jumped down in the hole and dug down 1 more foot, how deep would the hole be?

Once Again There is Something Strange Here!!Maybe you didnt notice, but we have the following:

-10 1 = -11

This is a 10 foot hole. Take away 1 more foot of dirt and you end up with an 11 foot hole

The strange thing is How did you solve it?

This is a subtraction problem, but to solve it you had to add!-10 1 = -11The first thing you need to understand about this is... A negative sign is essentially the same as a subtraction sign.Next The subtraction sign doesnt tell you what you should do. You still have to compare the signs in front of the two numbers!-10 1 = -11Since a negative is the same as a subtraction sign

Thus the answer is -11 because 10 is bigger than 1.We always keep the sign in front to the bigger number. ThenWhen we add we get 10 + 1 = 11 We always add when the signs are the same! In factThe signs are the same and we already know we must add.Lets Try Some Practice Problems! -44 18 The signs are the same so we add 44 + 18 = 62The answer is -62 because 44 is bigger than 18.-10 + 54 Different signs 54-10 44Big number on topThe answer is

We subtractPositive 44 because the big number is positive. -21 15 Add because the signs are the same. 21 + 15 = 36The answer is -36 because 21 is bigger than 15.What Rules Have We Learned?Different Signs : We SubtractSame Signs : We AddAlways Keep The Sign of The Bigger Number!

You Rock!!