What is an Integer? (No decimals – No Fractions) Negative numbers Positive numbers Zero
Getting Started 9 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 = -9 This 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 = -9 First you need to understand that… You must compare what is in front of the two numbers. The addition sign doesn’t tell you what to do.
-10 + 1 = -9 The signs are different… We already know we must subtract to solve this. 10 - 1 9 We always keep the sign in front of the bigger number. Thus the answer is -9. In fact… We 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 didn’t 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 = -11 The first thing you need to understand about this is... A negative sign is essentially the same as a subtraction sign. Next… The subtraction sign doesn’t tell you what you should do. You still have to compare the signs in front of the two numbers !
-10 – 1 = -11 Since 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. Then… When we add we get … 10 + 1 = 11 We always add when the signs are the same! In fact… The 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 = 62 The answer is -62 because 44 is bigger than 18.
-10 + 54 Different signs… 54 -10 44 Big number on top The answer is… We subtract Positive 44 because the big number is positive.
-21 – 15 Add because the signs are the same. 21 + 15 = 36 The answer is -36 because 21 is bigger than 15.
What Rules Have We Learned? Different Signs : We Subtract Same Signs : We Add Always Keep The Sign of The Bigger Number!