Allison Concepcion's Scribe Post: How to divide integersThere are many ways to divide integers some ways will work some cannot. Dividing integers is a bit more complex than multiplying integers but the same sign rule applies. A positive and a positive equals a positive. A negative and a positive equals a negative, and a negative and a negative equals a positive.
What does ÷ mean? This symbols means you are sharing _?_ into _?_ equal groups in this case lets just say you are sharing (+8) into 2 equal groups. When you are dividing integers the numerator is what you have ( you have 8) and the denominator represents how many groups there are (you have 2 groups) e.g.
8- What you have
2- How many groups you have
First off, if you are dividing two positives, there are two possible ways to show your work.
Step 1: Have (+8) and have 2 groups.
Share (+8) into 2 equal groups.
Step 2: Now you share (+8) into two equal groups
Your answer will be 4
Now that you've figured out how to show your work in one way, here's another way of how to show your work.
You are asking yourself, how many groups of (+2) are in (+8)?
Step 1: have your (+8)
Step 2: Now, ask yourself how many groups of (+2) are in (+8)
There are 4 groups of (+2) in (+8)
Your answer is 4
If you are dividing a negative and a positive integers, try to use the same method as before.
Step 1: Share (-8) into 4 equal groups
Step 2: You share (-8) groups into 4 equal groups
Your answer is -2
Method 2: How many groups of (+4) are in (-8)?
You cannot do this method because there are no groups of positive 4 in negative 8.
This time you are dividing a negative by a negative and also see if one of the two methods work.
Method 1: Share (-8) into (-4) groups.
It is not going to work because there is no such thing as (-4) equal groups.
Method 2: How many groups of (-4) are in (-8)?
Step 1: Have your (-8)
Step 2: Now ask yourself, how many groups of (-4) are in (-8)
1 group + 1 group = 2 groups
Your answer is 2.
Now, you are dividing a positive by a negative, same rules apply try the same two methods to see if one of the two methods work.
Step 1: Share (+8) into (-4) equal groups
You cannot do this method because there is no such thing as sharing positive 8 into negative 4 equal groups.
Method 2: How many groups of (-4) are in (+8)?
Once again you cannot do this method because there are no groups of (-4) in (+8)
Since none of these methods work there is another different method that we can use which is called Multiplicative Inverse. Multiplicative inverse is basically the opposite of dividing so instead od dividing to figure out the answer you have to multiply to get the answer.
Step 1: Ask your self (-4) multiplied by what will equal (+8)?
(-4)x (? ) =(+8)
Step 2: If you figure out what the missing number is that will be your answer.
(-4)x (? ) =(+8)
-2 will be your answer.
You cannot show this method by using a model you can only show this method by using multiplicative inverse.
(Skip to 7:09 to learn how to divide integers)