Integer Operation Chip Modeling

Modeling Integer Operations

Integers! The first time I heard that word I thought it was some sort of food, but I remembered I was in math class, later to to find out integers are negative and positive numbers. After that, we got to learn how add, subtract, multiply, and divide these numbers. At sometimes it got really confusing, and we got tutoring from my mom, but after a while we learned tips and tricks to make it easier to understand. Now that we are at the end of our unit and our big test is coming up, we need as much practice as possible, here are some of the problems that we practiced with. While you read, you can learn a lot of the tricks that we use.

6 +  -4  = 2

The answer to this problem is 2 because when you make zero pairs with the negative four and the positive six,everyone one of the negatives is cancelled out. But there are still two positives left after the zero pairs. The two left over is the answer. The answer is two.

4 -  -3  = 7

If you start out with positive 4, you can add as many 0 pairs as you want because 0 pairs equal 0. I added three 0 pairs. Now, you have to subtract negative 3. 0 pairs contain one negative and one positive. If you take away the negatives, all is left is the positives. So now it’s just 3 + 4 = 7!

-4 × -2  = 8

I am going to use the distributive property to explain this. Lets take the problem -4(2+-2), it equals zero. Now lets change this problem using distributive property. It would be (-4×2)+(-4×-2), we know that this problem has to equal zero because when using distributive property it still has to have the same answer. -4×2 equals -8. We know that a negative and a positive that are the same answer equals zero. Now, -8 plus -4×-2 has to equal zero. This means -4×-2 equals 8 because 8 is the only possibility. This is the reason why -4×-2 equals 8.
Here's another way: Since a negative is a hater and a positive is a lover. This expression means ‘If someone is a hater of haters, what are they?’ If you hate hating, you love! Therefore, it is a positive. So you just have to do 4 times 2 = 8!

-8 ÷ 4 = -2

We know that the answer is negative two because when you divide negative eight into four parts there is negative two in each part. This means that the answer is negative two. Another way that I know is if a negative is a hater and a positive is a lover, than a hater of a lover is a hater, this means that the answer is negative. After that I figured out how it was negative two.

Rules for adding, subtracting, multiplying and dividing integers:

(Clearly explain the rules as you understand them here. Use math language.)

Adding :

To add integers you just need to imagine a number line. When you add a positive integer, you have to go the right of the number line that many times. However, when you add a negative integer, you have to move to the left of the number line that many times.

Subtracting :

This is just the opposite of adding. Again, just imagine a number line. When you subtract a positive integer, you have to go the left of the number line that many times. However, when you subtract a negative integer, you have to move to the right of the number line that many times.

Multiplying :

Something that I do to remember how to multiply negative numbers is give the positive and negative number names. For example, the negative numbers are haters and the positive numbers are lovers. I will demonstrate: If the problem is 3x -5, I do if they are a lover of a hater they are a hater, so that means that the answer has to be negative. After I do that, I can usually find the answer.

Dividing :

To divide, what I often do is the same thing that I do with the multiplying, it works either way. But what I also do is after I split the groups up for dividing I count what is in each group rather than how many groups there are.