**Cool Interesting Facts about Integers**

What the Extension Project was About

One of the many asked questions in math that I hear is "When will we use this in life?" Well, learning about integers in a whole new way helped me better understand this concept. The integer extension project is all about learning the history about integers. Also, I got the opportunity to learn more ways to better use and understand integers. I learned many new ways to help people better explain integers, but here are just some of the ways that might help you.

Definitions of Old and New Words

In the very beginning of the project, I learned some very important terms that helped me throughout it. Those terms were:

1. Integer

2. Absolute value

3. Positive Numbers

4. Negative Numbers

5. Opposite

The definition of these words were:

1. The numbers that are after zero.

2.Two integers that are the same distance away from zero (Negative and Positive).

3. A whole number that can wither be greater then or less then zero.

4. The distance of a number (Negative or Positive) away from zero.

5. The numbers that come before zero.

Can you guess which word goes with which definitions? :)

History of the Negative Numbers

This was the one question that wanted me to start this extension. What is the history of negative numbers? Well, from the research did, here are some of the most interesting and important facts I found that you should know.

Rules for Integer and Integer Operation

You may already know what to do when adding, subtracting, multiplying, and dividing integers, but here's a quick review of all of them.

**By: Hunter Springer**

Key!

1. Integer with definition number 3.

2. Absolute value with definition number 4.

3. Positive numbers with definition number 5.

4. Negative numbers with definition number 1.

5. Opposite with definition number 2.

Did you get them right? :)

Integers were introduced by a man named Arbermouth Holst in 1563.

Negative numbers were finally excepted into the number line in the nineteenth century.

The Chinese were the first known culture to use Negative numbers.

The symbol for integers is Z, and Z stands for Zahlen, which is German for integers.

In Latin, the word integer means whole and complete, figuratively. Untainted, upright, and untouched, literally. The root word "in" in integer means "to touch."

Did you know any of those facts? :)

Positive+Positive=Positive

Negative+Negative=Negative

Negative+Positive=Varieties of answers; it depends on the sign

Positive+Negative=Varieties of answers; it depends on sign

Adding Integers:

Subtracting Integers

Multiplying Integers

Positive*Positive=Positive

Negative*Negative=Positive

Positive*Negative=Negative

Negative*Positive=Negative

Dividing Integers

Positive/Positive=Positive

Negative/Negative=Positive

Positive/Negative=Negative

Negative/Positive=Negative

Positive-Positive=Varieties of answers; it depends on sign

Negative-Negative=Varieties of answers; it depends on sign

Positive-Negative=Positive

Negative-Positive=Negative

Got it? :)

Integers in Everyday Life

Why are we learning this? It's not like we're going to use it in real life! This remain you of someone you know, or you? :) You may not believe me, but we use integers everyday and don't even realize it! Here are just a few examples of using integers in your daily routine.

When dealing with temperature, we're using negative and positive numbers. This can affect the way we dress and act. For example, if it's in the negatives or also known as below zero, you're going to dress heavily. If it was in the high positives or really hot, then you would dress lightly to stay cool.

Using money is another thing that involves integers. You can get or find money, which is the positive integers. Also, you can lose or owe money to someone. That would be the negative integers.

Even the most simplest things can be using integers, like going up or down with stairs or in elevators. Traveling up an elevator or stairs would be going up into the positive numbers. Once your below ground, however, you're going into the negative side of the number line. Ground level would be the 0 on the number line.

The location of where you are right now is an integer. If you're above sea level, then you're in the positive integers. If you are below it, however, then you are in the negative integers. The sea level would actually be zero on the number line because it's splitting the two positive and negative sides.

See what I mean about using integers in everyday life? :)

Rational and Irrational Numbers

You may be thinking right now "What in the world is irrational and rational number?" "How do I solve problems dealing with them? From all the research I did, I can answer all of those questions right now.

1. Rational means a number that can be expressed exactly by a ratio of two.

2. Irrational means a number that can't be exactly expressed as a ratio of two.

Now, solving irrational number problems can be a little tricky because there are many steps to go with them, but I'll try to explain it the best and lease painful way possible. :)

Now you try! Figure out the problem listed below.

X=0.7

_

Key!

The fraction for 0.7 is 7/9.

_

You Solve the Problems!

Adding

Makayla was helping build a house, and she had to climb up a latter. She started in the basement, which is 1 floor below the main level. She climbed up 3 floors before tranfering to another ladder. That latter took her up 2 more floors. She then traveled down 1 floor because she dropped her hammer. What floor is Makayla on now?

Subtracting

Hunter and her friends went scuba diving last week and they went down 50 feet. The the girls continued down another 25 feet when they saw a school of fish pass by above them. Curiosity overtook them, and they went up another 10 feet. How far underwater are Hunter and her friends?

Multiplying

On a regular day, Jenna would buy 3 apples for $1.89 each. Today, however, there was a sale for 30 cents off each apple bought. How much money did Jenna end up having to spend on the apples today?

Dividing

Abby had 24 cookies, and she wanted to share them with each of her friends equally. She gave each friend, including herself 3 cookies. Before she gave each friend a cookie, she dropped 3 cookies on the ground and had to throw them away. How many friends did Abby give cookies to?

Key!

Adding: Makayla is on the 4th floor.

Subtracting: Hunter and her friends are -65 feet below the surface.

Multiplying: Jenna will spend $4.50 today on 3 apples.

Dividing: Abby has 6 friends that will receive 3 cookies.

Other Awesome and Cool Facts

The original number line looked like this:

Three very common irrational numbers are PI, E, and Golden Ratio.

PI: The circumference to the diameter of a circle

E: The base of the Natural Logarithms.

Golden Ratio: A special number equal to about 1.618.

Conclusion

I hope you learned a lot about the world of integers. Overall, I thought this project was actually pretty fun. If I could, I would probably do another extension dealing with math. It's always fun to me to learn about new things that I didn't know before. I hope you all are the same way. Also, I hope you leaned a lot from this presentation over integers.

Hope you learned a little bit more about integers!!! :)

Here are some problems listed below that you can try and solve!

Did you get those problems right? :)

1. A formula for writing a repeating decimal as a fraction is making it into an equation that includes the repeating decimal.

2. Choose a variable and make it the equal to the repeating decimal.

3.Look at the repeating decimal to determine how many repeating digits there are.

4.Take the original equation and multiply each side by the place value following the decimal.

5. Subtract the old repeating decimal to both the new equation to equation and variable to get rid of the repeat.

6. Then, you get the new equation.

7. Divide the left number by the same number, and the right side by the left sides amount. The right side will cancel out, and then you’ll finally have your fraction.

Example for the very end: divide the left number, 7,by the same number, 7, and the right side, 6, by the left side, 7. The right side will cancel out, 7/7, and then on the right side you finally have your fraction, 6/7.