Math extension

Math extension

History

In the 19th century, negative numbers were accepted. The word integer was introduced in 1563 by a man named Arbermouth Holst who was doing an experiment. The word integer in Latin means untouched, hence, undivided, and whole. The symbol for an integer is Z. The symbol Z is often used to denote a set of integers. The symbol originates from the word “Zhalen” which means ‘Number’ in German.

Rules

2 ways integers are used in everyday life.

Arbermouth Holst

Integers are like elevations. If I'm a sea diver and I go down 50 feet into the water, then I'm at -50. Then I go up 75 . There I am at a positive 25. It's like that because sea level is 0.

A way that integers can take part in our life is like finding your locker on the first day of school. My locker number is 105 and it's hard for me to find, so I look at other numbers. I see a locker that says 7 on it. and I know that to get to 105 I need to go at least 100 lockers. That's like going up positive 100. I go up 100 lockers and find myself at locker number 107. I realize I went up to far and need to go down a couple of lockers. Since I'm going down then I'm also having to add a negative number. I find my locker -2 away from locker 107.

When you are adding two integers with the same sign you would want to drop the sign and just add, when you find your sum you would just add the sign back. When you are adding two integers with different signs then you would use the sign that belongs to the integer with the biggest absolute value. (distance from zero) Then you would subtract the two numbers to find your answer and add the sign. You can determine the difference between two integers with the same signs easily. When the signs are both positive then you just want to subtract regularly and then determine the sign. If you are subtracting two negative integers then, you actually add them together and keep the sign a negative. When you are trying to determine the difference for two integers with different signs then, if the absolute value of the positive number is greater then you would just subtract and keep the positive sign. But, if the negative numbers absolute value is greater then you would just subtract the numbers and keep the sign as a negative. For multiplying and dividing integers then you must know that when the signs are the same (either both positive or negative) the answer will always be positive. But, if the signs are different then the answer will be negative. Then you would just multiply and divide as normal and then add your sign based upon your integers.

Integer: A whole number that can be either greater or less than zero, a positive or negative.

Negative number: A number that is less than zero, to the left of the zero on the number line.

Positive number: A number that is greater than zero, to the right of the zero on the number line.

Opposite: Two integers are opposites if they have the same absolute value but are on different sides on the number line.

Absolute Value: The distance from zero.

2 real-life word problems

Rational and Irrational

I have 60 minutes to complete 4 tasks. It takes me 20 minutes to complete each task. My mom gave me 5 extra minutes at the end. Did I have enough time to complete every task? 60/4=15 minutes, 4*20= 80 minutes>> the actual amount of time it took me, 60-80= -20, -20 +5= -15 minutes. therefore, I didn't complete my tasks on time.

If it is 49F in Kansas and -2F in Missouri what is the sum?

49+ (-2) = 47F

A rational number is an integer or a fraction. An irrational number cannot be represented as a simple fraction. A common irrational number is Pi. it's the ratio of the circumference to the diameter of a circle. Another common irrational number is e. It is often called Euler's number after Leonhard Euler. A final irrational number is the golden ratio. the golden ration often appears in art and geometry.