Integers

Integers

Integers - are a set of positives or negatives and their opposites (negatives or positives).

ex. 4 is a positive number. The opposite of positive 4 is negative 4 (-4). -5 opposite 5

note: 4 is bigger than -4.



Addition Rules

1. If the signs are the same (-3 + -4), then add the numbers and keep the sign of the numbers. -3 + -4 = -7 2 + 6 = 8 -5 + -9 = -14


2. If the signs are different ( -2 + 5), than subtract the small actual number (2) from the bigger actual number (5). Keep the sign of the bigger number (5). -2 + 5 = 3 -14 + 7 = -7

Subtraction Rule

1. Change the subtraction symbol to a plus then change the second number to it's opposite. -3 - 7 = -3 + -7 = -10 12 - 5 = 12 + -5 = 7 18 - -9 = 18 + +9 = 27


2. The two pencil mark rule - when you have an integer minus a negative you do two marks. You change the minus to a plus, then the negative sign to a plus. 17 - -8 = 17 + +8 = 25 -6 - -9 = -6 + +9 = 3

Subtraction really doesn't exsist! Any regular subtraction problem is really a number plus a negative.

Multiplication and Division

You think of multiplication as repeated addition.

1. 3 x 2 = 2 + 2 + 2 = 6 then 3 x -2 = -2 + -2 + -2 = -6


2. When the signs are the same ( 4 x 5 or -9 x -3), the answer is a positive ( 4 x 5 = 20 and -9 x -3 = 27).


3. When the signs are different ( 6 x -4 or -2 x 8), the answer is a negative ( 6 x -4 = -24 and -2 x 8 = -16).

It's the same rules for division.

Here's two sights that will help you learn, or if you just want to learn more: http://www.mathleague.com/help/integers/integers.htm http://www.math.com/school/subject1/lessons/S1U1L10GL.html

Here's something for practice: http://www.math-drills.com/integers.shtml

Factors

A factor is a number that can be divided evenly with 1 or more numbers.

12: 1, 12, 2, 6, 3, 4

1 x 12 = 12

2 x 6 = 12

3 x 4 = 12

The factors of 12 are 1, 12, 2, 6, 3, 4. Each pair of numbers multiplied together get 12. The way you do factors is take a number like 12. 1 abveously goes into 12 because 1 can go into any number above 0. Every number goes into itself. 1 x 12 = 12. Since 12 is an even number, 2 can go into it. But how many times? To figure it out, you go backwards. 12 divided by 2 is 6. 2 goes into 12 6 times. 2 x 6 = 12. You do the same thing to 3 and 4. It's easier if you start at 2 then work your way up.

Some tricks:

1. 2 if the number is even.
2. 3 if the sum of the digits are divisible by 3.
3. 5 if the number ends in 0 or 5.
4. 6 if the number is divisible by 2 and 3.
5. 9 if the sum of the digits are divisible by 9.
6. 10 if the number ends in o.
7. 11 (for 2 digit numbers) if the number is doubled.
8. 11 (for 3 digit numbers) if the two outside numbersadd up to the middle number.
   

When would you use factors? You use them when you have a party. How many candies go in each bag? I have 6 bags and 12 candies. 12 divided by 6 is 2. 2 and 6 are factors of 12. You would put 2 candies in each bag.

A great website for more practice is http://www.math.com/school/subject1/lessons/S1U3L1EX.html!!!!

Greatest Common Factor (GCF)

The Greatest Common Factor or GCF is the largest common factor of two or more numbers.

36: 1, 36, 2, 18, 3, 12, 4, 9, 6

48: 1, 48, 2, 24, 3, 16, 4, 12, 6, 8

The GCF would be 12 because 12 is the highest number they both have. The way you would do this is by listing the factors of each number. I look at the lowest number and it's factors. (36) Which ever factor is the highest number, I start there and work my way down. First, 36 can't go into 48. So, I move down to the next highest number. 18 can't go into 48 either. I go down again. 12 can go into 48. Maybe some of the lower numbers could go into it. But 12 is the highest one that can be divided by both numbers evenly. You would do the same with 3, 4, and maybe even 5 numbers. It's easier than you think.

Another website that would be good is http://www.helpwithfractions.com/greatest-common-factor.html!!!!

GOOD LUCK!!!!

Exponents and scientific notation

Exponents

An exponent is a number that shows how many times the base is used as a factor. A base is when a number is raised to a power, or has an exponent, the number used as a factor is the base. The first thing you do is look at the number 5 to the 2nd power. In the number 5 to the 2nd power, the 5 is the base, and the 2 is the exponent. So it would look like 5 x 5 because it's 5 times itself 2 times. It would not be 5 x 2 because you don't multiply the base and the exponent. http://www.mathgoodies.com/ is a great website to learn more about exponents.

Scientific Notation

The scientific notation is a way to write very big or small numbers by using powers of 10. First, you look at the number 364,000,000. The decimal should always be at the very end of the number when doing scientific notations. Next, you move the decimal after the first number. Who many spaces did you move to get the decimal after the first number? You start at the end then count how many spaces, including the 6 and 4, it takes to get behind the 3. The answer would be 8 spaces. So, when you write it out, it would look like 3.64. You won't need the zeros at the end because it's the same value. When you write the whole problem out to show the value of the number it would be 3.64 x 10 to the 8th power because 10 x 8 = 100,000,000. 100,000,000 x 3.64 = 364,000,000. http://www.purplemath.com/ really helps learning about exponents and scientific notation.

Life Situation

I know sometimes you think you won't need to know this, but in your lifetime it will save time. Scientists use this method to save them time in writing really small or big numbers when they do their work. Do you want to write a million zeros in your numbers? Or do you want to save time? Hmmm........

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