Integer Operations

I guess you are here to learn about integer operations. Well, once again you are in the right place!





First let's look at our vocabulary.



integer- it is the whole number.



opposite- entirely different; exactly contrary.

How To Do The Problems

This is how you do integer operations in addition.

Here is an ex. 3 + - 4 = -1

You are probably wondering how to do it. Well, this is how you do it!

1. You need to look at the signs. ex. (negative numbers and positive numbers)


2. Now you need to see if the signs are different. In this case they are. ex. 3 + - 4 = - 1 You can see the 3 is a positive number and the 4 is a negative number.


3. Now that you know that those signs are opposite from each other you need to subtract.


4. The rule for addition is keeping the sign of the bigger number. ex. 4 is the bigger number so since 4 was a negative number then the answer has to be a negative number.


5. So that is how you get -1 for the answer. ex. 3 + - 4 = - 1

This how you solve problems is subtraction.

ex. 4 - (- 12) = 16

1. Once again you need to look at the signs. (You can see that you are subtracting negative 12 from positive 4.)


2. Now you need to change the subtraction to addition and the negative 12 to positive 12.
   ex. 4 + (+ 12)


3. Since you did that you now just need to do addition. ex. 4 + 12 = 16

Now say you had a problem like this: 4 - 12 = - 8

What you need to do is once again make the subtraction an addition and then make the positive 12 into negative 12. ex. 4 + - 12 = - 8

Then that is how you do it!

This how you solve problems in multiplication.

Say you have this problem: 5 x - 6 = - 30

First here are the rules for multiplication.

1. If the signs are different then the answer would always be a negative number.
   ex. 5 x - 6 = - 30.


2. If the signs are the same then the answer would also would be a positive number.
   ex. - 5 x - 6 = 30.


3. So for 5 x - 6 = - 30 you know how to solve it because of the rules.

This how you solve problems in division. ( the / stands for division)

The operation is - 14 / - 7 = 2

The rules for division are the same as multiplication.

So you can see that the operation is going to be a positive number because the signs are the same.

Now all you need to do is just divide. ex. - 14 / - 7 = 2

That is how you do integer operations in addition, subtraction, multiplication, and division.

Here is a cool link to have more information on integer operations!

Amby's Math Resources - Integers: Operations with Signed Numbers

Solving Equations

Are you wondering how to solve equations? Well you have came to the right place!



The vocabulary you need to know is variable and equation.



variable - it can be changed or varied.

equation - a statement of equality between two quantities , as shown by the equal sign(=)

How To Solve The Problem

Now here is a example of a equation 3 + q = 10

You need to ask your self what is being done to my variable?

What's being done to your variable is adding.

Now do the inverse operation (opposite) to both sides of the equation.

example 3 + q = 10 the opposite of adding is subtracting.

So now you need to do this 3 + q = 10

Underneath the 3 and 10 you need to put minus 3

example 3 - 3 which aculaty would just equal Q because 3 minus 3 would just equal 0.

But for the 10 you would do 10 - 3 which would equal 7.

So now that you have just the number 7 and Q you now do Q =7

Now you want to make sure you are fully right about the answer and you would need to check it.

First you need to rewrite the equation.

example 3 + q = 10

So now that you rewrote it you can plug the number that you got which was 7.

example 3 + 7 = 10

So does 3 = 7 = 10?

Well it does so that is when you know that you got the right answer!

The next step is to write that 10 = 10 and also that q = 7.

Now there are other equations like 4m = 20 and the inverse operation for that would be division. Now you just do the same thing I just showed but you need to do it in division not subtracting.

The other operation is division and it is a little bit different from the others because you do not write the number you are timing underneath the problem you would right it across from the equation.

example 4 x 12 = s/4 x 4

Real Life Application

So say you have 4 people and there is 20 goody bags and they all want five goody bags. So how would you do this? Will you have enough?

example 4m =20

Now you need to do 4m divided by 4 and 20 divided by 4.

example 4m divided = m and 20 divided by 4 = 5

Hey you have enough goody bags to each person 5!

Now you need to check it!

Once again you need to rewrite out your equation and plug in 5.

example 4 x 5 = 20

so 20 = 20 and m=5

.

Here is an awesome link to learn more about solving equations!

MathSteps: Grade 6: Linear Equations: What Is It?

Factors and GCF

Factors and GCF

You are probably now wondering how do factors and GCF. You are in an excellent place! GCF stands for Greatest Common Factor. I guess now you are wondering what factor means. Well it is a number that divides the number evenly.

Finding the Factors

This is how you find the factors of a number.

1. You will have a number like 56 for instance. You will need to write down factors that can go into 56.

example 56= 1,56,2,28,4,14,7,8,

hint you will know when you are done writing down all the factors if you times the last number by itself.

2. When you write the numbers out put them in pairs.

example 2 x 28 =56 4 x 14 =56 7 x8 =56

Finding the GCF

Here is how you find the GCF.

1. Find the factors of two numbers.

example 30= 1,30,2,15,3,10,5,6 24= 1,24,2,12,3,8,4,6

hint if you have more than two numbers, you can just find the factors of the lowest number, even in this situation.

2. Now you need to look at the two numbers and think if any of their factors can go into the two numbers.

example the factor that the numbers have in common is 6 so 6 is the GCF.

Real Life Application

So say you have the fraction 16/20 and you want to simplify it.

1. Find the GCF of 16 and 20.

example 16= 1,16,2,8,4 20= 1,20,2,10,4,5 The GCF is 4.

2. You need to divide 16 and 20 by 4 to simplify the fraction.

example 16/20 divided by 4/4 = 4/5.

Here is an awesome link to explain more about GCF.

How To Find The Greatest Common Factor (GCF)

Exponents and Scientific Notation

You probably are wondering how to do exponents and scientific notation. Well, you are in the right place.

EXPONENTS
So say you have 2 to the 3rd power. The answer is 8. Now you probably are wondering how to solve that. So let me explain that to you.

ATTENTION: DO NOT DO 2 x 3 = 6.

This the right way to do it!

1. Find out what the base and exponent is.
   
   Example 2=base and 3=exponent
   
2. You need to think in your head what 2 multiplied 3 times is.
   
   Example 2 x 2 x 2
   
3. Solve the equation.
   
   Example 2 x 2 x 2 = 8
   
   

SCIENTIFIC NOTATION
Scientific notation is a way of writing a shorter version of a really big number. Here's an example.

The closest star to the Sun is the Alpha Centauri. It is 43,000,000,000,000 km away. When I write it in scientific notation which is 4.3 x 10 to the 13 power, it is much easier than to write it as 43,000,000,000,000.

Here's how I got the answer.

1. You always put the decimal point after the first number.
   
   Example 4.3
   
2. Then count how many decimal spots you move from the right until you get to the decimal point.
   
   Example For 43,000,000,000,000, I counted 13 spots.
   
3. Finally, you will write the number that you put the decimal point between then you would put down 10 to the 13 power.
   
   Example 4.3 x 10 to the 13 power

Down below is a link that you can look at to get more information about the scientific notation!

http://www.kidscosmos.org/kid-stuff/sci-note.html

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