Division and Exponents

Division 

Division of whole numbers is basically for any whole numbers r and s, w doesnt equal 0, the quotient of r divided by s, written r divided is the whole K, if it exists such that r =s x k


Example of this would be:

18 divided by 3 =  6    -------------   6 times by 3 = 18

24 divided by 6 = 4    -------------    6 times by 4 = 24

35 divided by 5 = 7   -------------    5 times by 7 = 35
              
        *this is called  inverse operation, it means to undo eachother
          so to undo dividing is to multiply.
Another way to work out division would be to make a picture.

If i had 15 basketballs and had 3 groups to divide the 15 balls into, how many balls would be in each group?
0 = basketball
Group 1-- o o o o o
Group 2-- o o o o o
Group 3-- o o o o o
What you need to do is put one basketball in each group so you have an the same amount or basketballs in each group.
Ask yourself how many groups are you supposed to have? answer is 3
How many balls are in each group? 5
this would be 3 times 5 = 15

You can also ask yourself how many basketballs do you have total? answer is 15
How many groups do you need? 3
How many times does 3 go into 15? 3,6,9,12,15.. so the answer would be 5.

Hopefully that helps you understand the concept of inverse operations.
                                 Exponents 

Image from
My absolute favorite!
there are basic rules that are needed to be followed for exponents.
Exponentiation- means for any number B and any whole number N with B and N not both zero.
Basically this means that if you have B raised to N that it will = B times B times  times B
making B occur N times.
where B is called the base and N is called the exponent.
4 raised to the 0 power is equal to 0.. because 4 times 0= 0
4 raised to the 1 power is equal to 1.. because 4 times 1 =1
4 raised to the 2nd power is equal to 16 .. because 4 times 4= 16
What is 3 raised to the 2nd power?

9 -- because 3 times 3=9

now if you had 3 raised to the 10th power it would look like .. 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3-- there are ten 3's being multiplied together. There are 10 of them there because 3 was being raise to the 10th power.

If you have 2 raised to the 4th power being multiplied by 2 raised to the 3rd power.. what would you do to the exponents?
would you Add them?
                 Subtract them?
        or      Multiply them?

you would add them so it would be 2 raided to the 7th power. it would look like 2 x 2 x 2 x 2 x 2 x 2 x 2 --
seven 2's are being multiplied together.
The only time where you will be adding exponents is if the bases being multiplied are the same. 

If you are dividing you would do the same exact thing just subtract the exponents.
hopefully this video will help you see, because it was hard for me to explain since i cant raise exponents on my computer

Subtraction- Taking away!

Three concepts of subtraction occur in problems, Take away concept, comparison concept, and the missing addend concept.

TAKE AWAY CONCEPT:
an example would be: If you had 20 pencils and you had to give away 10 how many would you have left? -- 20-10=
Answer:10
That's pretty simple!

If you click on this it should help you understand this concept!

COMPARISON CONCEPT:
Example: if you had 20 pencils and your friend had 10 pencils. How many more pencils do you have than your friend? 20-10= 10.
Example.

Notice that your still coming up with the same answers with take away concept and the comparison concept. You will also come up with the same answer on the missing addend concept, which is my favorite one!

MISSING ADDEND CONCEPT:
Example: you have 12 kids in a class room and you need a total of 18 students to participate in the activity for it to work. So how many more students are needed to complete the activity? you would do 12+_____=18
your answer would be 6-- 12+6=18. you count up until you reach the number after the equal sign.
Missing Addend example.

Meanings and relationships of the operations.

Addition continued.

In my previous post I discussed the different ways of doing addition.
We also lectured on number properties. The first property is the Identity Property for Addition, which means for any whole number b, 0+b=b+0=b
and 0 is a unique identity for addition. so basically this would be 0+ any whole number would = that whole number.
0+36=0
36+0=36
So that's pretty simple.
The second property is called the Associative Property for Addition.
This means a+(b+c) = (a+b)+c
Notice that we are just moving the parenthesis, not the letters!
This is a video to help you understand this concept.

The last concept that we discussed is called that Commutative Property. This means for any whole numbers a and b, a+b=b+a
So basically, it doesnt matter which ways you put the numbers your going to get the same out come.
2+3=5
3+2=5

Addition

The last class period we went over different ways children can learn to do addition and subtraction. The first way that was discussed was left to right addition. To be honest I don’t think I have ever in my life done this way of addition. The book mentions that a lot of students understand to add from left to right because they are used to reading from left to right, and to switch addition on them from right to left often confuses them. I watched this video on left to right addition that helped me, It also shows a way that you can get the same answer by skipping around, and not adding the numbers in order! I thought that was pretty cool! Amy had mentioned that there are so many different ways to do attrition and that we won’t be learning them all, but it just amazes me that for 21 years I have old known how to add one way.



The second way we discussed is also in the video, it’s the last method that he does. Most people understand this form of addition because it is normally how we were taught to add in the younger grades, this said to be the traditional algorithm. Algorithm means a step by step process for computing. We also talked about partial sums. Partial sums are digits for each place value are added, and the partial sums are recorded before they are any regrouping. Here is another video that might help students learn.