Dividing Fractions

To Divide fractions all you have to do is the three simple steps:

1. You multiply the first fraction by the reciprocal of the second fraction. A reciprocal is when you flip the other fraction around.

2. Then you multiply the numerators and the denominators as if it were a multiplication problem.

3. Finally you simplify the fraction. If it can be.

An example of this would be,

4/5 / 1/2 = 4/5 x 2/1 = 8/5 = 1 3/5

flip the Simplify

fraction

around

Multiplying Fractions

Multiplying Fractions

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More Adding & Subtracting Fractions

5 3 More Add Subtract Fractions

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daily scribe

terminating decimals- a decimal that ends or terminates.
example: 0.5, 0.84, 1.03.

repeating decimals- a decimal that ends with a repeated digit or block of digits.
_ _ _
example: 0.333, 0.1212, 0.777
you only put the line (-) to show that its a repeating decimal.


writing a repeating decimal as a fraction!
1. identify how many digits repeat.
2.place the repeating digits over the same number of 9's.
3. simplify.


when you do on a calculator 6 divided by 9 ( that is because where do the fraction 6\9) on the calculator screen only 10 digits come up. so when you do that it should come up as 0.6666666667. so as you can see there is a 7 at the end, if it could hold more than 10 digits then the number 6 would go on for ETERNITY'S so 7 comes up because the calculator automatically knows to round it up.

Repeating Decimals & Fractions

Repeating Decimals

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Converting Fractions to Decimals

5 2 Ex 1 & 3 Hex

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The class of 12/7/09

Today we learned the least common denominator which is the same thing as LCM. We practiced these methods but with 3 numbers. We used the ladder method to find the LCM. We also worked with fractions today by taking the LCM and putting it into a fraction.

Comparing & Ordering Fractions

Ordering fractions Hex

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Scribe

Friday in class we learned how to find the the least common multiple (LCM) of two numbers.

There are three was you can find the LCM:
1.) The first was is by listing out the multiples of two numbers then you find the smallest number that is a multiple of the two numbers. For example if you wanted to find the LCM of 6 and 12 you would list out some of the multiples of 6: 6,12,18,24,30, etc. Then you would list some of the multiples for 12:12,24,36,48,60, etc. Lastly you would find the smallest multiple of 6 and 12 which is 12.

2.) The second way is by finding the prim factorization. The first step is to find the prime factorization of the two numbers. Then you use the the Venn diagram and use the greatest power of each factor. Then you right the LCM as a product. For example if you want to find the LCM of 12 and 6 you would find the prime factorization of twelve which is 2*2*3. Then you would find the prime factorization of 6 which is 2*3. Then you do then Venn diagram and come up with 2 to the second times 3 to the second which equals 24. So the LCM of 12 and 6 is 24.

3.)The third way is the double latter method. When you do the double latter method you would put two numbers on the same latter. You then find a number that is divisible by both number and so on and so forth. Then you take the numbers on the out side and multiply them all together. For example to find the LCM of 24 and 30 you would divide 2 by 24 and 30 which is 12 and 15. Then you divide those by 3 which is 4 and 5. Then you will come up with 2*3*4*5 which equals 120. So 120 is the LCM.

Least Common Multiple

Here are three methods to find the least common multiple.

Least Common Multiple

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12-02-09 notes

Today in class we went over how to simplify fractions and greatest common factors.

You simplify a fraction by dividing the numerator and the denominator by the same number. For an example if your fraction is 5/25 . You would divide the numerator (5) by 5, because it is the largest number you can divide it by without getting a fraction 5 divided by 5 =1. Then you divide the denominator by 5 because it is the number you divided the numerator by. So 25 divided by 5=5. So the simplified fraction is 1/5. That is how you simplify a fraction. If the numerator is larger than the denominator. Then after you simplify it you change it to a mixed number. For an example the fraction could be 15/5 after you simplify it it would be 5/3. After you simplify it you can it to the mixed number which would be 1 and 2/3



You get the common factor by listing the prime factors of each number. Then you multiply the greatest common factor by each other. If there are no common prime factors, the greatest common factor is 1. For an example 18's common factors are 2,3,3. 24's common factors are 2,2,2,3. So now you take the great common number which in the case is 3. Now do 3*3 which is 9. So the greatest common factor is 9.

Notes by,
Kasey D.

Simplifying Fractions

Here are examples of how to simplify fractions and find equivalent fractions.

Simplifying Fractions

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Greatest Common Factor & Prime Factorization

Here are our notes on Greatest Common Factor using Prime Factorization and the ladder method.

Greatest Common Factor

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Notes 12-1-09

Prime numbers are only divisable by one and itself.
Composite nimbers are divisable by more than two factors.

Prim Factorization= A composite number written as the product of its prim factors.

An easy way to find the (GCF) is to use the latter method. All you do is divid a prime factor by two until you get to a prime number. Then you take the same numbers on each latter and multiply them together to get the (GCF).

You can also use a vendiagram. You put one of the prime factors on one saide and the other on the other side. Then u use the latter method to find numbers that both prime factors have in common. Then you multiply the numbers that are the same to get the (GCF).

Quia Notes :]

To get on to Quia you go to Edline.www.reading.k12.ma.us and sign in,next you go to classes and shortcuts. Then go to Pre algebra hexagons. Under links you will find the link that says "Quia." It will bring you right to the games if you click on it. The first game link is a Java games and there are many games under that link there are matching flashcards and concentration, Be sure to know the category's each game is under! There's a variety of games and this is a good way to study in a fun way.

One fun game is Rags to Riches. Its similar to who wants to be a million air. When you get one question wrong you start over so its a good idea to write all the correct answers on a sheet so when you come back to it you know its right and you can "win" 1 million dollars. Another game is the challenge board. This is similar to Jeopardy. You can play 2 player or single player. You type in your names then you click on number of points you want under the category you want and see which player can get more points.

Another really fun game is concentration. Concentration and matching are very similar. You have to know the question and answer then you have to try to math it with the least amount of trys as possible. This isn't a game where you should click around try to write down the problems and the answer so if you find the answer on the game board you can find the match.

Another important thing Quia helps with is adding and subtracting positive and negative numbers. You have to remember if the greater number in the problem is positive the answer is positive. If the greater number is negative the answer is going to be a negative number.

*Tonight's homework is the order of operations sheet. Due tomorrow.*
Quia is a good study source.

Also on Quia it helps you review order of operations. PEMDAS.
P=parenthesis
E=exponents
M=multiply
D=divide
A=adding
S=subtraction
Please enjoy Mickey OR Donald acting OR singing

Review for Tuesday

*If a negative sign is NOT in parenthesis the answer is ALWAYS negative

a problem -x4 (4 is a power)
^
-34 (4 is a power) 2(3+4)2 (2 is a power)
-3*3*3*3 ^
^ 2*72 (2 is a power)
-9*3*3 ^
^ 2*49 (7*7=49)
-27*3 ^
^ 98
-81

*odd powers are negative *evens powers are positive
*remember P(please)(parenthesis)
E (enjoy)(exponents)
M(mickey)(times) or D(donald)(divide)
A(acting)(add)or S(singing)(subtract)

Order of Operations with exponents

More practice with negative numbers and order of operations.

Order Of Operations With Exponents

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Order of Operations with exponents

Here are our notes from today.

Ch. 4.2 Hexagons

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Divisibility and Exponents

Divistibility Rules~
by 2- its ends in 0,2,4,6,8 for example, 84 is divisible by 2
by 3- if the sum of its digits is divisible by 3 for example, 9/3=3
by 4- if the last 2 digits are divisible by 4 for example,128 7*4=28
by 5- if it ends in 0, or 5 for example, 20 or 25
by 9- if the sum of its digits is divisible by 9 for example, 72/8=9
by 10- if the number ends in a 0 for an example 30

Factors~
10-1,2,5,10
21-1,3,7,21
24-1,2,3,4,6,8,12,24
31-1,31 -this is a prime number
A prime number is 1 and the number itself

Exponents~
Exponents can be used to show repeated multiplacation
3^7=3*3*3*3*3*3*3 3= base 7=exponent
-a power has two parts
-a base has an exponent
-the expression 3^2 is read "three to the second power
(-4)(-4)=8^2

Divisibility, Factors & Exponents

Notes from today on divisibility rules and order of operations with exponents.

4 1, 4 2 Hex

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intergers scribe #1

Intergers

multiplying intergers- a posotive * a positive = a positive

a negitive * a negitive = a positive

a negitive * a positive = negitive

a positive * a negitive = a negitive

8*7= 56

-8*-7=56

-8*7= -56

dividing intergers- a posotive / a posotive = posotive

a negitive / a negitive = posotive

a negitive / a posotive = negitive

a posotive / a negitive = negitive

24/12=2

-24/(-12)= 2

-24/ 12= -2

addition of intergers- same signs add and keep different signs subtract, take the sighn of the bigger number.

5+12= 17

-5+12= 7

subtraction of intergers- change subtraction to adding the opposite.

9 - 27= ____

9+ (-27)= -18

Chapter 1 review

Ch 1 Review

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Integer practice with all four operations

Here are the slides with answers from our practice today.

Koosh Ball Integer Practice

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Multiplying & Dividing Integers

Lesson on multiplication and division of integers.

Multiplication & Division of integers

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Subtracting Integers

Notes from today's lesson on subtracting integers.

Subtraction of Integers

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Absolute Value

Notes from today's class on Absolute Value.

Absolute Value

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Integers and Opposites

Here are the notes from today on integers and opposites. Use the presentation to be sure your Frayer model vocabulary templates are complete.

Integers and Opposites

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Evaluating Expressions

Here's our work from today on evaluating expressions and order of operations.

1 3 Hex

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Introduction to Pre-Algebra

Notes from today, Oct. 26 on order of operations.

1 2 Hex

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Variables & Patterns Problem 2.3

Notes from class

Variables & Patterns Problem 2.3

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Variables & Patterns Problem 2.2 & 2.3 intro

Notes from Tuesday, Oct. 6

Variables & Patterns Problem 2.2 & 2.3 intro

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Variables & Patterns Problem 2.1

Variables & Patterns Problem 2.1

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How to make a coordinate graph.

Notes from Monday, September 14

V&P 1 Hex

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Introduction to Variables & Patterns

Here are the notes from class on Tuesday, Sept. 8, 2009. V&P Intro To Unit, Jj

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Ms. Favazza'a Wordle

This is a Wordle I created that shares a little of who I am as a person. You will create one with your Glyph assignment next week.

Please make a comment about my Wordle and answer the question: "What do you want people to know about you when you meet them for the first time?"
1. Click on comment.
2. Sign in with a name and use your first name only.

Welcome!

Hello! You found our class blog! This is the place to talk about what's happening in class; to ask a question you didn't get a chance to ask in class; for parents to find out "What did you do in school today?"; to share your knowledge with other students. Most importantly it's a place to reflect on what we're learning in math this year.

One key to being successful involves working with and discussing new ideas with other people -- THIS is the place to do just that. Use the comment feature below each post, or make your own post, contribute to the conversation and lets get down to some serious blogging!