Today in math we reviewed for a test on friday. The test will contain numerous things and today we reviewd adding and subtracting fractions, and mixed numbers. You could either stay at the smart bored and do problems, or you and a partner could work on problems in your textbook.An example of subtracting fractions is 2 and 1/2 - 1 3/4=2 2/4 -1 3/4. You had to make it into the same denominator and now you have to make mixed numbers. The mixed numbers would be 10/4 - 7/4= 3/4, so 3/4 would be your answer. We also learned how to subtract with varibles. The equation would be 12/b - 5/b. Since they have the same denominator you with minus the numerators and leave the denominator as c. That would make your answer to be 7/b. This would be the same rule for adding with varibles.
Accelerated Pre-Algebra (10-11) A peek inside our classroom. This is an interactive learning community for students and parents of my 7th Grade Accelerated Pre-Algebra class for the school year 2010/2011. The discussion and information will be as meaningful as you make it.
Tuesday, November 30, 2010
Monday, November 29, 2010
Daily Scribe 11/29 Caroline Hagan
Today in class we learned how to convert decimals into fractions!
Some examples of this are:
.35= 35/100= 35/100 / 5/5 (GCF of both numerator and denominator)= 7/20 REMEMBER: you always want to write the simplest form for your final answer.
.325 = 325/1000 =325/1000 / 25/25 = 13/40
2.45 = 2 45/100 / 5/5 = 2 9/20
Next we wrote these decimals as fractions in simplest form:
0.8 = 8/10 = 8/10 / 2/2= 4/5
1.3 = 1 3/10--------------------------Mixed number for simplest form if converting decimal to fraction
NEGATIVE:
-0.625 = - 625/1000 = - 625/1000 / 25/25 = 25/40 / 5/5 = - 5/8
*** For eighth fractions you keep adding 125 to each decimal to get the next eighth fraction : 0--0.000, 1/8---0.125, and so on..
We also reviewed what Terminating and Repeating decimals are :
Terminating Decimal: A decimal that ends.
Repeating Decimal: A digit or block of digits that repeat.
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
Example 1 : 0.33333.....
3/9 = 1/3
Example 2 : 0.454545...
45/99 = 5/11
Extra!!! o.99999...... = 1 !!!
Sunday, November 28, 2010
Saturday, November 27, 2010
Sunday, November 21, 2010
Wednesday, November 17, 2010
Daily Scribe-Courtney
Today in class we learned how to write and solve fractions as a decimal. We also learned about terminating decimals, repeating decimals, and how to write mixed numbers as a fraction. REMEMBER: the lowest common denominator is the same as the least common multiple!
How to slove fractions as a decimal
When solving fractions as a decimal, you should divide the numerator by the denominator.
Example:
Numerator Denominator answer
1/4..........................1 / 4 =0.25
2/7..........................2 / 7 = 0.29
9/10........................9 / 10 = 0.90
Terminating decimal- A decimal which ends or "terminates" dividing the numerator of a fraction by the denominator produces a remainder of zero.
Repeating decimal- A decimal with a digit or digits that repeat in an identical pattern forever.
Examples of a terminating decimal- 4/5 1/25 0.75 3.125
~these all have a remainder of zero, and don't go on forever
Examples of a repeating decimal- 4/11 7/15 66.666... 4.424242.... 5.987987987....
~the remainder will repeat forever, in a pattern
Remember: .99999......... repeating would actually equal 1
Writing mixed numbers as decimals
First, you should multiply the denominator by the regular number. Then, add the numerator to your answer when you multiply the denominator and number. To write a mixed number as a decimal, first write it as an improper fraction. Then, divide the improper fraction by the numerator, then the denominator.
Examples: 3 2/5 (three and two fifths)
First, multiply 5*3 (denominator and number), then add 2 (numerator) to get ... 17
Then, divide the numerator (17) by the denominator (5). 5
17/5......................3.40
3 2/5= 3.40
1 8/10 (one and eight tenth)
First, multiply 10*1 (denominator and number), then add 8 (numerator) to get......18
Then, divide the numerator (18) by the denominator (10). 10
18/10................1.80
What does 20/9 equal?
First, find out what multiple of 9 goes into 20, or one that is the closest to 20.
9*2=18, which is the closest to 20.
2 would be used as the whole number; not the denominator or numerator, since it's the closest multiple to 20. Since 2*9=18, the left over number is 2, because 20-18=2.
The numerator is 2, which is the left over number, and the denominator from the regular number which is 9, stays the same.
The answer is 2 2/9
How to slove fractions as a decimal
When solving fractions as a decimal, you should divide the numerator by the denominator.
Example:
Numerator Denominator answer
1/4..........................1 / 4 =0.25
2/7..........................2 / 7 = 0.29
9/10........................9 / 10 = 0.90
Terminating decimal- A decimal which ends or "terminates" dividing the numerator of a fraction by the denominator produces a remainder of zero.
Repeating decimal- A decimal with a digit or digits that repeat in an identical pattern forever.
Examples of a terminating decimal- 4/5 1/25 0.75 3.125
~these all have a remainder of zero, and don't go on forever
Examples of a repeating decimal- 4/11 7/15 66.666... 4.424242.... 5.987987987....
~the remainder will repeat forever, in a pattern
Remember: .99999......... repeating would actually equal 1
Writing mixed numbers as decimals
First, you should multiply the denominator by the regular number. Then, add the numerator to your answer when you multiply the denominator and number. To write a mixed number as a decimal, first write it as an improper fraction. Then, divide the improper fraction by the numerator, then the denominator.
Examples: 3 2/5 (three and two fifths)
First, multiply 5*3 (denominator and number), then add 2 (numerator) to get ... 17
Then, divide the numerator (17) by the denominator (5). 5
17/5......................3.40
3 2/5= 3.40
1 8/10 (one and eight tenth)
First, multiply 10*1 (denominator and number), then add 8 (numerator) to get......18
Then, divide the numerator (18) by the denominator (10). 10
18/10................1.80
What does 20/9 equal?
First, find out what multiple of 9 goes into 20, or one that is the closest to 20.
9*2=18, which is the closest to 20.
2 would be used as the whole number; not the denominator or numerator, since it's the closest multiple to 20. Since 2*9=18, the left over number is 2, because 20-18=2.
The numerator is 2, which is the left over number, and the denominator from the regular number which is 9, stays the same.
The answer is 2 2/9
Tuesday, November 16, 2010
Daily Scribe
November 16, 2010
By Larisa Kreismanis
Today in class we learned about the differences between multiples and factors and how to find the least common multiple (LCM) of numeric expressions and variable expressions.
Multiples and Factors
Multiple- A multiple is a number(n) times another number continuing in a numeric pattern. For example,
The first five multiples of 8 are 8, 16, 24, 32, and 40.
Factor- A factor is a number that you can multiply by another number to get the number you need factors for. Factors can be whole numbers or fractions.
For example,
16 is a factor of 32 because 16*2=32
Least Common Multiple (LCM)
The least common multiple of a number is the smallest number that is a multiple of two or more numbers. You can find the least common multiple (LCM) by listing the multiples of the numbers and find which is the smallest multiple in common. For example,
The LCM of 12 and 20 is 60
Multiples of 12 – 12, 24, 36, 48, 60, 72
Multiples of 20 – 20, 40, 60, 80, 100
LCM= 60
Finding Least Common Multiple (LCM)
Using Prime Factorization
You can also find the LCM by using prime factorization. The least common multiple (LCM) is the smallest number that two numbers can be divided into. When finding the LCM by using prime factorization, you find the prime factorization for both numbers. Then you pick the set of prime factors that overlap each other and you multiply them by the numbers that do not overlap each other. The product of these numbers will then be the LCM. For example,
The LCM of 25 and 40 is 200.
Prime Factorization for 25= 5*5.
Prime Factorization for 40= 2*2*2*5.
5 is the only overlapping number, so to find the LCM you multiply 2*2*2*5*5=200.
Finding The Least Common
Multiple in Variable Expressions
When finding the LCM in variable expressions you find the prime factorization for both numbers. Then, including the variables, you pick the sets of numbers that overlap each other, then you multiply the sets of numbers and variables that overlap each other by numbers that do not overlap each other. For example,
The LCM of 15ab2 and 12abc is 60ab2c.
The prime factorization of 15ab2 = 3*5*a*b*b.
The prime factorization of 12abc = 2*2*3*a*b*c.
The overlapping numbers are 3,a,b so to find the LCM you multiply 2*2*3*5*a*b*b*c to get 60ab2c.
Monday, November 15, 2010
Saturday, November 13, 2010
Daily Scribe
11/13/10 Brett Higgins
Today in class we worked on how to write algebraic fractions in simplest form. We started off class by correcting the homework from the night before. We then took notes on how to write a algebraic fraction in simplest form.
The first thing you do is write out the prime factorization of the expression. then you divide the numerator by the denominator by the common factors.
example: 9x /3xy would be written as 3*3*x /3*x*y
The next step would be to cross out the same numbers or variables and make them 1, they would be made into a 1 because anything divided by itself is 1. You could cross out a 3 and a x and make the equation and make it 3 over and that would be your answer. If you do these steps and your answer is a larger answer like
3*4*3*x /7*5*h, you would multiply 3*4*3*x and 7*5*h
and get 36x/ 35h because 3*4*3*x=36x and 7*5*h=35h to simplify the problem even more
We did 3 example problems and they were...
1. b/abc = 1/ac
2. 2mn/6m = N/3
3. 24xxy/8xy = 3x/1
At the end of class we worked on a order of operations worksheet were we had to show our steps on how we got the answer.
example: 9-5/(8-3)*(-2)-6 = 5
9-1*(-2)-6
9-(-2)-6
9+2-6
11-6
Today in class we worked on how to write algebraic fractions in simplest form. We started off class by correcting the homework from the night before. We then took notes on how to write a algebraic fraction in simplest form.
The first thing you do is write out the prime factorization of the expression. then you divide the numerator by the denominator by the common factors.
example: 9x /3xy would be written as 3*3*x /3*x*y
The next step would be to cross out the same numbers or variables and make them 1, they would be made into a 1 because anything divided by itself is 1. You could cross out a 3 and a x and make the equation and make it 3 over and that would be your answer. If you do these steps and your answer is a larger answer like
3*4*3*x /7*5*h, you would multiply 3*4*3*x and 7*5*h
and get 36x/ 35h because 3*4*3*x=36x and 7*5*h=35h to simplify the problem even more
We did 3 example problems and they were...
1. b/abc = 1/ac
2. 2mn/6m = N/3
3. 24xxy/8xy = 3x/1
At the end of class we worked on a order of operations worksheet were we had to show our steps on how we got the answer.
example: 9-5/(8-3)*(-2)-6 = 5
9-1*(-2)-6
9-(-2)-6
9+2-6
11-6
Friday, November 12, 2010
Wednesday, November 10, 2010
Daily Scribe: November 10th
In class today we learned all about finding the greatest common factor of a variable expression. We started the class off with a Do Now. The Do Now was simplifying three variable expressions. The three problems were..
1. 3*x*y*x
Answer: 3x2y
2. a*b*a*b*b*-2
Answer: -2a2b3
3. 4x2+3
Answer: 103
And after the Do Now we went over the homework from that night. After correcting the homework we watched a slide show about how to find the greatest common factor of variable expressions. In order to find the GCF, we learned that you have to first find the prime factorization of the coefficient or the number. And then you write the variable in expanded form which means no exponents. Next, you find the common factors. Lastly, you re-write the variable with the number first, then the variables in alphabetical order with the exponents. We then did some problems to help us understand this better. We were given two variable expressions and we had to find the GCF of them. Remember to use the Venn Diagram to help you figure out the answer.
1. 4xy2 and 2x2y
2 * 2 * x * y * y 2 * x * x * y
(The numbers or variables in common are in bold!!)
Answer: 2xy
2. 6a2b2 and 4ab3
2 * 3 * a * a * b * b 2 * 2 * a * b * b * b
Answer: 2ab2
3. 10m3n and 15m2n2
2 * 5 * m * m * m * n 3 * b * m * m * n * n
Answer: 5m2n
Overall, today in class we learned all about finding the GCF of a variable expression which was just adding onto what we learned, well reviewed in class the other day which was finding the GCF between two numbers!
Tuesday, November 9, 2010
November 9,2010
Today in class we learned about prime factorization. We learned a new method called the birthday cake method. To do this method you start out with the number you want and than you find the lowest prime factor that goes into that number. you than put the answer on the top of the original number and do this again. Than you take all of the numbers on the side and add them up. We also learned the definition of prime and composite numbers today. Prime Number-is a number that can only be divided by 1 and its self. An example of this would be 2,3,5,7, ect. The cool thing about 2 is that it is the only even prime number. Composite Number- is when the number has more factors than just one and its self. Examples of this would be 28,27,24 ect.
Monday, November 8, 2010
Daily Scribe 11-8 Hunter Lambroff
Today in class we reviewed some things from previous years and we also learned some new things about "pemdas" and how it can effect an equasion.
We started off with a Do Now of trying to write down divisibility rules 2 - 10, so here are the answers.
2 - If a number is divisible by 2, it ends in either 0, 2, 4, 6, or 8.
3 - If a number is divisible by 3, the sum of it's digets is divisible by three.
4 - If a number is divisible by 4, then the last two digits of the number are divisible by 4.
5 - If a number is divisible by 5, it either ends in 0 or 5.
6 - If a number is divisible by 6, it must be divisible by both 2 and 3.
7 - The rule is SUPER complicated, so you'll just have to divide.
8 - If a number is divisible by 8, the last three digits of the number are divisible by 8.
9 - If a number is divisible by 9, the sum of it's digits is divisible by 9.
10 - If a number is divisible by 10, the number must end in 0.
Next, we learned about factors.
Factors are integers that divide into another number evenly.
Then, we did some problems to find the factors of a given mumber.
We also learned that prime numbers are numbers that it's only factors are itself and 0.
Later, we learned how exponents are used to show repeated multiplication, it would be alot easier to say 5^7 than 5*5*5*5*5*5*5. You must remember that exponents mean you multiply the. It doesn't mean that you multiply the integer by the exponent. When you write exponents, you write them to the top right of the integer, if it is only miltiplied once you don't have to write anything.
When you add variables, perenthases, and negative numbers in to the process, it can get tricky. When there is a negative variable and it's exponent is even, the product is even. If it's odd, the prodict's odd. If there are parenthases around the negative variable or number, and the exponent ids on the outside, it means that you do the negitive number, times itself as a positive/negative a ceartian amount of times. Parenthases and the exponents effect the equasion and it's answer.
We started off with a Do Now of trying to write down divisibility rules 2 - 10, so here are the answers.
2 - If a number is divisible by 2, it ends in either 0, 2, 4, 6, or 8.
3 - If a number is divisible by 3, the sum of it's digets is divisible by three.
4 - If a number is divisible by 4, then the last two digits of the number are divisible by 4.
5 - If a number is divisible by 5, it either ends in 0 or 5.
6 - If a number is divisible by 6, it must be divisible by both 2 and 3.
7 - The rule is SUPER complicated, so you'll just have to divide.
8 - If a number is divisible by 8, the last three digits of the number are divisible by 8.
9 - If a number is divisible by 9, the sum of it's digits is divisible by 9.
10 - If a number is divisible by 10, the number must end in 0.
Next, we learned about factors.
Factors are integers that divide into another number evenly.
Then, we did some problems to find the factors of a given mumber.
We also learned that prime numbers are numbers that it's only factors are itself and 0.
Later, we learned how exponents are used to show repeated multiplication, it would be alot easier to say 5^7 than 5*5*5*5*5*5*5. You must remember that exponents mean you multiply the. It doesn't mean that you multiply the integer by the exponent. When you write exponents, you write them to the top right of the integer, if it is only miltiplied once you don't have to write anything.
When you add variables, perenthases, and negative numbers in to the process, it can get tricky. When there is a negative variable and it's exponent is even, the product is even. If it's odd, the prodict's odd. If there are parenthases around the negative variable or number, and the exponent ids on the outside, it means that you do the negitive number, times itself as a positive/negative a ceartian amount of times. Parenthases and the exponents effect the equasion and it's answer.
Monday, November 1, 2010
Daily Scribe
Today in class we studied for our test that is tomorrow. Some people played games on the computers, did work sheets, or played kosh ball. Whatever you did I hope that you are ready for the test tomorrow. It is on integers, and some of our vocab words. They are opposite, integer, and absolute value. George told you what they are. You have to also know if you are multipling or dividing integers if it is going to be a positive or negative number. I hope you all studied.
We also have a notebook quiz. This is to see if your notebook is organized. So you should make sure that you have the dates and what number homework it on the page.
If you don't know all of these things and if your notebook isn't organize then you better get studing!
We also have a notebook quiz. This is to see if your notebook is organized. So you should make sure that you have the dates and what number homework it on the page.
If you don't know all of these things and if your notebook isn't organize then you better get studing!
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