Monday, November 30, 2009

Today in class, we reviewed multiplying and dividing by fractions. Multiplying and dividing by fractions is easier than adding and subtracting by fractions.

When you multiply by fractions, all you have to do is multiply across. You multiply the numerators together, and the denominators together. For example:

2/5 * 5/8. You multiply the numerators, 2 and 5, together, then the denominators, 5 and 8, together, and you end up with 10/40, which can be simplified to 1/4ths.

Another example is 1/2 * 3/4. you multiply 1 and 3 to get 3 in the numerator, and 2 and 4 to get 8 in the denominator, so you get 3/8ths.

When you divide by fractions, you take the first number and keep it the same, and you multiply it by the reciprocal of the second number, which is the fraction flipped, so 3/4 would be 4/3. For example:

1/2 divided by 5/6, you first make it 1/2 and 6/5, then multiply, so 1/2 * 5/6 is 5/12ths.

Another example is 3/4 divided by 4/5. you switch around 4/5 to 5/4, and then multiply to get 15/12, which is equivalent to 1 and 1/4.

It is the same thing with negatives, except that if you are multiplying or dividing one negative and one positive, it will be negative, and if it is two negatives, it will be positive. For example:

-5/8 *1/2 is -5/16.
-3/4 *-6/7 is 9/14



Wednesday, November 18, 2009

Adding & Subtracting Fractions

Here is the work we did today with adding and subtracting fractions including negative numbers and variables.


Tuesday, November 17, 2009

Fractions, Decimals & Least Common Multiple

Here are our notes from today:

Daily Scribe!

Today in math class, we reviewed turning fractions into decimals, and we learned that the least common multiple is the same as the lowest common denominator in a fractions. You turn a fraction into a decimal by dividing the numerator by the denominator. When you're turning a mixed number into a decimal, the decimal will be more than one, and the whole number will be before the decimal point. For example, if the mixed number was 2 and 1/10, the decimal would be 2.10 .
To find the decimal of a fraction, you can put the fraction over 100, then it is easier to find the decimal. For example, if you take 1/5 and put it over 100 as 20/100, it sound like 20 hundreths, which is written as .02 in decimal form.
We learned about two kinds of decimals called terminating and repeating decimals. A repeating decimal is a decimal that never ends, and goes on and on and on and on and on repeating the same 1 or 2 numbers. An example of a terminating decimal is 0.3176 because it doesn't repeat the same numbers on and on forever, and it comes to an end after 4 numbers. On the other hand, the decimal 0.33333 repeats the same number over and over again, which means it is a repeating decimal.
HOW TO TURN A REPEATING DECIMAL INTO A FRACTION!
1. Identify how many digits there are that repeat over and over again.
2. Place the repeating digits in a fraction over the same amount of 9's.
3. Simplify as much as possible.
For Example: the repeating decimal 0.66 would be 6/9, which can be reduced to 2/3
☺ BY ASHLEY V ☺

Monday, November 16, 2009

Daily Scribe

Today we learned about the Least Common Multiple (LCM). The least common multiple is the smallest number that two numbers have in common. For example the least common multiple of 10 and 30 is 30 because 10 times 3 is 30 and 30 times 1 is 30.

We also found out how to find the LCM using prime factorization. First you need to write the prime factorization. Next you need to use the GREATEST power of each factor, so if you had one number that was two to the third power and another that was two to the second, two to the third would go into the prime factorization. Then you write the least common multiple as a product.

This is what we learned in class today.

Least Common Multiple

Here are our notes from today on Least Common Multiple.

Thursday, November 12, 2009

Today in class we learned about how to find he GCF of a variable expression and how to simplify and make equivalent Algebraic Fractions:



GCF in a Variable Expression:
First, you must find the prime factorization of the coefficient. Then write the variable in expanded form. Next , all you have to do is find common factors. It's that simple!

Examples:
8xy2 and 6x3y
2*2*2*x*y*y 2*3*x*x*x*y
So, the GCF of 8x2 and 6x3y is 2xy

Note: When finding the GCF of a variable expression always list the numbers in numerical order then the letters in alphabetical order.

You can also use a Venn Diagram to find the GCF:

8xy2 6x3 y
2*2*2*x*y*y 2*3*x*x*x*y
Their similarities(which are underlined) would go in the middle.





Algebraic Factions:

To write Algebraic Fractions in simplest form, first write the prime factorization of the expression.
Then, divide the numerator and denominator by the common factors.

Example:
4ab2 2*2*a*b*b = b2
16ac 2*2*2*2*a*c = 4c

GCF of variable expressions & simplifying fractions

Wednesday, November 11, 2009

Yesterday in class we learned about primes and composites, greatest common factor (GCF), and prime factorization.

Primes and Composites

-Primes can only be divided by 1 and itself.
-Composites can be divided by more than 2 numbers
-1 is not a prime or a composite because it can ONLY be divided by 1

-Some examples of prime numbers are 2,5,7,11
-Some examples of composites are 4,6,9,12

Prime Factorization

-Prime factorization is a composite number written as the product of its prime factors
-Divide by prime numbers starting with 2

Example: Find the prime factorization of 18. To start you would divide 18 by 2 and get 9. The next step is to break 9 down even more. Since 9 is not divisible by 2 you go to the next prime number which would be 3. Then 9 divided by 3 equals 3. Last step is to put the two numbers we divided by and the end result next to each other. So the prime factorization of 18 would be 2*3*3.


How to Find GCF


To find greatest common factor you first have to find the prime factorization of the first number. Then you need to find the prime factorization for the second number. Then you make a compare the two numbers' prime factorizations. (To make this easier, you could make a venn diagram). the factors that are the same are the ones you are looking for. The highest common factor is your GCF.

Example: Find the greatest common factor of 16 and 28. to start you would find the prime factorization of the two numbers. The prime factorization of 16 is 2*2*2*2. The prime factorization of 28 is 2*2*7. you next compare the two prime factorizations. Seven is the greatest out of the two of them but since 7 is not in the prime factorization of 16, then it can't be the GCF. The only other common factor is 2 so that is the GCF. The greatest common factor of 16 and 28 is 2.

Tuesday, November 10, 2009

Primes, Composites, Prime Factorization

Today's notes on prime and composite numbers; how to find the prime factorization of numbers and the Greatest Common Factor.

Monday, November 9, 2009