Equivalent Fractions

Today we began looking at equivalent fractions. When 2 or more fractions represent the same number they are called equivalent fractions. We discussed that we can find equivalent fractions by multiplying the top and bottom number of the fraction by the same number. For example:

2/3 If I multiply the top and bottom by 2 I get 4/9. I can get even more equivalent fractions by multiplying by other numbers like 3 or 4...

I can also write equivalent fractions by simplifying fractions. When I simplify, I am dividing the top and bottom by any number that both numbers have in common (common factors). Here is an example.

18/24 I know that 18 and 24 have a 6 in common so I can divide the top and bottom by 6 giving me an answer of 3/4. If I couldn't think of 6 but only thought of 2 then I could divide by 2 and then try and simplify again until the fractions was in simplest form.

Next we discussed simplifying monomials. Here are the steps from class:

1. Factor top and bottom
2. Cross out all common factors
3. The answer is all factors left over on the top and the bottom (answer is a fraction)

Here is an example:

8x2y
6x2y2

Factored we get

2 * 2 * x * x * y
2 * 3 * x * x * y * y

After we cross out common factors we will notice that we are left with:

2
3 * y

So our answer is 2/3y.

Enjoy trick-or-treating. Let me know if you have questions.

Greatest Common Factor (GCF)

In today's lesson we learned three things: GCF of numbers, relatively prime, and the GCF of monomials. As long as we have good notes and can follow the steps we should be able to find the GCF of both numbers and monomials.

Let's start with the GCF of numbers. We talked in class about 2 different ways to find the GCF of numbers. The first way is to list the factors of each number. This works really well if we have small numbers. Here's an example:

16: 1, 2, 4, 8, 16

32: 1, 2, 4, 8, 18, 32

40: 1, 2, 4, 5, 8, 10, 20, 40

Now that the factors are listed we can find the largest one that they have in common and that is our answer. So the GCF is 8.

The second way, which works well if we have large numbers, is to find the prime factorization of each number and then find the common prime numbers and multiply them. Here's what I mean using the same example from above (now I can't make a factor tree on this website, so I have skipped the step and already listed the prime numbers).

16: 2 * 2 * 2 * 2

32: 2 * 2 * 2 * 2 * 2

40: 2 * 2 * 2 * 5

We can see that they each have three 2's in common (2 * 2 * 2). So if I multiply them together I get 8.

Next we discussed the term relatively prime. Two or more numbers are relatively prime if their greatest common factor is one. If the only factor they have in common is one they are relatively prime.

Finally we discussed finding the GCF of monomials. Here are the steps that we wrote down in class:

1. Factor the monomials (see last weeks notes if you need help)
2. Find all the common factors (circling them helps)
3. Your answer is all common factors multiplied together (everything you circled)

Here is an example (Remember we discussed the look of exponents on here during class):

12m2n3: 2 * 2 * 3 * m * m * n * n * n

70m3n: 2 * 5 * 7 * m * m * m * n

We notice that these monomials have a 2, m, m, and n in common. If I multiply those together I get the answer of 2m2n

Welcome To Online Pre-Algebra

Welcome to our Pre-Algebra class "blog". For those of you new to blogging, this is a way for us to communicate after class time for help on homework. Why do we need a class blog? Well, I am glad you asked. Many of you have mentioned the fact that you understand homework in class but not when you get home. "It is easier, when you do it on the board" is a common phrase I hear from you all. So, with the help of technology, my goal is to provide additional help, notes, examples, etc., to aid in our homework endeavors.

Each day, I plan to post our lesson so you can refresh your memory when you are at home doing your homework. You will also be able to post a question (comment) that I can receive and reply additional help. This is a trial run, so let's see how helpful it really is.