Multiplying Fractions

As we discussed in class, multiplying fractions is probably the easiest operation to perform with fractions. You don't have to find a common denominator to multiply fractions, you just have to know how to multiply. When you multiply fractions, you simply multiply the top numbers together and you multiply the bottom numbers together. For example:

3/4 * 5/6 = ?

Multiply the top numbers 3 * 5 = 15
Multiply the bottom numbers 4 * 6 = 24

So, 3/4 * 5/6 = 15/24 = 5/8

Now, there is a way to simplify before you multiply making your final answer easier to simplify or already simplified. This process is called cross simplifying and it only works during multiplication. Here is how it works. If there are numbers that are opposite of each other in the problem and they have something in common (something you can divide evenly into both numbers) then you can simplify those numbers. Here is the example again from above:

3/4 * 5/6 = ?

Since 3 and 6 are opposite each other in the problem and they have a 3 in common I can simplify those numbers. So the 3 on top becomes a 1 and the 6 on bottom becomes a 2. Here is the new problem.

1/4 * 5/2 = 5/8

Keep in mind that you get the same answer either way you do the problem, but when you are dealing with larger numbers it will make it easier on you if you can simplify before you multiply. Here are some steps to follow:

1. Change mixed numbers to improper fractions
2. Cross simplify if possible
3. Multiply the top numbers/multiply the bottom numbers
4. Simplify again if possible

Notice step one, if we are dealing with mixed numbers we must first convert them into improper fractions before we can work the problem. Unlike addition/subtraction you MUST change mixed numbers to improper fractions or you will get the wrong answer.

Here is an example of a mixed number problem:

3 3/5 * 1 5/9 = ?

18/5 * 14/9 =

2/5 * 14/1 = 28/5 = 5 3/5

If you run into problems remember you can post me a question and I will try respond.

Adding and Subtracting Unlike Fractions

We learned in the previous section about adding and subtracting fractions when we were already given a common denominator. The process is very simple when there is a common denominator because you just have to add/subtract the top numbers and then simplify. You keep you bottom number the same.

Now when you have fractions that don't have common denominators, before you can add/subtract you must first find a common denominator. A common denominator is just like find the least common multiple of two numbers. We want to find a number that both denominators will divide into evenly. Keep in mind the least common denominator (LCD) can be no smaller than the largest denominator. For example:

1/3 + 5/6 The LCD can be no smaller that 6 because is the largest denominator. Fortunately for us the LCD is 6. We will talk more about this in a minute.

Once you have found the LCD, you then write an equivalent fraction using the LCD. Remember last chapter when we wrote equivalent fractions we would just multiply the top and bottom number by the same number of our choosing? We do the same thing now except we don't get to choose any random number. We have to use a very specific number.

Here is how we put it all together:

1/3 + 5/6 - First we find the common denominator which is six. Then we rewrite the problem using the common denominator.

?/6 + ?/6 - Here is where the equivalent fraction thought comes into play. We need to find out what times 3 gives us the LCD of 6. And we know that it is 2. So, if we multiply the bottom by 2, what do we have to do to the top? That's right, multiply it by 2. The second fraction already has the LCD so the top number stays the same.

2/6 + 5/6 = 7/6=11/6 (this is one and one sixth, this how mixed numbers will look)

Here is another example:

5/9 + 1/6 = 10/18 + 3/18 = 13/18

Remember if you are dealing with mixed numbers it is easier to change them into improper fractions before finding a common denominator. Make sure you simplify if at all possible. Finally, watch you signs when adding and subtracting with positive and negative numbers.

Let me know if you have any questions.

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.