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.