### Linda's Last Fraction Post

Thursday, May 7, 2009
Hello everyone! Mr. Harbeck assigned us all to do a fractions review post so this is mine. In this post you'll learn about how to add, subtract, multiply, and divide mixed, improper, and proper fractions. The first thing we need to know about how to do all this is to know what a fraction is first of all. A fraction is a part of a whole. They're expressed as a/b usually.
eg.
1/2
The two is the whole, or the total amount of possible pieces to make one whole. The one indicates how many pieces there are in the fraction.
When adding fractions we basically compare. When we compare fractions the wholes must be the same size. So when adding, we must find a common denominator. The easiest way to do so is to multiply both the numbers, although it is not the only way.

In the image above the example is 1/2 + 3/4. As mentioned previously, when adding fractions we basicially compare so when we compare the wholes need to be the same. For the wholes to be the same we must have a common denominator. Luckily, in this example 4 is our common denominator. So we re-write out equation with 4 as the denominator. Since our denominators have changed, so must our numerators. Whatever you do to the bottom, you must do to the top. So we ask ourselves, what did we do to 2 to get 4? We multiplied by 2, so we multiply the numerator by 2. So our answer is 2/4, the equivalent fraction to 1/2. What did we do to 4 to get 4? We multiplied by 1. So we multiply 3 by 1, 3/4. Remember to simplify, or change improper fractions to mixed numbers.

SUBTRACTING FRACTIONS

Like adding fractions, to subtract fractions we also find a common denominator. Once you've found a common denominator and the numerators are changed appropriately, you can then normally subtract the numerators.

Subtracting mixed fractions is basicially the same as subtracting any old fraction, except you need to make the mixed fraction into an improper fraction. To do so, you multiply the whole number by the denominator and add the numerator to find the numerator, and the denominator stays the same. Then, you can subtract as you usually do.

MULTIPLYING FRACTIONS

Multiplying fractions is a fairly simple business. To multiply fractions, you multiply the numerator by the numerator, and denominator by the denominator. Your answer could quite conceivably be somewhat of a large number. It is best to simplify to lowest terms, as shown in the image above.

DIVIDING FRACTIONS

There are many ways to divide fractions. One of the simplest ways to divide fractions, is to multiply the first fraction by the second fractions recipricol. This method works everytime. Refer to the image above to see an example of this method. Remember to always simplifly to answer to lowest terms.

Another way to divide fractions is to use a ratio table. Mr. H's analogy of Paint Can and Room works well in interesting ways. To use the ratio table we find how many paint cans are needed for one whole room, in theory. On the left side is PC, or paint can. On the left, is RM, or room. RM is where the second fraction goes. We're trying to find out how many times the second fraction (RM) goes into the first fraction (PC). So, we need to get the fraction on the right to one whole. (eg. 5/5, 1/1, 3/3, etc. etc.) Remember, whatever you do to one side, you do to the other.

Once you have reached one whole, whatever the answer on the left is, should be your answer. To check if your answer is correct, you can try other methods. If both your results are the same, your answer is most likely correct.

WORD PROBLEMS

Ned has 10 chocolate bars and he is giving his brother 2/3 of his 10 chocolate bars. To find a fraction of something you multiply. I multiplied the amount of chocolate bars Ned has, and the amount he promised to give his brother. Ned should give his brother 6 2/3 chocolate bars.
Ned's brother does not get all whole chocolate bars, because one of them is 2/3, which isn't a whole.

We're to solve this word problem two ways and here is the second way I solved this word problem.
I used 10 as a representation of 100% because it's an easy number to work with. I then converted 2/3 into a decimal and then into a percent as well, which was 66.6 repeated. Roughly speaking, 66.6 repeated is quite close to 6 2/3. I also used pictures to solve this question, to make absolute sure and to see if all my answers were the same.

The image above is an representation of the chocolate bars. Each chocolate bar was split into 3 equal pieces. 2/3 of each chocolate bar was coloured in. If I were to make the chocolate bars wholes, I would have 6 2/3 chocolate bars.
So, Ned's brother really doesn't get all whole chocolate bars because of the 2/3 that is left over.

The best way to answer a word problem such as this would be to use a ratio table, and when we use a ratio table we're dividing.

15 scoops of flour make 6 2/3 cakes. What I did here was began with 2 1/4 scoops equaling 1 cake. My objective was to find out how many cakes 15 scoops made, so I plugged 15 under scoops. Then I had to figure out how I got from 9/4 (improper version of 2 1/4) to 15/1, which is the same as saying 15. I used some simple algebra and found that I had to multiply 20/3 to get from 9/4 to 15/1. Since I did that to one side, I have to have done it to the other side. On the cake side, I got 6 2/3.

Thanks for your time everyone! I hope this post was up to standards. If you have any questions concerning this post or something is incorrect feel free to comment!