Adding and Subtracting Fractions

The very first thing I'd like you to do for this section is to read through 5-3 in your textbook and STOP at Section 2 (Adding and subtracting with mixed numbers). Don't worry about notes or quickchecks or anything - just simply read this part of 5-3 silently to yourself.

Now, let's sum everything up:

Fractions can be added and subtracted as long as they have the same denominator (bottom number). Kind of like being in the same "family" - everyone has the same last name.

In the first section, we learned that we can easily add and subtract fractions with the same denominator simply by adding or subtracting the numbers on top. Basically, solve the problem with the TOP numbers and leave the bottom number the same (and don't forget to simplify if necessary!)

Example:
 3/5 and 1/5 have the same denominator, so I can easily add them by just adding the top numbers and keeping the denominator the same:

3/5 + 1/5 = 4/5.

The tricky part comes in when you have two fractions with different denominators. Before we can add or subtract them, we have to give them the same denominator (put them into the same "family"). So, how do we do this?

1) Find the LCM of the two denominators. The example in the book shows us 2/3 + 1/5. Since our denominators here are 3 and 5, our LCM = 15.

2) Now we need to change our fractions to new fractions that have a denominator of 15. Recall that to find any equivalent fraction, we must do the same thing to the top that we did to the bottom. So, 2/3 equals SOMETHING over 15, and 1/5 also equals SOMETHING OVER 15:

2/3 = ?/15
1/5 = ?/15

To find out what goes where the question marks are, figure out how we got from the old denominators to the new denominators. For the first one (2/3), how did we get to 15? We know that we can multiply 3 by 5 to get 15. Now, do the same thing to the top: 2 x 5 = 10. Our new fraction is 10/15.

Let's figure out the second fraction (1/5). How did we get from a denominator of 5 to a denominator of 15? we know we can multiply 5 by 3 to get 15. Now, do the same thing to the top: 1 x 3 = 3. Our new fraction is 3/15.

3) Now our new fractions can finally be added because they have the same denominator!

10/15 + 3/15 = 13/15. ---> This is already in simplest form, and so it is our answer.

To sum up the summary (lol!):

- Fractions need to have the same denominator in order to be added or subtracted.
- If they already have the same denominator, just add or subtract the top numbers, leave the bottom the same, and simplify if necessary.
- If they do NOT have the same denominator:
1) Find the LCM of the denominators.
2) Convert the fractions to equivalent fractions with the LCM as your common denominator.
3) Solve.

Try p.250, 5 - 12 individually. Check as a class. When you're ready to continue, the next post will address the rest of 5-3.

P.S.: To L-Dubs - thank you SO much for my Lyme Disease plushie! It's seriously the cutest thing ever. Made me smile. His name is Lymie. I will post pics of Lymie helping me work soon. :)