5-3 Continued (Adding & Subtracting Mixed Numbers)

Fractions are pesky, aren't they? They're always asking us to change them around.

Read through the rest of p. 248 and 249 as a class.

Let's sum up what we learned. Sometimes, when adding and subtracting with mixed numbers, I have to think of myself as a secret, government-appointed scientist who has to solve an important calculation before an asteroid destroys the earth, just 'cause fractions irritate me that much. But - if you use the super-secret fraction-action method, you'll be fine.

1) Convert your mixed numbers into improper fractions. Here's a diagram from mrmelsonmath624.blogspot.com to remind you how we do this:


If you don't remember how to convert mixed numbers to improper fractions, you'll need to practice that before you move on. Since I can't accurately display mixed numbers from this keyboard, I'd like you to look at pg. 250, #15.

Once you convert those mixed numbers to improper fractions, you should have:
81/8 + 15/4.

2) Now we proceed as with regular fractions. Since we can't add them 'til they've got the same bottom number, we find the LCM of the denominators. The LCM of 8 and 4 is 8.

3) Convert the fractions to new fractions that have 8 as the denominator (thankfully, we only need to convert one of them):

15/4 = ?/8    ---> We know we can multiply 4 by 2 to get 8, so we'll do the same thing to the top:

15/4 = 30/8

4) Now, add your new fractions: 81/8 + 30/8 = 111/30.

5) Finally, simplify. This will most likely result in a mixed number. Remember, to convert (or simplify) an improper fraction to a mixed number, we divide the top by the bottom, and use the remainder as the top of the fraction and the original denominator for the bottom. Here's a diagram from ricksmath.com:



In our case, we divide: 111 ÷ 30.

111 ÷ 30 = 3 remainder 21. So, for our mixed number, our whole number is 3, the top of our fraction is 21, and the bottom is 30:

3 and 21/30 (again, sorry I can't display mixed numbers properly on here). But wait! Our mission is not done. Our answer is not in simplified form. Our whole number stays the same, but the fraction can be simplified. Our final answer is:

3 and 7/10.

I know this is a lot to take in. It takes practice and lots of remembering what you've already learned about fractions, but you can do it!

Are you ready to try p. 250, 15 - 18?

I'll be posting more tomorrow on 5-4. It'll be there when you're ready. Also, please take a look around the room - there's a fractions poster on the Math board that will remind you of some fraction principles.