Ok, I'm weird, but I love fractions because they are easier for me than decimals are. So, here are some basic fraction facts to start your mystical journey with my little fractional friends.
The Basic Idea
Remember that the whole number one in fractional form is any number over itself. Examples: 2/2, 3/3, 4/4, 290347509843/290347509843, etc. Think Gemini duality, Yin/Yang, or Cat's tie if that helps you remember.
One way to look at fractions is to see them as a collective, perhaps the Borg Collective if you're into that sort of thing. That'll make sense later as I show you how fractions assimilate one another. Anyhoo, getting back on track, the bottom part of a fraction is called the denominator and it represents the collective, group, bag of coins, or whatever your dream of perfect wholeness is. The top number is the numerator, and it is the part you have out of the possible whole.
So little “you” as the numerator sits up in the nosebleed seats while the big fat denominator below you sneers at you in the skybox. Or, the numerator is sort of like the dollar you spent on the lottery ticket versus the jackpot denominator you wish you'd get. Once more, the fraction is the part over the whole.
For example, in the fraction 5/6 you have 5 jelly beans out of a possible 6 jelly beans. You might want to practice this in every day applications. For example, I have 4 chores to do today. I've completed 3 chores. I've done ¾ of my chores, and I need to do one more out of four, or ¼ of my chores before I can play Death to Veggie Zombies.
Fractions are less than the number one. That means, if you subtract a fraction from one, you'll get the missing piece left over. Example: 1 - 1/3 = 2/3. If you switch that around, and add 1/3 + 2/3 you get the number one. 1/3 + 2/3 = 3/3 = 1.
“How the heck did you do those problems?” you may ask. Ah, I assimilated the whole number into the collective denominator. Remember, the whole number one can be written as anything over itself. What was the perfect denominator of wholeness in both of these problems above? The bottom number was 3! So, 1 - 1/3 = 2/3 could be re-written by turning the whole number one into, you guessed it, 3/3. Ah the perfection, three out of three, it is one perfect whole. So now our problem is 3/3 -1/3 = 2/3.
You subtract only the top numbers to get your answer. Let's strip away the denominators for a moment and it'll become a little more familiar. 3 - 1 = 2. But, remember you're dealing with a fraction, a number less than one, so you have to put that nasty, big denominator that it'll never live up to - right below it. The final answer is 2/3 or two out of three.
One more time? You have one whole group of three jelly beans. You eat one jelly bean out of the three your nose-picking neighbor gave you. You end up with how many out of 3? Two out of three, or 2/3. To double check your answer and make yourself sick just so you can make sure you ate only one of those jelly beans, let's check our work. You have 2/3 left, or two out of three jelly beans. You are pretty sure you ate one jelly bean out of three or 1/3 of the jelly beans. So, you add only which numbers? Those pesky little top numbers, of course!! So, in the problem 2/3 + 1/3. What do you get? 3/3 or 1. Ahh, perfect whole numbers, most of the time you won't see those as the answers to fraction problems, but hey, you have to start somewhere.
Thoroughly confused? Well, did I mention I'm an English teacher, not a math teacher?
