What is there to the power of the number one? What is there to the power of any number? For some people numbers cause them anxiety.
For most, fractions put real terror in their heart.
Unfortunately, this fear has nothing to do numbers, but everything to do with how we were taught elementary school math. But let's look at the power of the number one.
On the surface, the number one does not look at all powerful.
Some have sung that it is the loneliest number.
Some teams claim that they're number one. This is not what I am talking about.
Instead I'm talking about two powerful concepts involving the number one.
Now don't laugh. I'm not fooling here.
If you struggle with fraction math, it's because no one ever taught you about the power of the number one.
So what are these two concepts? What do they mean? The first concept is the infinite ways that the number one can be denoted or represented.
The number one can be written as 1 of course. But it can also be written as 2/2, 3/3, 4/4, 5/5.
.
.
on to infinity.
Now don't say "Duh, that was obvious!" I haven't explained the power here yet.
The second concept is that anything multiplied by one is itself.
I hope you aren't laughing. This is really important.
You probably remember learning your multiplication tables. I never understood why they bothered with the ones table.
It was so obvious, but it wasn't until much later that I learned the power of the ones table especially when you combine this concept with the first concept, the many ways that one can be represented. So let's apply the power.
For those who are struggling with fraction math, these two concepts are the key to solving all your fraction problems. Take for instance, the addition of fractions, like 2/3 + 5/8.
Everyone knows you can't add those two because they are not alike fractions.
Adding thirds to eighths is like adding apricots to peaches.
But if we could convert them both to nectarines, then we could add them.
Luckily for us, conversion of fractions is possible and easy.
Just multiple each fraction by one, which we know doesn't change its value. But which representation of the number one do we want? We want different representations such that we end up with like denominators (that's the number on the bottom).
Having like denominators makes the two fractions alike so that we can add them. So let's look at the two fractions denominators, 3 and 8.
If we multiplied 2/3 by 8/8 and 5/8 by 3/3, this would give us a common denominator of 24 (3 times 8).
It also yields the fractions 16/24 (2 times 8) and 15/24 (5 times 3) respectively which hasn't changed the value of the original fractions one iota.
Now adding these two like fractions is just a matter of taking the sum of the two numerators (the numbers on top) which adds up to 31/24 (16 + 15 = 31). The power of one has come to the rescue.
So why don't most people know about the power of the number one? It's because the public schools insist on teaching the addition of fractions before they teach the multiplication of fraction.
After all, everyone knows addition is easier than multiplication. Except that in the case of fractions, this isn't true.
But to overcome this shortsightedness, they go on about multiplying diagonally across the plus sign. Uh? You can't multiply across the plus sign! That's confusing.
I don't care if it works; if it's confusing then there's room for something to go wrong and more times than not, it does go wrong.
The top multiplication happens but the bottom doesn't, or vise versa.
Wrong multiplication always leads to the wrong answer. So what can you do? Teach your child the power of one.
When you find your child is up to his neck trying to learn fraction math, do him a favor.
Teach him fraction math yourself (without the textbook) Teach him to multiply fractions first.
Multiplying fractions is actually easier than adding fractions; just multiply the top numbers across (the numerators) and multiply the bottom number across (the denominators).
Done! Now teach him about the power of one.
With these two skills; multiplying fractions and multiplying by the number one, the conversion of fractions is possible.
Being able to convert fractions to like denominators is what you need to do in order to be able to add them together. Now that's understandable! Understanding leads to correct answers.
As an aside, the power of the number one can also be used to simplify the multiplication of fractions. Just as we multiplied by one in the form of 3/3, we can also remove one from a multiplication the same way.
Take for example the following multiplication, 3/8 times 1/9.
By the above procedure, we would multiply 3 by 1 and 8 by 9 to get 3/72 which reduces to 1/24.
But why not apply the power of one and reduce it before we multiple. 3/8 times 1/9 is equal to (3*1)/(8*9) which is equal to (1*3)/(8*(3*3)). Well is not 3/3 equal to one? Then pull it out.
That leaves 1/(8*3) or 1/24.
Let's apply this to 5/8 times 2/15.
Rewritten that is equal to (5*2)/(8*15), which is equal to (2*5)/(2*2*2*3*5).
Pull out the 2/2 and the 5/5, and that leaves 1/(2*2*3), which equals 1/12. Wait a minute! Where did the one on top of the 12 come from? It was always there just like the good 1 it is.
We just don't normally write it.
Anything multiplied by one is itself, so that top number was not just (2*5), it was actually (1*2*5), so that when we pulled the 2/2 and 5/5, we are left with the 1 on top.
Once again, the power of one comes through.
I'll bet that at the beginning you thought that there was no way I could speak so much on the power of the number one. Well, actually, I've only scratch the surface, Exploring the power of numbers can be interesting, helpful, and, dare I say it, lots of fun.
Before I close, I have one more tip to share. When working with fractions, use a visual or draw a picture.
When you're adding fractions, a picture can be worth a thousand words. A picture gives you a visual clue if your answer is accurate.
A picture can cement the concept. Take 1/3 of a pie. If you divide that 1/3 pie segment into 8 equal pieces, then you have just converted 1/3 into 8/24 visually.
If you take a whole pie that was divided into thirds and then divide each third into eighths.
You've divide the whole pie into 24 pieces. Shade in the equivalent of one third (8 of the 24 pieces) and shade in the equivalent of one eighth (3 of the 24 pieces).
Count the number of 24th pieces that are shaded and you'll have the sum of 1/3 and 1/8, or the sum of 8/24 and 3/24 which is 11/24.
Is that not cool? It really works! Now eat the pie and celebrate a job well done.
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