Maurice Cotterell: Good morning.
How are you doing?
I'm Maurice and today we're going to look at transposing, trans change, posing, position,
changing position.
But I have a wicked story for you right now.
John is in the wild and of course John is not wild, so the wild cats are running at
John and he's running and getting real tired, but guess what?
There is a glimpse of hope, there's a river near by so John runs and jumps into the river.
Why the river of all places?
Couldn't he climb a tree?
No, cats don't like water.
So John jumps into the river, goes on the other side and he's now safe.
Where John and the cat is concerned, John isolated the cats on the other side, he left
the cats on one side he's now on the other side safe.
All right, now you may ask what does this have to do with transposing?
All right let me tell you now.
John's situation on one side is dry on the other side is wet, how does dry and wet relate
to each other?
Dry and wet they're opposites.
Now look at this: Here is John and that's a cat getting close
to John.
That's our river right there and john gets across on the other side and of course he's
now wet on the other side.
How does dry and wet relate to each other again, dry and wet are opposite.
Now lets take an analytical view of what we have before us.
The river looks like our equal sign, positive plus sign on one side when it goes across
the other side it becomes just like dry and wet it becomes opposite which is a negative
sign.
Likewise multiplication on one side of the equal sign, going to the next side it becomes
division.
We have subtraction going to the other side becoming addition and likewise if it's division
on this side when it goes to the other side it becomes a multiplication.
What we see here is that signs with numbers go from one side of the equal sign to the
other side they change their signs, their operation.
We're multiplying by five on this side when it goes over we're dividing by five.
We're adding four on this side, when it goes over we're subtracting four.
We're subtracting three on this side when it goes over we're adding three.
We're dividing by seven on this side and of course when it goes over we're multiplying
by seven.
Now lets look at a few examples.
X plus four equals seven, just like John and the cat it's x here being the cat and four
being John, John going on to the other side plus four changes to a minus four so x now
is equal to three.
All right and if it's three x equals 12 the three here is being multiplied by the cat,
but then the three goes to the other side instead of a multiplication it's now doing
the opposite when it goes across which is division, you're so right.
So that's 12 divided by three so x equals four.
If we have situations of subtraction where we have x minus five equals six, x equals
six, this minus five changing position, changing location and also changing the sign.
So plus five so x equals 11.
Let's look at one with the division.
X divided by three is equal to four, now x is now equal to four, over here we're dividing
by three, when dividing by three goes to the next side we have a multiply by three so x
is equal to 12.
Last and final example.
What if we have a situation of x divided by two plus four equals seven.
Now let's think about it.
We need to isolate x on this side.
If you're a sniper and you're going to rescue x you want to take out everyone that's around
x where would you start?
Would you start with the person closest to x?
Certainly not, you're going to start with the person furthest on the periphery and work
your way in.
So guess what we're going to take four over first all right so x divided by two and that's
now equal to seven our four on this side is a plus four so going to the other side it
becomes a minus four, so x divided by two is equal to three and of course we're dividing
by two here so when that two goes over it becomes multiplication so x is equal to three
multiplied by two x equals 6.
Thank you very much for joining us.
I hope this video helps quite a bit in terms of your understanding of transposing and how
it actually relates to every day life.
Going across the river condition changes, going across the equal sign the sign of the
operation also changes.
Thank you very much.
Join us next when we look at the order of operations and how it relates to every day
life.
Thank you!