An electrician has the following lengths of cable: 23
inches, 49 inches, and 8 feet.
How much cable does he have in Feet?
So these are the lengths.
Each of these are the length of a cable in
inches, inches, and feet.
And we want to know the total length, if you add all of
these up, and we need the total length in feet.
And so the best way to do that is to convert each of these
lengths into feet, and then add them all up.
So let's start with this one right over here: 23 inches.
So it's always important to have your intuition give a
little bit of a check on what the answer should look like.
There are many inches per foot, so when you convert this
into feet, you should have a smaller number.
There are 12 inches per foot.
So this should be a small number.
This is not even 2 feet.
24 inches would be 2 feet.
So this should be less than 2 feet.
But let's do it mathematically.
So to do it mathematically, we want this inches to cancel out
with inches.
And the way you do that, is you put that in the
denominator.
So it cancels out with the inches.
And so we want feet per inches, or foot per inches.
I guess I'll just write ft.
It could be feet or foot, singular or
plural, it doesn't matter.
So how many feet are there per inches?
Or another way to think about it, how many inches
are there per foot?
1 foot is equal to 12 inches, or you could say 1 foot for
every 12 inches, or you could read this as 1/12
of a foot per inch.
Either way, if we multiply this, the inches cancel out.
That's why we know, at least mathematically, if we just did
it mechanically, why we shouldn't multiply by 12.
But also it should make complete sense.
We should be dividing by 12 because when you express this
distance in feet, it should be a smaller number, so we should
divide by 12.
So what does this give us?
This is equal to 23 times 1 is 23/12.
This inches cancels out with that inches, and we're just
left with feet.
So that is 23/12 feet.
And this is an improper fraction, but I'll leave it as
an improper fraction for now because they're actually
easier to manipulate than mixed numbers.
So that's that first cable.
Let's do the second one right here: 49 inches.
So the second cable is 49 inches, and
we do the same thing.
We want to convert it to feet.
We have inches in the denominator.
We should end up dividing by something because we want a
smaller number.
49 inches will be a smaller number of feet
by a factor of 12.
So what we care about is feet per inches, and we know that
there is 1 foot for every 12 inches, or 1/12
of a foot per inch.
It can be read either way.
When you multiply, the inches will cancel out, and we will
be left with 49 times 1, which is 49, over 12 feet.
That is the second cable.
And then we have this last cable right
here, this 8-foot cable.
The very last one is 8 feet, and if we want, we can convert
that into an improper fraction.
At this point, there's two ways we can do it.
Everything is in feet.
Here, it's improper fractions.
We could, if we want, convert these into mixed numbers and
then add them up, or we can convert this into an improper
fraction that has the same denominator, and
then add them up.
And the easiest way, I think, is to just have this with the
denominator 12.
So 8 feet is the same thing as what over 12?
Well, what's 8 times 12?
It's 96, right?
96 divided by 12 is 8.
8 is the same thing as 96/12.
These are equivalent.
Let me make sure this 8 and 96/12 is the exact same thing.
I picked 12 because these have 12 in the denominator.
And then I said, 12 times 8 is 96.
So 8 feet is the same thing as 96/12 feet.
And now I can add everything up.
The total length of cable he has is-- I'll do it over here.
It's 96/12 plus 23/12 plus 49/12, and everything is in
feet, so this answer will give us in feet.
We have all of the same denominators.
Our denominator is 12.
And so our numerator's going to be 96 plus 23 plus 49.
Let's add that up over here.
So 96, 23, 49, we have to add it up.
6 plus 3 is 9.
9 plus 9 is 18.
1 plus 9 is 10.
10 plus 2 is 12.
12 plus 4 is 16.
So that's 168.
So this expression right here is equal to 168/12, which is a
valid answer.
And, of course, all of these are in feet,
so it's 168/12 feet.
But let's write this now as a mixed number, so that we have
a better idea of really how many feet it is.
And to do that, we just divide 168 by 12.
So 12 goes into 168.
It doesn't go into 1.
It goes into 16 exactly one time.
1 times 12 is 12.
We subtract.
16 minus 12 is 4.
Bring down the 8.
12 goes into 48 four times.
4 times 12 is 48.
And we have no remainder.
So 168/12 is exactly 14, so this is
exactly equal to 14 feet.
So our electrician has exactly 14 feet of cable.