Okay, in this video I just want to do some arithmetic basics. What I want to do is just show you
a little trick
of how to convert a terminating decimal into a fraction.
Hopefully the decimal you have to do this with is not
doesn't have a long decimal expansion. If it does it can be a pretty
pretty tedious endeavor. At least the way that I do it.
So I wanna show, for example, that we can write .5 as
well as 1/2. 1.75 is the fraction 7/4.
and 2.88 as the fraction 72/25.
So this is how I do it.
So let's start with .5.
Umm, the first thing I do is you can write
any number, umm, you can take any number and divide it by one and that's still the exact same number that you started with.
And what I'm gonna do is
umm, on my one I'm gonna add on
a couple zeros, and what I'm gonna do is
my goal is to, I want to get rid of the decimal
in the numerator. Okay so I'm going to get rid of the decimal in the numerator.
So to do that, if I multiply basically the top by ten,
and the bottom by ten all I'm really doing is moving the decimal one place
that means I would have to move it
one place in the denominator. So if I move it one place,
and I move the decimal one place as well,
I'm gonna be left with the number 5/10.
And now I just try to simplify this if, if possible.
Well, 5/10 I can write five is five times one.
I can write ten is five times two.
Remember if you have all multiplication in the top and all multiplication in the bottom,
you can cancel out common factors.
And hey, that just simply leaves us with the fraction 1/2.
Okay, so let's try out 1.75; let's try the same trick.
Okay, so I'm gonna write 1.75 over 1.
And the idea is if I move the decimal place twice
175, you have to add on
basically two zeros in the denominator.
Okay and remember the numerator of a
fraction is bigger than the denominator. The original number you started with
was bigger than one, and that's certainly true. So just a little
quick little check to make sure you're on the right path. The tedious part
about this is just trying to really reduce it more than anything.
Umm, so this is where you kind of have to know factors.
Well, let's see, I think 175
umm, I think about $1.75. well,
quarters go into $1.75, so that means we can multiply 25 by something.
Well, I think we would need 27, 'er, excuse me,
25 times 7. That's gonna give us
175, and then I think, well, how many quarters are in a dollar?
There's four quarters in a dollar, so that means 25 times 4,
that's gonna give us 100, and again same thing. We can just cancel out the 25s,
and we're left with simply the fraction 7/4.
So plug 7/4 into your calculator,
or better yet convert it back into a decimal, and you'll see that you get 1.75 back.
Umm, one last one so 2.88,
same thing I'm gonna write this as over one.
If I move the decimal place
to the right two times in the numerator, that means I'm gonna have to add
two zeros to the denominator, and, okay. So again now I have to start looking for
common factors.
Well, one thing, if they're both even what I like to do, that means we can take
two times something on the top, and if we divide all the numbers, we'll get 144.
so 2 times 144 is gonna be 288, and two times 50 is gonna give us 100.
So we can cancel out our two's
and that leaves us with 144/50, but now the same trick I think we can
actually reduce this again.
Notice both numbers are divisible by two because they're both even.
Well, since they're both even, notice you can write 144 as 2 times 72,
and then 50 as 2 times 25.
So same trick, we can cancel out our two's.
We're left with 72/25.
And now I think, huh, does this reduce any further?
If you think about factors of 25, umm, the factors of 25,
the only thing that you can multiply whole number wise
would be 15 and 25, and
Well, you know, one doesn't really help in terms of reducing your fraction.
Five doesn't go into the number seventy-two,
and likewise 25 won't go into the number 72,
so that means we've now reduced our fraction as much as possible,
and it says you can write the decimal 2.88 as 72/25.
Alright I hope these examples makes some sense. Like I said,
you know, I'm not do this one now, but if somebody gave you, you know,
3 4 7 8, you know, uh, umm, a big number,
Umm, it's gonna be a little tedious to simplify it because you're gonna get 1234789.
We're going to do one, two, three, four, five, six times,
so one, two, three, four, five, six, so now you'd have to start reducing a big number like that.
Umm, yuck, I would not want to simply that down,
but, you know, I don't think in a, in a typical class they're not,
you're not gonna see these sorts of problems. If they do tell your teacher
that they're, uh, umm, being,
being bullies. So all right, umm, I hope this video helps you out, makes some sense.
If you have any questions or comments, please feel free to post them.