This is YourMathGal,
Julie Harland.
Please visit my website
at yourmathgal.com where all
of my videos were organized
by topic.
We're going
to continue solving basic
proportions and we're going
to do these four problems
on this video.
Notice the differences,
these proportions have
decimals in them.
So, it will be easier
to use a calculator,
although you could also just
use, you know,
a piece of paper
and do your multiplication
and division by hand.
So, let's do the
first problem.
Here it is.
Now, in this one, let's do it
without a calculator even
though I said use a calculator
to solve for X. So,
how could I do this one?
Well, for one thing,
I'm going to notice this is a
proportion and remember
that in a proportion,
if you have A over B equals C
over D then you can take the
numbers diagonally
across the equal sign
and multiply this together.
A times D and that will equal
the other two numbers
multiply together.
Remember, this only works
in a proportion
where there's an equal sign.
If it is times, uh-uh,
can't do that.
It's just a
multiplication problem.
All right, so,
let's do that on this problem
and I was to look
for where the variable is
and that's what I'm going
to multiply first.
So, I see X is multiplied
by 3, so I'm going
to write 3X equals
and then the other diagonal is
the 5.8 times 5.1,
5.8 times 5.1.
I'm using parenthesis
for multiplication
so it doesn't get confuse
with a times sign with the dot
and we'll divide both sides
by 3.
Now, it's true
that you can multiply 5.8
times 5.1 and then do division
with 3.
I'm going to see
if I can cancel first
and if you know your
divisibility,
divisibility test for 3,
you think of this 5.1 as 51,
3 goes into 51, actually goes
in 17 times.
So, remember how you do this.
If this is a whole number
down here, 3 into 51 is 17,
but you have to move
in one decimal place 'cause it
was really 5.1.
So, then I'll only have
to do 5.8 times 1.7
and you could do
that anyway you want.
There's different ways
to do multiplication.
I'll do the standard way most
people do.
So, 8 times 7 is 56,
so it's 6 carry the 5
and that's 35 plus 5 will give
you 40.
And then we have 1 times 8,
1 times 5, and I get 986.
And remember what we do is we
have to move the decimal
in for each of these places,
two places total.
So, our answer is 9.86.
So, this answer is actually X
equals 9.86.
Let's do it
without a calculator.
Now, if you have a calculator,
it's a lot easier.
You just put
in your calculator 5.8 times
5.1 and then divided by 3.
So, in your calculator you
would enter, you know,
depending on what kind
of calculator,
just 5.8 times 5.1 divided
by 3 and you will get the same
answer with calculator.
Now, in this problem we don't
need to round.
It came out exactly to 9.86.
For the rest of the problems,
we're going
to use a calculator
because I've given problems
that unfortunately are not
as easy to do.
Bigger numbers,
lots of decimals.
So, although you could do this
without a calculator,
we're just going to try
to get how
to solve proportions,
that's going
to be the main idea here.
So, try this one on your own
with a calculator first
and then come back to me.
So, we've got X times 7.8.
So, we've got 7.8X equals
and then we're going
to multiply those two numbers
together, 29 times 2.31.
Now, you don't need
to this multiplication now.
You could always wait
and do everything
in your calculator
in one step.
So, I'm going
to divide both sides by 7.8
and then we're simply going
to enter that in
the calculator.
So in your calculator,
you want to put 29 times 2.31
divided by 7.8.
And what comes
up in the calculator--
[ Pause ]
My calculator has 8.58846,
it goes on and on and on.
Notice that we're rounding
to the nearest hundredth,
that's two places
after the decimal point.
So, we want
to cut it off right here.
Now, since there's an 8
after the hundredth place,
we're going to round this
up so instead of 8.58,
it will be 8.59.
But it doesn't equal that.
It's approximately equal
and so I do a little a
squiggly line.
It's 8.59.
So, that's X
to the nearest hundredth.
All right,
here's the second prob--
the third problem actually.
So, go ahead and try this one
on your own.
All right,
so I find the X is diagonally
with the 41.
So, we've got 41X equals
and then we'll multiply those
two numbers together,
the other diagonal,
0.15 times 3.9
and we'll divide it by 41.
And of course,
f you were doing this long
hand, you would actually have
15 times 39 and figure
out that the decimal goes
in three spaces
and then you'll have to divide
by 41 and do long division
to at least three places
after the decimals
so you could round
in the nearest hundredth.
With the calculator,
we'll just enter it.
0.15 times 3.9 divided by 41.
And in my calculator,
I get 0.01426, et cetera.
What matters is that I have
to really go--
look at the third number here.
So 4, so it's just not
round up.
So, this is rounded
in the nearest hundredth,
approximately 0.01
which is 100.
By the way,
when you use a calculator,
I always put my numbers
in twice as a double check.
So, I would probably do this
two times to make sure I
didn't accidentally enter
something incorrectly.
All right, next problem,
again try this one
on your own first.
Put the video on pause,
work it, round
to the nearest hundredth.
All right, so we're looking
for X here
and it's crossed diagonally
from 46.1.
So, 46.1X equals 21 times the
3.8, right,
'cause those are the other two
numbers and then we'll divide
by 46.1.
And we're going
to also approximate that.
So, in our calculator,
we want to put in 21 times 3.8
and then divide by 46.1.
In the calculator,
I get 1.7310, et cetera.
So, again I'm going
to just keep it at 1.73,
I'm not going to round up,
so this is approximately 1.73.
And there you have it.
So, we've done just some more
proportions,
more basic proportions
but we're using a calculator
to help us
with these messy
arithmetic problems.
If you want
to see what happens
if you have some problems
that have some fractions
in it, go to the next video
problems like this.
Maybe you might have 2/3
over an X equals 5
over 4 something like that.
I'll go over problems
like this on the next video
on basic proportions.
This is YourMathGal,
Julie Harland.
Please visit my website
at yourmathgal.com where all
of my videos were organized
by topic