WEBVTT

00:00:00.420 --> 00:00:04.340
We're asked to multiply 5/6
times 2/3 and then simplify

00:00:04.340 --> 00:00:05.570
our answer.

00:00:05.570 --> 00:00:07.450
So let's just multiply
these two numbers.

00:00:07.450 --> 00:00:13.090
So we have 5/6 times 2/3.

00:00:13.090 --> 00:00:15.030
Now when you're multiplying
fractions, it's actually a

00:00:15.030 --> 00:00:17.470
pretty straightforward
process.

00:00:17.470 --> 00:00:20.190
The new numerator, or the
numerator of the product, is

00:00:20.190 --> 00:00:22.880
just the product of the two
numerators, or your new top

00:00:22.880 --> 00:00:25.340
number is a product of the
other two top numbers.

00:00:25.340 --> 00:00:29.240
So the numerator in our product
is just 5 times 2.

00:00:29.240 --> 00:00:37.250
So it's equal to 5 times 2 over
6 times 3, which is equal

00:00:37.250 --> 00:00:43.490
to-- 5 times 2 is 10 and
6 times 3 is 18, so

00:00:43.490 --> 00:00:44.710
it's equal to 10/18.

00:00:44.710 --> 00:00:50.820
And you could view this as
either 2/3 of 5/6 or 5/6 of

00:00:50.820 --> 00:00:53.640
2/3, depending on how you
want to think about it.

00:00:53.640 --> 00:00:54.750
And this is the right answer.

00:00:54.750 --> 00:00:57.220
It is 10/18, but when you look
at these two numbers, you

00:00:57.220 --> 00:00:59.460
immediately or you might
immediately see that they

00:00:59.460 --> 00:01:01.500
share some common factors.

00:01:01.500 --> 00:01:03.990
They're both divisible by 2,
so if we want it in lowest

00:01:03.990 --> 00:01:07.020
terms, we want to divide
them both by 2.

00:01:07.020 --> 00:01:12.800
So divide 10 by 2, divide 18 by
2, and you get 10 divided

00:01:12.800 --> 00:01:17.510
by 2 is 5, 18 divided
by 2 is 9.

00:01:17.510 --> 00:01:19.920
Now, you could have essentially
done this step

00:01:19.920 --> 00:01:20.630
earlier on.

00:01:20.630 --> 00:01:22.530
You could've done it actually
before we did the

00:01:22.530 --> 00:01:23.220
multiplication.

00:01:23.220 --> 00:01:24.450
You could've done
it over here.

00:01:24.450 --> 00:01:26.450
You could've said, well, I have
a 2 in the numerator and

00:01:26.450 --> 00:01:29.260
I have something divisible by 2
into the denominator, so let

00:01:29.260 --> 00:01:32.710
me divide the numerator by
2, and this becomes a 1.

00:01:32.710 --> 00:01:37.090
Let me divide the denominator
by 2, and this becomes a 3.

00:01:37.090 --> 00:01:42.070
And then you have 5 times 1
is 5, and 3 times 3 is 9.

00:01:42.070 --> 00:01:44.200
So it's really the same thing
we did right here.

00:01:44.200 --> 00:01:47.370
We just did it before we
actually took the product.

00:01:47.370 --> 00:01:49.220
You could actually
do it right here.

00:01:49.220 --> 00:01:53.890
So if you did it right over
here, you'd say, well, look, 6

00:01:53.890 --> 00:01:56.190
times 3 is eventually going
to be the denominator.

00:01:56.190 --> 00:02:00.030
5 times 2 is eventually going
to be the numerator.

00:02:00.030 --> 00:02:03.660
So let's divide the numerator by
2, so this will become a 1.

00:02:03.660 --> 00:02:05.180
Let's divide the denominator
by 2.

00:02:05.180 --> 00:02:07.550
This is divisible by 2,
so that'll become a 3.

00:02:07.550 --> 00:02:13.630
And it'll become 5 times 1
is 5 and 3 times 3 is 9.

00:02:13.630 --> 00:02:15.210
So either way you do
it, it'll work.

00:02:15.210 --> 00:02:18.450
If you do it this way, you get
to see the things factored out

00:02:18.450 --> 00:02:20.910
a little bit more, so it's
usually easier to recognize

00:02:20.910 --> 00:02:23.200
what's divisible by what, or you
could do it at the end and

00:02:23.200 --> 00:02:25.400
put things in lowest terms.