0:00:00.600,0:00:05.570
So we're asked to add 3/15 plus[br]7/15, and then simplify

0:00:05.570,0:00:06.590
the answer.

0:00:06.590,0:00:09.810
So just the process when you[br]add fractions is if they

0:00:09.810,0:00:12.000
already-- well, first of all, if[br]they're not mixed numbers,

0:00:12.000,0:00:14.650
and neither of these are, and[br]if they have the same

0:00:14.650,0:00:15.280
denominator.

0:00:15.280,0:00:17.190
In this example, the[br]denominators

0:00:17.190,0:00:18.370
are already the same.

0:00:18.370,0:00:20.460
The denominator is 15.

0:00:20.460,0:00:24.590
So if you add these two[br]fractions, your sum is going

0:00:24.590,0:00:28.860
to have the same denominator,[br]15, and your numerator is just

0:00:28.860,0:00:30.910
going to be the sum of the[br]numerator, so it's going to be

0:00:30.910,0:00:37.490
3 plus 7, or it's going[br]to be equal to 10/15.

0:00:37.490,0:00:39.340
Now, if we wanted to simplify[br]this, we'd look for the

0:00:39.340,0:00:43.080
greatest common factor in both[br]the 10 and the 15, and as far

0:00:43.080,0:00:45.680
as I can tell, 5 is the largest[br]number that goes into

0:00:45.680,0:00:46.480
both of them.

0:00:46.480,0:00:53.640
So divide the 10 by 5 and you[br]divide the 15 by 5, and you

0:00:53.640,0:00:59.020
get-- 10 divided by 5 is 2[br]and 15 divided by 5 is 3.

0:00:59.020,0:01:00.900
You get 2/3.

0:01:00.900,0:01:04.099
Now, to understand why this[br]works, let's draw it out.

0:01:04.099,0:01:08.865
Let's split something[br]up into 15 sections.

0:01:08.865,0:01:11.470
So let me split it up[br]into 15 sections.

0:01:11.470,0:01:13.670
Let me see how well[br]I can do this.

0:01:13.670,0:01:16.300
Well, actually, even a better[br]way, an easier way might be to

0:01:16.300,0:01:17.740
draw circles.

0:01:17.740,0:01:20.070
So let me do the 15 sections.

0:01:20.070,0:01:22.260
So let me draw.

0:01:22.260,0:01:25.800
So that is one section[br]right over there.

0:01:25.800,0:01:33.340
That is one section and then if[br]I copy and paste it, that

0:01:33.340,0:01:39.710
is a second section, and then[br]a third section, fourth

0:01:39.710,0:01:44.760
section, and then we have[br]a fifth section.

0:01:44.760,0:01:46.960
Let me copy and paste[br]this whole thing.

0:01:46.960,0:01:49.920
So that's five sections[br]right there.

0:01:49.920,0:01:53.300
Let me copy and then[br]paste that.

0:01:53.300,0:01:56.200
So that is 10 sections,[br]and then let me

0:01:56.200,0:01:57.080
do it one more time.

0:01:57.080,0:01:58.570
So that is 15 sections.

0:01:58.570,0:02:01.010
So you can imagine this whole[br]thing is like a candy bar or

0:02:01.010,0:02:04.950
something, and we have now split[br]it up into 15 sections.

0:02:04.950,0:02:07.870
Now, what is 3/15?

0:02:07.870,0:02:10.419
Well, it's going to be[br]3 of the 15 sections.

0:02:10.419,0:02:17.570
So 3/15 is going to be one,[br]two, three: 3/15.

0:02:17.570,0:02:20.880
Now, to that, were adding[br]7 of the 1/15

0:02:20.880,0:02:23.490
sections, or 7 of the sections.

0:02:23.490,0:02:26.260
So we're adding 7[br]of those to it.

0:02:26.260,0:02:35.240
So that's one, two, three,[br]four, five, six, seven.

0:02:35.240,0:02:37.940
And you see now, if you take the[br]orange and the blue, you

0:02:37.940,0:02:41.310
get one, two, three, four, five,[br]six, seven, eight, nine,

0:02:41.310,0:02:45.800
ten of the sections, or[br]10 of the 15 sections.

0:02:45.800,0:02:49.230
And then to see why this is the[br]same thing as 2/3, you can

0:02:49.230,0:02:53.220
just split this candy bar into[br]thirds, so each third would

0:02:53.220,0:02:54.760
have five sections in it.

0:02:54.760,0:02:55.460
So let's do that.

0:02:55.460,0:02:59.300
One, two, three, four, five,[br]so that is 1/3 right there.

0:02:59.300,0:03:01.590
One, two, three, four,[br]five, that is

0:03:01.590,0:03:03.360
another third right there.

0:03:03.360,0:03:06.810
And notice, when you do it like[br]this, we have filled out

0:03:06.810,0:03:11.190
exactly two-- one, two--[br]of the thirds.

0:03:11.190,0:03:13.780
This is the third third, but[br]that's not filled in.

0:03:13.780,0:03:16.210
So 10/15 is the same[br]thing as 2/3.