0:00:00.303,0:00:03.046
- [Voiceover] Let's say that[br]we have the fraction 9/10,

0:00:03.046,0:00:08.046
and I want to add to[br]that the fraction 1/6.

0:00:09.567,0:00:13.039
What is this, what is this going to equal?

0:00:13.839,0:00:14.827
So when you first look at this, you say,

0:00:14.827,0:00:16.602
"Oh, I have different denominators here.

0:00:16.602,0:00:18.599
It's not obvious how I add these."

0:00:18.599,0:00:21.038
And you'd be right and the way to actually

0:00:21.038,0:00:23.546
move forward is to find[br]a common denominator,

0:00:23.546,0:00:26.181
to convert both of these fractions into

0:00:26.181,0:00:28.536
fractions that have a common denominator.

0:00:28.536,0:00:30.498
So how do you think about[br]a common denominator?

0:00:30.498,0:00:32.125
Well, a common denominator's[br]gonna have to be

0:00:32.125,0:00:36.478
a common multiple of these two[br]denominators of 10 and six.

0:00:36.478,0:00:38.638
So what's a common multiple of 10 and six?

0:00:38.638,0:00:41.436
And it's usually simplest to[br]find the least common multiple,

0:00:41.436,0:00:43.502
and a good way of doing that[br]is start with the larger

0:00:43.502,0:00:47.312
denominator here, 10, and say,[br]okay is 10 divisible by six?

0:00:47.952,0:00:50.978
No. Okay, now, is 20 divisible by six?

0:00:51.588,0:00:56.005
No. Is 30 divisible by six?[br]Yes. 30 is divisible by six.

0:00:56.005,0:00:57.722
So I'm just going through[br]the multiples of 10

0:00:57.722,0:00:59.556
and saying, "Well what is[br]the smallest multiple of 10

0:00:59.556,0:01:03.644
that is divisible by six?"[br]And that's going to be 30.

0:01:03.644,0:01:05.639
So I could rewrite both of these fractions

0:01:05.639,0:01:07.605
as something over 30.

0:01:07.605,0:01:10.296
So nine over 10. How would I write that as

0:01:10.296,0:01:11.898
something over 30? Well I multiply

0:01:11.898,0:01:15.984
the denominator, I'm multiplying[br]the denominator by three.

0:01:17.074,0:01:19.617
So I've just multiplied[br]the denominator by three.

0:01:19.617,0:01:22.088
So if I don't want to change[br]the value of the fraction,

0:01:22.088,0:01:23.586
I have to do the same[br]thing to the numerator.

0:01:23.586,0:01:26.186
I have to multiply that by three as well

0:01:26.996,0:01:29.854
because now I'm just multiplying[br]the numerator by three

0:01:29.854,0:01:31.433
and the denominator by three,[br]and that doesn't change

0:01:31.433,0:01:32.954
the value of the fraction.

0:01:32.954,0:01:35.751
So nine times three is 27.

0:01:35.751,0:01:38.549
So once again, 9/10 and 27/30

0:01:38.549,0:01:40.964
represent the same number.

0:01:40.964,0:01:43.564
I've just written it now[br]with a denominator of 30,

0:01:43.564,0:01:45.631
and that's useful because[br]I can also write 1/6

0:01:45.631,0:01:49.100
with a denominator of 30. Let's do that.

0:01:49.100,0:01:51.621
So 1/6 is what over 30?

0:01:51.621,0:01:52.724
I encourage you to pause the video

0:01:52.724,0:01:53.850
and try to think about it.

0:01:53.850,0:01:56.149
So what did we do go from six to 30?

0:01:56.149,0:01:59.248
We had to multiply by five.

0:01:59.908,0:02:01.628
So if we multiply the denominator by five,

0:02:01.628,0:02:04.623
we have to multiply the[br]numerator by five as well,

0:02:04.623,0:02:09.623
so one times five, one times five is five.

0:02:11.008,0:02:13.749
So 9/10 is the same thing as 27/30,

0:02:13.749,0:02:16.453
and 1/6 is the same thing as 5/30.

0:02:16.453,0:02:20.226
And now we can add, now we can add

0:02:20.226,0:02:21.817
and it's fairly straightforward.

0:02:21.817,0:02:23.267
We have a certain number of 30ths,

0:02:23.267,0:02:25.335
added to another number of 30ths,

0:02:25.335,0:02:30.062
so 27/30 + 5/30, well that's going to be

0:02:30.062,0:02:35.062
27, that's going to be 27 plus five,

0:02:35.471,0:02:40.201
plus five, plus 5/30,

0:02:41.181,0:02:43.583
plus 5/30, which of course

0:02:43.583,0:02:47.361
going to be equal to 32/30.

0:02:47.361,0:02:50.781
32 over 30, and

0:02:50.781,0:02:54.321
if we want, we could try[br]to reduce this fraction.

0:02:54.801,0:02:56.805
We have a common factor of 32 and 30,

0:02:56.805,0:03:00.196
they're both divisible by two.

0:03:00.196,0:03:03.505
So if we divide the numerator[br]and the denominator by two,

0:03:03.505,0:03:06.118
numerator divided by two is 16,

0:03:06.118,0:03:08.902
denominator divided by two is 15.

0:03:09.452,0:03:12.640
So, this is the same thing[br]as 16/15, and if I wanted

0:03:12.640,0:03:16.215
to write this as a mixed[br]number, 15 goes into 16 one time

0:03:16.215,0:03:17.574
with a remainder one.

0:03:17.574,0:03:20.255
So this is the same thing as 1 1/15.

0:03:20.795,0:03:22.534
Let's do another example.

0:03:22.534,0:03:27.018
Let's say that we wanted[br]to add, we wanted to add

0:03:27.018,0:03:31.881
1/2 to

0:03:31.881,0:03:36.881
to 11/12, to 11 over 12.

0:03:36.893,0:03:38.033
And I encourage you to pause the video

0:03:38.033,0:03:40.864
and see if you could work this out.

0:03:40.864,0:03:42.502
Well like we saw before, we wanna find

0:03:42.502,0:03:43.883
a common denominator.

0:03:43.883,0:03:45.102
If these had the same denominator,

0:03:45.102,0:03:46.264
we could just add them immediately,

0:03:46.264,0:03:48.527
but we wanna find a common denominator

0:03:48.527,0:03:50.222
because right now they're not the same.

0:03:50.902,0:03:53.468
Well what we wanna find is a multiple,

0:03:53.468,0:03:55.794
a common multiple of[br]two and 12, and ideally

0:03:55.794,0:03:58.164
we'll find the lowest common[br]multiple of two and 12,

0:03:58.164,0:04:00.264
and just like we did before,[br]let's start with the larger

0:04:00.264,0:04:01.901
of the two numbers, 12.

0:04:01.901,0:04:05.291
Now we could just say[br]well 12 times one is 12,

0:04:05.291,0:04:07.949
so that we could view that[br]as the lowest multiple of 12.

0:04:07.949,0:04:10.632
And is that divisible by two? Yeah, sure.

0:04:10.632,0:04:12.790
12 is divisible by two.

0:04:12.790,0:04:15.855
So 12 is actually the least[br]common multiple of two and 12,

0:04:15.855,0:04:17.213
so we could write both of these

0:04:17.213,0:04:19.013
fractions as something over 12.

0:04:19.013,0:04:21.625
So 1/2 is what over 12?

0:04:21.625,0:04:24.446
Well to go from two to[br]12, you multiply by six,

0:04:24.446,0:04:27.104
so we'll also multiply[br]the numerator by six.

0:04:27.104,0:04:30.588
Now we see 1/2, and 6/12,[br]these are the same thing.

0:04:30.588,0:04:33.954
One is half of two, six is half of 12.

0:04:34.914,0:04:38.485
And how would we write[br]11/12 as something over 12?

0:04:38.485,0:04:40.855
Well it's already written[br]as something over 12,

0:04:40.855,0:04:43.258
11/12 already has 12 in the denominator,

0:04:43.258,0:04:45.029
so we don't have to change that.

0:04:45.615,0:04:48.268
11/12, and now we're ready to add.

0:04:48.600,0:04:51.350
So this is going to be equal to six,

0:04:52.520,0:04:55.820
this is going to be equal to six plus 11,

0:04:56.510,0:05:01.510
six plus 11 over 12.

0:05:02.378,0:05:06.021
Over 12. We have 6/12 plus 11/12,

0:05:06.021,0:05:09.318
it's gonna be six plus 11 over 12,

0:05:10.728,0:05:15.087
which is equal to, six plus 11 is 17/12.

0:05:15.087,0:05:16.504
If we wanted to write[br]it as a mixed number,

0:05:16.504,0:05:19.487
that is what, 12 goes[br]into 17 one time with

0:05:19.487,0:05:24.487
a remainder of five, so 1 5/12.

0:05:24.530,0:05:25.710
Let's do one more of these.

0:05:25.710,0:05:29.007
This is strangely fun. Alright.

0:05:29.007,0:05:31.043
Let's say that we wanted to add,

0:05:31.523,0:05:35.894
We're gonna add 3/4 to,

0:05:36.504,0:05:40.584
we're gonna add 3/4 to 1/5.

0:05:41.414,0:05:43.974
To one over five.

0:05:43.974,0:05:44.659
What is this going to be?

0:05:44.659,0:05:46.157
And once again, pause the video and

0:05:46.157,0:05:47.870
see if you could work it out.

0:05:47.870,0:05:49.291
Well we have different denominators here,

0:05:49.291,0:05:52.052
and we wanna find, we wanna rewrite these

0:05:52.052,0:05:53.457
so they have the same denominators,

0:05:53.457,0:05:54.792
so we have to find a common multiple,

0:05:54.792,0:05:57.095
ideally the least common multiple.

0:05:57.095,0:05:59.738
So what's the least common[br]multiple of four and five?

0:06:00.548,0:06:01.862
Well let's start with the larger number,

0:06:01.862,0:06:04.718
and let's look at its[br]multiples and keep increasing

0:06:04.718,0:06:07.061
them until we get one[br]that's divisible by four.

0:06:07.061,0:06:10.064
So five is not divisible by four.

0:06:10.064,0:06:13.622
10 is not divisible by four,[br]or perfectly divisible by four

0:06:13.622,0:06:14.702
is what we care about.

0:06:14.702,0:06:17.059
15 is not perfectly divisible by four.

0:06:17.059,0:06:20.763
20 is divisible by four, in[br]fact, that is five times four.

0:06:20.763,0:06:23.514
That is 20. So what we[br]could do is, we could write

0:06:23.514,0:06:27.460
both of these fractions as[br]having 20 in the denominator,

0:06:27.460,0:06:28.714
or 20 as the denominator.

0:06:29.454,0:06:32.266
So we could write 3/4[br]is something over 20.

0:06:32.996,0:06:35.319
So to go from four to[br]20 in the denominator,

0:06:35.319,0:06:36.949
we multiplied by five.

0:06:36.949,0:06:38.466
So we also do that to the numerator.

0:06:38.466,0:06:41.398
We multiply by three times five to get 15.

0:06:41.398,0:06:44.183
All I did to go from four[br]to 20, multiplied by five.

0:06:44.183,0:06:45.820
So I have to do the same[br]thing to the numerator,

0:06:45.820,0:06:47.736
three times five is 15.

0:06:47.736,0:06:52.658
3/4 is the same thing[br]as 15/20, and over here.

0:06:52.658,0:06:55.004
1/5. What is that over 20?

0:06:55.004,0:06:58.358
Well to go from five to 20,[br]you have to multiply by four.

0:06:58.358,0:06:59.995
So we have to do the same[br]thing to the numerator.

0:06:59.995,0:07:03.861
I have to multiply this[br]numerator times four to get 4/20.

0:07:04.451,0:07:07.181
So now I've rewritten this[br]instead of 3/4 plus 1/5,

0:07:07.181,0:07:10.815
it's now written as 15/20 plus 4/20.

0:07:10.815,0:07:12.973
And what is that going to be?

0:07:12.973,0:07:17.932
Well that's going to be[br]15 plus four is 19/20.

0:07:17.932,0:07:22.024
19/20, and we're done.