[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:02.24,0:00:06.23,Default,,0000,0000,0000,,This tutorial is about the basic\Nconcepts of fractions.
Dialogue: 0,0:00:06.76,0:00:11.20,Default,,0000,0000,0000,,What they are, what they look\Nlike, and why we have them.
Dialogue: 0,0:00:12.34,0:00:17.05,Default,,0000,0000,0000,,A function is a way of writing\Npart of a whole.
Dialogue: 0,0:00:17.77,0:00:22.81,Default,,0000,0000,0000,,And it's formed when we divide a\Nwhole into an equal number of
Dialogue: 0,0:00:22.81,0:00:27.37,Default,,0000,0000,0000,,pieces. Now let's have a look.\NI've got a representation here.
Dialogue: 0,0:00:28.12,0:00:29.08,Default,,0000,0000,0000,,Of a whole.
Dialogue: 0,0:00:30.20,0:00:36.75,Default,,0000,0000,0000,,And let's say we want to divide\Nit into 4 equal pieces.
Dialogue: 0,0:00:38.52,0:00:44.76,Default,,0000,0000,0000,,So there we've\Ntaken 1 hole
Dialogue: 0,0:00:44.76,0:00:51.00,Default,,0000,0000,0000,,and divided it\Ninto 4 equal
Dialogue: 0,0:00:51.00,0:00:57.24,Default,,0000,0000,0000,,pieces. So each\Npiece represents 1/4.
Dialogue: 0,0:00:58.51,0:00:59.81,Default,,0000,0000,0000,,Wow.
Dialogue: 0,0:01:00.87,0:01:04.18,Default,,0000,0000,0000,,I've now taken 1/4 away.
Dialogue: 0,0:01:05.80,0:01:09.44,Default,,0000,0000,0000,,Now I've removed
Dialogue: 0,0:01:09.44,0:01:15.06,Default,,0000,0000,0000,,two quarters. If\NI take a third.
Dialogue: 0,0:01:15.99,0:01:22.99,Default,,0000,0000,0000,,That's 3/4.\NAnd if I take the false so I've
Dialogue: 0,0:01:22.99,0:01:24.82,Default,,0000,0000,0000,,now got all four pieces.
Dialogue: 0,0:01:25.44,0:01:30.40,Default,,0000,0000,0000,,I've taken all of them for\Nquarters, which is exactly the
Dialogue: 0,0:01:30.40,0:01:32.66,Default,,0000,0000,0000,,same as taking the whole.
Dialogue: 0,0:01:33.24,0:01:38.08,Default,,0000,0000,0000,,Let's just return for a moment\Nto the two quarters.
Dialogue: 0,0:01:38.60,0:01:42.84,Default,,0000,0000,0000,,Now\Ntwo
Dialogue: 0,0:01:42.84,0:01:46.49,Default,,0000,0000,0000,,quarters. Is exactly
Dialogue: 0,0:01:46.49,0:01:52.70,Default,,0000,0000,0000,,the same. As if I'd started\Nwith my whole and actually
Dialogue: 0,0:01:52.70,0:01:54.21,Default,,0000,0000,0000,,divided it into.
Dialogue: 0,0:01:55.01,0:01:57.61,Default,,0000,0000,0000,,2 pieces of equal size.
Dialogue: 0,0:01:58.45,0:02:00.20,Default,,0000,0000,0000,,And you can see that that's
Dialogue: 0,0:02:00.20,0:02:06.04,Default,,0000,0000,0000,,exactly the same. As two\Nquarters so I can write two
Dialogue: 0,0:02:06.04,0:02:10.48,Default,,0000,0000,0000,,quarters. As one\Nhalf.
Dialogue: 0,0:02:12.27,0:02:15.100,Default,,0000,0000,0000,,Let's have a look at\Nanother illustration now.
Dialogue: 0,0:02:17.19,0:02:19.40,Default,,0000,0000,0000,,Here I have a bar of chocolate.
Dialogue: 0,0:02:20.74,0:02:22.37,Default,,0000,0000,0000,,It's been divided.
Dialogue: 0,0:02:22.93,0:02:29.14,Default,,0000,0000,0000,,Into six pieces of equal size.\NSo we've taken a whole bar and
Dialogue: 0,0:02:29.14,0:02:31.53,Default,,0000,0000,0000,,divide it into six pieces.
Dialogue: 0,0:02:32.27,0:02:36.54,Default,,0000,0000,0000,,So each piece is\N16.
Dialogue: 0,0:02:38.33,0:02:42.51,Default,,0000,0000,0000,,Now, let's say I'm going to\Nshare my bar of chocolate with
Dialogue: 0,0:02:42.51,0:02:43.55,Default,,0000,0000,0000,,the camera man.
Dialogue: 0,0:02:44.65,0:02:50.77,Default,,0000,0000,0000,,So I want to divide the bar\Nof chocolate into two pieces.
Dialogue: 0,0:02:51.37,0:02:53.17,Default,,0000,0000,0000,,So if I do that.
Dialogue: 0,0:02:55.16,0:02:59.06,Default,,0000,0000,0000,,Where each going to have one
Dialogue: 0,0:02:59.06,0:03:05.94,Default,,0000,0000,0000,,236. So 1/2 is\Nexactly the same as 36.
Dialogue: 0,0:03:06.81,0:03:11.14,Default,,0000,0000,0000,,But there's not just one\Ncameraman. We've got two
Dialogue: 0,0:03:11.14,0:03:16.43,Default,,0000,0000,0000,,cameramen, so I need to share\Nit. Actually, between three of
Dialogue: 0,0:03:16.43,0:03:23.48,Default,,0000,0000,0000,,us. So now if I put my bar back\Ntogether and I need to share it
Dialogue: 0,0:03:23.48,0:03:27.06,Default,,0000,0000,0000,,between 3:00. Where\Neach going to get.
Dialogue: 0,0:03:28.43,0:03:30.81,Default,,0000,0000,0000,,Two pieces.
Dialogue: 0,0:03:32.55,0:03:38.11,Default,,0000,0000,0000,,So 1/3 is exactly the\Nsame as 26.
Dialogue: 0,0:03:38.91,0:03:45.54,Default,,0000,0000,0000,,But Let's say I\Nwant to eat all my chocolate bar
Dialogue: 0,0:03:45.54,0:03:51.17,Default,,0000,0000,0000,,myself, so I'm going to have all\Nsix pieces, so they're all mine.
Dialogue: 0,0:03:51.70,0:03:55.69,Default,,0000,0000,0000,,Not going to share them, so I\Ntake all six pieces.
Dialogue: 0,0:03:56.31,0:03:58.60,Default,,0000,0000,0000,,And I've taken away the whole
Dialogue: 0,0:03:58.60,0:03:58.98,Default,,0000,0000,0000,,bar.
Dialogue: 0,0:03:59.54,0:04:06.47,Default,,0000,0000,0000,,So.\NFractions we can look at.
Dialogue: 0,0:04:07.01,0:04:08.35,Default,,0000,0000,0000,,In two ways.
Dialogue: 0,0:04:09.32,0:04:13.20,Default,,0000,0000,0000,,We can look at it as the number
Dialogue: 0,0:04:13.20,0:04:15.85,Default,,0000,0000,0000,,of pieces. That we've used.
Dialogue: 0,0:04:17.13,0:04:23.61,Default,,0000,0000,0000,,Divided by the\Nnumber of pieces.
Dialogue: 0,0:04:24.28,0:04:27.26,Default,,0000,0000,0000,,That make a whole.
Dialogue: 0,0:04:27.26,0:04:32.95,Default,,0000,0000,0000,,Oh
Dialogue: 0,0:04:33.99,0:04:36.89,Default,,0000,0000,0000,,As the whole.
Dialogue: 0,0:04:37.71,0:04:44.17,Default,,0000,0000,0000,,Divided by. Number of pieces\Nor number of people that we've
Dialogue: 0,0:04:44.17,0:04:45.48,Default,,0000,0000,0000,,divided it into.
Dialogue: 0,0:04:46.29,0:04:52.49,Default,,0000,0000,0000,,So here we have a whole bar\Ndivided into 6 pieces.
Dialogue: 0,0:04:53.88,0:04:57.51,Default,,0000,0000,0000,,Here we have the number of\Npieces that we've taken divided
Dialogue: 0,0:04:57.51,0:05:01.47,Default,,0000,0000,0000,,note 5 the number of pieces that\Nmake up the whole bar.
Dialogue: 0,0:05:03.54,0:05:10.83,Default,,0000,0000,0000,,Let's have a look\Nat some other fractions.
Dialogue: 0,0:05:10.83,0:05:16.93,Default,,0000,0000,0000,,Let's say\Nwe have
Dialogue: 0,0:05:16.93,0:05:18.45,Default,,0000,0000,0000,,3/8.
Dialogue: 0,0:05:20.00,0:05:25.35,Default,,0000,0000,0000,,So we've divided a whole up into\N8 pieces of equal size.
Dialogue: 0,0:05:25.89,0:05:27.64,Default,,0000,0000,0000,,And we've taken three of them.
Dialogue: 0,0:05:28.27,0:05:29.59,Default,,0000,0000,0000,,3/8
Dialogue: 0,0:05:31.15,0:05:34.96,Default,,0000,0000,0000,,We could have 11 twelfths.
Dialogue: 0,0:05:35.80,0:05:41.77,Default,,0000,0000,0000,,So we've divided a whole up into\N12 pieces and taking eleven of
Dialogue: 0,0:05:41.77,0:05:46.06,Default,,0000,0000,0000,,them. We could have\N7/10.
Dialogue: 0,0:05:47.16,0:05:52.42,Default,,0000,0000,0000,,Here we will have divided a hole\Ninto 10 pieces of equal size and
Dialogue: 0,0:05:52.42,0:05:53.93,Default,,0000,0000,0000,,taken Seven of them.
Dialogue: 0,0:05:54.71,0:05:56.24,Default,,0000,0000,0000,,And we can have.
Dialogue: 0,0:05:56.80,0:06:04.70,Default,,0000,0000,0000,,Any numbers in our fraction so\Nwe could have 105 hundreds or
Dialogue: 0,0:06:04.70,0:06:07.99,Default,,0000,0000,0000,,three 167th and so on.
Dialogue: 0,0:06:08.90,0:06:12.16,Default,,0000,0000,0000,,Now we've looked at representing
Dialogue: 0,0:06:12.16,0:06:16.90,Default,,0000,0000,0000,,fractions. Using piece of Cod\Ncircular representation are
Dialogue: 0,0:06:16.90,0:06:19.45,Default,,0000,0000,0000,,rectangle with our bar of
Dialogue: 0,0:06:19.45,0:06:24.01,Default,,0000,0000,0000,,chocolate. Let's have a look at\None more before we move on and
Dialogue: 0,0:06:24.01,0:06:25.48,Default,,0000,0000,0000,,let's let's see it on.
Dialogue: 0,0:06:26.11,0:06:28.00,Default,,0000,0000,0000,,A section of number line.
Dialogue: 0,0:06:29.56,0:06:31.88,Default,,0000,0000,0000,,So let's say we have zero here.
Dialogue: 0,0:06:32.54,0:06:34.44,Default,,0000,0000,0000,,And one here.
Dialogue: 0,0:06:34.95,0:06:37.30,Default,,0000,0000,0000,,So let's look at what 3/8 might
Dialogue: 0,0:06:37.30,0:06:44.15,Default,,0000,0000,0000,,look like. While I need to\Ndivide my section into 8 pieces
Dialogue: 0,0:06:44.15,0:06:45.82,Default,,0000,0000,0000,,of equal size.
Dialogue: 0,0:06:46.69,0:06:49.99,Default,,0000,0000,0000,,Now obviously this is an\Nillustration, so I'm not
Dialogue: 0,0:06:49.99,0:06:53.66,Default,,0000,0000,0000,,actually getting my router\Nout to make sure I've got
Dialogue: 0,0:06:53.66,0:06:54.76,Default,,0000,0000,0000,,equal size pieces.
Dialogue: 0,0:06:55.83,0:07:01.89,Default,,0000,0000,0000,,But hopefully. That's about\Nright. So we've got 12345678
Dialogue: 0,0:07:01.89,0:07:09.24,Default,,0000,0000,0000,,pieces of equal size and I'm\Ngoing to take three of them.
Dialogue: 0,0:07:09.24,0:07:12.91,Default,,0000,0000,0000,,So if I take 1, two
Dialogue: 0,0:07:12.91,0:07:17.60,Default,,0000,0000,0000,,3/8. That's where my 3\Neights will be.
Dialogue: 0,0:07:20.63,0:07:22.64,Default,,0000,0000,0000,,Let's have a look at\Nanother one.
Dialogue: 0,0:07:24.59,0:07:28.34,Default,,0000,0000,0000,,This time will look at
Dialogue: 0,0:07:28.34,0:07:33.21,Default,,0000,0000,0000,,11 twelfths. So we need to\Ndivide our line up into.
Dialogue: 0,0:07:34.30,0:07:40.03,Default,,0000,0000,0000,,Pieces so we have 12 pieces\Nof equal size.
Dialogue: 0,0:07:48.39,0:07:55.35,Default,,0000,0000,0000,,OK, so we wanted\Neleven of them, so
Dialogue: 0,0:07:55.35,0:08:02.31,Default,,0000,0000,0000,,we need to count\N11 one 23456789 ten
Dialogue: 0,0:08:02.31,0:08:05.79,Default,,0000,0000,0000,,11. So at 11
Dialogue: 0,0:08:05.79,0:08:08.80,Default,,0000,0000,0000,,twelfths. Is represented there.
Dialogue: 0,0:08:10.24,0:08:16.79,Default,,0000,0000,0000,,Let's look more\Nclosely at our
Dialogue: 0,0:08:16.79,0:08:18.97,Default,,0000,0000,0000,,fraction half.
Dialogue: 0,0:08:20.04,0:08:26.09,Default,,0000,0000,0000,,Now we've already seen that half\Nis exactly the same as two
Dialogue: 0,0:08:26.09,0:08:31.17,Default,,0000,0000,0000,,quarters. And it's exactly the\Nsame as 36.
Dialogue: 0,0:08:32.10,0:08:38.83,Default,,0000,0000,0000,,Well, it's also the same\Nas 4 eighths 5/10.
Dialogue: 0,0:08:40.64,0:08:44.21,Default,,0000,0000,0000,,2040 deaths
Dialogue: 0,0:08:45.60,0:08:50.77,Default,,0000,0000,0000,,9900 and 98th and so on. We\Ncould go on.
Dialogue: 0,0:08:51.50,0:08:58.12,Default,,0000,0000,0000,,And what we have\Nhere is actually equivalent
Dialogue: 0,0:08:58.12,0:09:05.38,Default,,0000,0000,0000,,fractions. Each one of these\Nfractions are equivalent at the
Dialogue: 0,0:09:05.38,0:09:08.15,Default,,0000,0000,0000,,same as each other.
Dialogue: 0,0:09:10.46,0:09:14.09,Default,,0000,0000,0000,,Now, this form of the fraction
Dialogue: 0,0:09:14.09,0:09:20.98,Default,,0000,0000,0000,,half. Is our fraction in its\Nlowest form, and often we need
Dialogue: 0,0:09:20.98,0:09:23.61,Default,,0000,0000,0000,,to write fractions in their
Dialogue: 0,0:09:23.61,0:09:29.12,Default,,0000,0000,0000,,lowest form. It's much easier to\Nvisualize them actually in this
Dialogue: 0,0:09:29.12,0:09:32.12,Default,,0000,0000,0000,,lowest form than it is in any
Dialogue: 0,0:09:32.12,0:09:36.36,Default,,0000,0000,0000,,other form. So we often want to\Nfind the lowest form.
Dialogue: 0,0:09:37.71,0:09:43.68,Default,,0000,0000,0000,,Well, let's have a look 1st at\Nfinding some other equivalent
Dialogue: 0,0:09:43.68,0:09:46.94,Default,,0000,0000,0000,,fractions. So let's say I take
Dialogue: 0,0:09:46.94,0:09:52.48,Default,,0000,0000,0000,,3/4. How do I find an\Nequivalent fraction? Well, what
Dialogue: 0,0:09:52.48,0:09:58.18,Default,,0000,0000,0000,,I can do is multiply the top\Nnumber and the bottom number.
Dialogue: 0,0:09:59.27,0:10:00.88,Default,,0000,0000,0000,,By the same number.
Dialogue: 0,0:10:01.38,0:10:05.26,Default,,0000,0000,0000,,So let's say I multiply by two.
Dialogue: 0,0:10:05.87,0:10:10.72,Default,,0000,0000,0000,,If I multiply the top number by\Ntwo, I must also multiply the
Dialogue: 0,0:10:10.72,0:10:14.82,Default,,0000,0000,0000,,bottom number by two so that I'm\Nnot changing the fraction.
Dialogue: 0,0:10:15.75,0:10:19.69,Default,,0000,0000,0000,,3 * 2 six 4 * 2
Dialogue: 0,0:10:19.69,0:10:26.45,Default,,0000,0000,0000,,is 8. So 6 eighths\Nis a fraction equivalent to 3/4.
Dialogue: 0,0:10:28.37,0:10:29.58,Default,,0000,0000,0000,,Let's try another one.
Dialogue: 0,0:10:30.35,0:10:33.71,Default,,0000,0000,0000,,This time, let's take our 3/4.
Dialogue: 0,0:10:34.44,0:10:39.43,Default,,0000,0000,0000,,And multiply it by three. The\Ntop numbers multiplied by three,
Dialogue: 0,0:10:39.43,0:10:45.34,Default,,0000,0000,0000,,so most the bottom number B3\Nthrees and 9 three force or 12,
Dialogue: 0,0:10:45.34,0:10:50.33,Default,,0000,0000,0000,,so nine twelfths is equivalent\Nto 6 eighths, and they're both
Dialogue: 0,0:10:50.33,0:10:51.69,Default,,0000,0000,0000,,equivalent to 3/4.
Dialogue: 0,0:10:53.07,0:10:57.44,Default,,0000,0000,0000,,Let's do one more this time.\NLet's multiply both the top
Dialogue: 0,0:10:57.44,0:11:02.60,Default,,0000,0000,0000,,number on the bottom number by\N10. So we have 3 * 10.
Dialogue: 0,0:11:03.35,0:11:04.72,Default,,0000,0000,0000,,Giving us 30.
Dialogue: 0,0:11:05.23,0:11:11.26,Default,,0000,0000,0000,,And 4 * 10 giving us\N40. So another fraction
Dialogue: 0,0:11:11.26,0:11:14.88,Default,,0000,0000,0000,,equivalent to 3/4 is 3040\Ndeaths.
Dialogue: 0,0:11:16.09,0:11:20.74,Default,,0000,0000,0000,,So it's very easy to find\Nequivalent fractions as long as
Dialogue: 0,0:11:20.74,0:11:25.82,Default,,0000,0000,0000,,you multiply the top number on\Nthe bottom number by the same
Dialogue: 0,0:11:25.82,0:11:29.20,Default,,0000,0000,0000,,number. Now we have some\Nmathematical language here.
Dialogue: 0,0:11:29.20,0:11:34.28,Default,,0000,0000,0000,,Instead of using the word top\Nnumber and write it down top
Dialogue: 0,0:11:34.28,0:11:38.67,Default,,0000,0000,0000,,number. And bottom\Nnumber.
Dialogue: 0,0:11:40.73,0:11:45.72,Default,,0000,0000,0000,,We have two words that\Nwe use. The top number
Dialogue: 0,0:11:45.72,0:11:47.72,Default,,0000,0000,0000,,is called the numerator.
Dialogue: 0,0:11:49.35,0:11:52.60,Default,,0000,0000,0000,,On the bottom number the
Dialogue: 0,0:11:52.60,0:11:58.52,Default,,0000,0000,0000,,denominator. Now let's have a\Nlook at seeing how we go the
Dialogue: 0,0:11:58.52,0:12:03.18,Default,,0000,0000,0000,,other way. When we have an\Nequivalent fraction, how do we
Dialogue: 0,0:12:03.18,0:12:05.71,Default,,0000,0000,0000,,find this fraction in its lowest
Dialogue: 0,0:12:05.71,0:12:08.30,Default,,0000,0000,0000,,form? Well, let's look at an
Dialogue: 0,0:12:08.30,0:12:13.42,Default,,0000,0000,0000,,example. Let's say we've\Ngot 8, one, hundreds.
Dialogue: 0,0:12:14.89,0:12:20.45,Default,,0000,0000,0000,,Now we need to find the number\Nthat the lowest form was
Dialogue: 0,0:12:20.45,0:12:24.82,Default,,0000,0000,0000,,multiplied by. And that we ended\Nup with eight one hundredths.
Dialogue: 0,0:12:25.61,0:12:29.84,Default,,0000,0000,0000,,Well, the opposite of\Nmultiplying is dividing, so we
Dialogue: 0,0:12:29.84,0:12:34.54,Default,,0000,0000,0000,,need to divide both the\Nnumerator and the denominator by
Dialogue: 0,0:12:34.54,0:12:35.95,Default,,0000,0000,0000,,the same number.
Dialogue: 0,0:12:36.46,0:12:40.13,Default,,0000,0000,0000,,So that we get back to a\Nfraction in its lowest form.
Dialogue: 0,0:12:40.78,0:12:46.28,Default,,0000,0000,0000,,Well, if we look at the numbers\Nwe have here 8 and 100, the
Dialogue: 0,0:12:46.28,0:12:50.60,Default,,0000,0000,0000,,first thing you should notice is\Nactually the both even numbers.
Dialogue: 0,0:12:51.13,0:12:54.71,Default,,0000,0000,0000,,And if they're both even\Nnumbers, then obviously we can
Dialogue: 0,0:12:54.71,0:12:56.50,Default,,0000,0000,0000,,divide them both by two.
Dialogue: 0,0:12:57.38,0:13:03.19,Default,,0000,0000,0000,,So let's start by dividing the\Nnumerator by two and the
Dialogue: 0,0:13:03.19,0:13:04.77,Default,,0000,0000,0000,,denominator by two.
Dialogue: 0,0:13:05.51,0:13:11.85,Default,,0000,0000,0000,,8 / 2 is four 100\N/ 2 is 50.
Dialogue: 0,0:13:12.97,0:13:17.00,Default,,0000,0000,0000,,Now we need to look at our\Nfraction. Again. We found an
Dialogue: 0,0:13:17.00,0:13:20.03,Default,,0000,0000,0000,,equivalent fraction, but is it\Nin its lowest form?
Dialogue: 0,0:13:20.83,0:13:25.24,Default,,0000,0000,0000,,Well again, we can see that\Nthey're both even numbers, both
Dialogue: 0,0:13:25.24,0:13:30.05,Default,,0000,0000,0000,,4 and 50 even, and so we can\Ndivide by two again.
Dialogue: 0,0:13:30.56,0:13:38.10,Default,,0000,0000,0000,,4 / 4 gives us\N2 and 50 / 2.
Dialogue: 0,0:13:38.75,0:13:44.10,Default,,0000,0000,0000,,Gives us 25, so another\Nequivalent fraction, but is it
Dialogue: 0,0:13:44.10,0:13:46.24,Default,,0000,0000,0000,,in its lowest form?
Dialogue: 0,0:13:46.96,0:13:53.33,Default,,0000,0000,0000,,Well, we need to see if there is\Nany number that goes both into
Dialogue: 0,0:13:53.33,0:13:56.97,Default,,0000,0000,0000,,the numerator and the\Ndenominator. Well, the only
Dialogue: 0,0:13:56.97,0:14:02.43,Default,,0000,0000,0000,,numbers that go into 2A one\Nwhich goes into all numbers, so
Dialogue: 0,0:14:02.43,0:14:09.26,Default,,0000,0000,0000,,that's not going to help us. And\Ntwo now 2 doesn't go into 25. So
Dialogue: 0,0:14:09.26,0:14:14.72,Default,,0000,0000,0000,,therefore we found the fraction\Nin its lowest form, so 8 one
Dialogue: 0,0:14:14.72,0:14:17.44,Default,,0000,0000,0000,,hundreds. The lowest form is 220
Dialogue: 0,0:14:17.44,0:14:23.48,Default,,0000,0000,0000,,fifths. So when a fraction is in\Nits lowest form, the only number
Dialogue: 0,0:14:23.48,0:14:27.74,Default,,0000,0000,0000,,that will go into both the\Nnumerator and the denominator is
Dialogue: 0,0:14:27.74,0:14:31.36,Default,,0000,0000,0000,,one. Those numbers have no other
Dialogue: 0,0:14:31.36,0:14:37.38,Default,,0000,0000,0000,,common factor. Now if we look\Nhere, we can see that in fact.
Dialogue: 0,0:14:37.95,0:14:41.91,Default,,0000,0000,0000,,We could have divided by 4.
Dialogue: 0,0:14:41.91,0:14:45.47,Default,,0000,0000,0000,,Straight away, instead of\Ndividing by two twice, well,
Dialogue: 0,0:14:45.47,0:14:49.43,Default,,0000,0000,0000,,that's fine. If you've notice\Ntthat for was a factor.
Dialogue: 0,0:14:49.99,0:14:54.58,Default,,0000,0000,0000,,Of both the numerator and the\Ndenominator, you could have gone
Dialogue: 0,0:14:54.58,0:15:01.25,Default,,0000,0000,0000,,straight there doing 8 / 4 was\Ntwo and 100 / 4 was 25 and then
Dialogue: 0,0:15:01.25,0:15:06.67,Default,,0000,0000,0000,,check to see if you were in the\Nlowest form. That's fine, but
Dialogue: 0,0:15:06.67,0:15:11.05,Default,,0000,0000,0000,,often. With numbers, larger\Nnumbers is not always easy to
Dialogue: 0,0:15:11.05,0:15:15.10,Default,,0000,0000,0000,,see what the highest common\Nfactor is of these two numbers,
Dialogue: 0,0:15:15.10,0:15:18.04,Default,,0000,0000,0000,,the numerator and the\Ndenominator. So often it's
Dialogue: 0,0:15:18.04,0:15:22.09,Default,,0000,0000,0000,,easier to work down to some\Nsmaller numbers, and then you
Dialogue: 0,0:15:22.09,0:15:25.77,Default,,0000,0000,0000,,can be certain that there are no\Nother common factors.
Dialogue: 0,0:15:28.02,0:15:28.54,Default,,0000,0000,0000,,Now.
Dialogue: 0,0:15:29.88,0:15:33.52,Default,,0000,0000,0000,,If we take all the\Npieces of a fraction
Dialogue: 0,0:15:33.52,0:15:37.15,Default,,0000,0000,0000,,like I did with my\Nchocolate, I took all
Dialogue: 0,0:15:37.15,0:15:38.36,Default,,0000,0000,0000,,six of them.
Dialogue: 0,0:15:39.76,0:15:43.60,Default,,0000,0000,0000,,That's the same as 6 / 6.
Dialogue: 0,0:15:44.11,0:15:45.59,Default,,0000,0000,0000,,And that was our whole.
Dialogue: 0,0:15:47.43,0:15:53.41,Default,,0000,0000,0000,,And any whole number can be\Nwritten this way, so we could
Dialogue: 0,0:15:53.41,0:15:59.56,Default,,0000,0000,0000,,have. 3 thirds if we take all\Nthe pieces, we've got one.
Dialogue: 0,0:15:59.87,0:16:05.86,Default,,0000,0000,0000,,8 eighths, if we take all the\Npieces, we've got one.
Dialogue: 0,0:16:05.87,0:16:09.34,Default,,0000,0000,0000,,Now I'm going to rewrite.
Dialogue: 0,0:16:09.90,0:16:13.24,Default,,0000,0000,0000,,Mathematical words numerator.
Dialogue: 0,0:16:13.79,0:16:17.44,Default,,0000,0000,0000,,Divided fight denominator.
Dialogue: 0,0:16:18.53,0:16:22.27,Default,,0000,0000,0000,,Because we're now going to
Dialogue: 0,0:16:22.27,0:16:28.19,Default,,0000,0000,0000,,look. Add fractions\Nwhere the numerator.
Dialogue: 0,0:16:30.49,0:16:33.94,Default,,0000,0000,0000,,Smaller than the denominator.
Dialogue: 0,0:16:36.59,0:16:41.38,Default,,0000,0000,0000,,And we have a name for these\Ntype of fractions and they
Dialogue: 0,0:16:41.38,0:16:42.58,Default,,0000,0000,0000,,called proper fractions.
Dialogue: 0,0:16:47.53,0:16:50.86,Default,,0000,0000,0000,,And examples.
Dialogue: 0,0:16:50.86,0:16:52.33,Default,,0000,0000,0000,,Half.
Dialogue: 0,0:16:53.32,0:16:58.14,Default,,0000,0000,0000,,3/4\N16
Dialogue: 0,0:16:59.38,0:17:06.66,Default,,0000,0000,0000,,7/8 5/10 and\Nseeing all these cases, the
Dialogue: 0,0:17:06.66,0:17:10.06,Default,,0000,0000,0000,,numerator is smaller number than
Dialogue: 0,0:17:10.06,0:17:16.41,Default,,0000,0000,0000,,the denominator. And as long as\Nthat is the case, then we have a
Dialogue: 0,0:17:16.41,0:17:20.73,Default,,0000,0000,0000,,proper fraction so we can have\Nany numbers 100 hundred and 50th
Dialogue: 0,0:17:20.73,0:17:24.55,Default,,0000,0000,0000,,for example. Now if
Dialogue: 0,0:17:24.55,0:17:30.70,Default,,0000,0000,0000,,the numerator.\NIs greater than
Dialogue: 0,0:17:30.70,0:17:32.82,Default,,0000,0000,0000,,the denominator?
Dialogue: 0,0:17:36.98,0:17:41.56,Default,,0000,0000,0000,,Then the fraction is called\Nan improper fraction.
Dialogue: 0,0:17:47.16,0:17:50.29,Default,,0000,0000,0000,,And some examples.
Dialogue: 0,0:17:50.35,0:17:53.10,Default,,0000,0000,0000,,Three over two or three halfs.
Dialogue: 0,0:17:53.93,0:17:59.49,Default,,0000,0000,0000,,7 fifths.\NEight quarters
Dialogue: 0,0:18:00.96,0:18:03.65,Default,,0000,0000,0000,,We could have 12 bytes.
Dialogue: 0,0:18:05.12,0:18:08.71,Default,,0000,0000,0000,,Or we could have 201 hundredths.
Dialogue: 0,0:18:09.78,0:18:14.87,Default,,0000,0000,0000,,And in all these cases, the\Nnumerator is larger than the
Dialogue: 0,0:18:14.87,0:18:19.59,Default,,0000,0000,0000,,denominator. And it shows that\Nwhat we've got is actually more
Dialogue: 0,0:18:19.59,0:18:20.62,Default,,0000,0000,0000,,than whole 1.
Dialogue: 0,0:18:21.54,0:18:26.09,Default,,0000,0000,0000,,All these fractions, the\Nproper ones are smaller than a
Dialogue: 0,0:18:26.09,0:18:31.10,Default,,0000,0000,0000,,whole one. We haven't taken\Nall of the pieces 3/4. We've
Dialogue: 0,0:18:31.10,0:18:37.46,Default,,0000,0000,0000,,only taken 3 out of the four\N161 out of the six, so that
Dialogue: 0,0:18:37.46,0:18:41.56,Default,,0000,0000,0000,,all smaller than a whole one\Nwith improper fractions.
Dialogue: 0,0:18:42.79,0:18:45.05,Default,,0000,0000,0000,,They are all larger than one
Dialogue: 0,0:18:45.05,0:18:50.87,Default,,0000,0000,0000,,whole 1. So if we take three\Nover 2 for example, what we've
Dialogue: 0,0:18:50.87,0:18:52.90,Default,,0000,0000,0000,,actually got is 3 halfs.
Dialogue: 0,0:18:54.79,0:18:58.99,Default,,0000,0000,0000,,Oh, improper fractions can be\Nwritten in this form.
Dialogue: 0,0:18:59.73,0:19:05.47,Default,,0000,0000,0000,,All they can be written\Nas mixed fractions.
Dialogue: 0,0:19:08.28,0:19:12.75,Default,,0000,0000,0000,,So let's have a look\Nat our three halfs.
Dialogue: 0,0:19:14.45,0:19:19.08,Default,,0000,0000,0000,,And what we can do is put two\Nhearts together to make the
Dialogue: 0,0:19:19.08,0:19:25.39,Default,,0000,0000,0000,,whole 1. And we've got 1/2 left\Nover, so that can be written as
Dialogue: 0,0:19:25.39,0:19:26.98,Default,,0000,0000,0000,,one and a half.
Dialogue: 0,0:19:28.04,0:19:32.32,Default,,0000,0000,0000,,So there are exactly the same,\Nbut written in a different form
Dialogue: 0,0:19:32.32,0:19:34.11,Default,,0000,0000,0000,,1 as a mixed fraction.
Dialogue: 0,0:19:34.62,0:19:39.71,Default,,0000,0000,0000,,And one other top heavy\Nfraction, an improper fraction
Dialogue: 0,0:19:39.71,0:19:44.24,Default,,0000,0000,0000,,where the numerator is larger\Nthan the denominator.
Dialogue: 0,0:19:46.39,0:19:48.20,Default,,0000,0000,0000,,Let's have a look at another
Dialogue: 0,0:19:48.20,0:19:53.91,Default,,0000,0000,0000,,example. Let's say we\Nhad 8 thirds.
Dialogue: 0,0:19:53.91,0:19:55.24,Default,,0000,0000,0000,,This out the way.
Dialogue: 0,0:19:56.78,0:20:00.32,Default,,0000,0000,0000,,Let's count
Dialogue: 0,0:20:00.32,0:20:05.79,Default,,0000,0000,0000,,out 1234567.\N8 thirds
Dialogue: 0,0:20:06.90,0:20:11.05,Default,,0000,0000,0000,,How else can we write that?\NHow do we write that as a
Dialogue: 0,0:20:11.05,0:20:11.68,Default,,0000,0000,0000,,mixed fraction?
Dialogue: 0,0:20:13.11,0:20:16.14,Default,,0000,0000,0000,,Well, what we're looking\Nfor is how many whole ones
Dialogue: 0,0:20:16.14,0:20:17.05,Default,,0000,0000,0000,,we've got there.
Dialogue: 0,0:20:18.31,0:20:22.40,Default,,0000,0000,0000,,Well, if something's been\Ndivided into 3 pieces.
Dialogue: 0,0:20:23.42,0:20:26.15,Default,,0000,0000,0000,,It takes 3 pieces to make the
Dialogue: 0,0:20:26.15,0:20:28.76,Default,,0000,0000,0000,,whole 1. So that's one whole 1.
Dialogue: 0,0:20:30.51,0:20:34.03,Default,,0000,0000,0000,,There we have another whole 12.
Dialogue: 0,0:20:34.89,0:20:42.11,Default,,0000,0000,0000,,And we've got 2/3 left over,\Nso 8 thirds is exactly the
Dialogue: 0,0:20:42.11,0:20:45.12,Default,,0000,0000,0000,,same as two and 2/3.
Dialogue: 0,0:20:48.77,0:20:50.71,Default,,0000,0000,0000,,Let's look at one more.
Dialogue: 0,0:20:51.71,0:20:55.48,Default,,0000,0000,0000,,Let's say we had Seven
Dialogue: 0,0:20:55.48,0:21:00.100,Default,,0000,0000,0000,,quarters. Now we know that there\Nare four quarters in each hole,
Dialogue: 0,0:21:00.100,0:21:06.45,Default,,0000,0000,0000,,one. So we see how many fours go\Ninto Seven. Well, that's one.
Dialogue: 0,0:21:06.96,0:21:13.08,Default,,0000,0000,0000,,And we've got 3 left over, so\Nwe've got one and 3/4.
Dialogue: 0,0:21:14.18,0:21:16.78,Default,,0000,0000,0000,,Let's have a look at one more.
Dialogue: 0,0:21:18.09,0:21:21.30,Default,,0000,0000,0000,,37 tenths
Dialogue: 0,0:21:22.92,0:21:27.89,Default,,0000,0000,0000,,Now we've split something up\Ninto 10 pieces of equal size.
Dialogue: 0,0:21:28.93,0:21:34.03,Default,,0000,0000,0000,,So we need 10 of those to make a\Nwhole one, so we need to see how
Dialogue: 0,0:21:34.03,0:21:37.03,Default,,0000,0000,0000,,many 10s, how many whole ones\Nthere are in 37.
Dialogue: 0,0:21:38.13,0:21:43.27,Default,,0000,0000,0000,,Well, three 10s makes 30, so\Nthat's three whole ones, and
Dialogue: 0,0:21:43.27,0:21:47.94,Default,,0000,0000,0000,,we've got 7 leftover, so we've\Ngot 3 and 7/10.
Dialogue: 0,0:21:49.02,0:21:52.43,Default,,0000,0000,0000,,Just move
Dialogue: 0,0:21:52.43,0:21:59.20,Default,,0000,0000,0000,,those. Now let's have\Na look at doing the reverse
Dialogue: 0,0:21:59.20,0:22:05.68,Default,,0000,0000,0000,,process. So if we start with a\Nmixed fraction, how do we turn
Dialogue: 0,0:22:05.68,0:22:08.17,Default,,0000,0000,0000,,it into an improper fraction?
Dialogue: 0,0:22:08.74,0:22:11.90,Default,,0000,0000,0000,,Let's look at three and a
Dialogue: 0,0:22:11.90,0:22:16.50,Default,,0000,0000,0000,,quarter. And if we look at this\Nvisually, we've got.
Dialogue: 0,0:22:17.17,0:22:18.66,Default,,0000,0000,0000,,3 hole once.
Dialogue: 0,0:22:20.54,0:22:23.87,Default,,0000,0000,0000,,And one quarter.
Dialogue: 0,0:22:27.50,0:22:29.43,Default,,0000,0000,0000,,And what we want to turn it
Dialogue: 0,0:22:29.43,0:22:33.60,Default,,0000,0000,0000,,into. Is all\Nquarters.
Dialogue: 0,0:22:34.64,0:22:36.47,Default,,0000,0000,0000,,So we have a whole 1.
Dialogue: 0,0:22:37.36,0:22:43.77,Default,,0000,0000,0000,,And if we split it into\Nquarters, we know that a whole 1
Dialogue: 0,0:22:43.77,0:22:45.25,Default,,0000,0000,0000,,needs four quarters.
Dialogue: 0,0:22:45.77,0:22:47.28,Default,,0000,0000,0000,,So we have four there.
Dialogue: 0,0:22:47.81,0:22:49.12,Default,,0000,0000,0000,,Another for their.
Dialogue: 0,0:22:49.68,0:22:52.68,Default,,0000,0000,0000,,Another folder plus this one.
Dialogue: 0,0:22:53.31,0:22:56.12,Default,,0000,0000,0000,,So we've got three force or 12.
Dialogue: 0,0:22:56.64,0:23:04.03,Default,,0000,0000,0000,,Plus the one gives us 13\Nquarters, so 3 1/4 is exactly
Dialogue: 0,0:23:04.03,0:23:07.11,Default,,0000,0000,0000,,the same as 13 quarters.
Dialogue: 0,0:23:07.66,0:23:12.42,Default,,0000,0000,0000,,Well, let's have a look at how\Nyou might do this.
Dialogue: 0,0:23:14.00,0:23:15.50,Default,,0000,0000,0000,,If you haven't got the visual
Dialogue: 0,0:23:15.50,0:23:21.50,Default,,0000,0000,0000,,aid. Well, what we've actually\Ngot here is our whole number.
Dialogue: 0,0:23:22.55,0:23:23.64,Default,,0000,0000,0000,,And the fraction.
Dialogue: 0,0:23:24.24,0:23:25.94,Default,,0000,0000,0000,,We wanted in quarters.
Dialogue: 0,0:23:27.07,0:23:30.69,Default,,0000,0000,0000,,So what we're doing\Nis right it again.
Dialogue: 0,0:23:31.92,0:23:36.55,Default,,0000,0000,0000,,We're actually saying We want\Nfour quarters for every hole
Dialogue: 0,0:23:36.55,0:23:39.79,Default,,0000,0000,0000,,one, so we've got three lots of
Dialogue: 0,0:23:39.79,0:23:44.91,Default,,0000,0000,0000,,four. And then what were\Nranting on is our one, and
Dialogue: 0,0:23:44.91,0:23:46.38,Default,,0000,0000,0000,,these are all quarters.
Dialogue: 0,0:23:47.60,0:23:51.42,Default,,0000,0000,0000,,So it's the whole number\Nmultiplied by the denominator.
Dialogue: 0,0:23:52.46,0:23:56.93,Default,,0000,0000,0000,,We've added the extra that\Nwe have here. Whatever this
Dialogue: 0,0:23:56.93,0:24:01.40,Default,,0000,0000,0000,,number is, and those are the\Nnumber of quarters we've
Dialogue: 0,0:24:01.40,0:24:07.21,Default,,0000,0000,0000,,got. So we've got our 3/4 of\N12 + 1/4, so 13 quarters.
Dialogue: 0,0:24:08.94,0:24:10.96,Default,,0000,0000,0000,,Let's have a look at one more
Dialogue: 0,0:24:10.96,0:24:16.48,Default,,0000,0000,0000,,example. Let's say we've got\Nfive and two ninths.
Dialogue: 0,0:24:18.31,0:24:21.09,Default,,0000,0000,0000,,We want to turn it\Ninto this format.
Dialogue: 0,0:24:22.36,0:24:28.63,Default,,0000,0000,0000,,Ninths well, if we want to take\Na whole one, we wouldn't need 9
Dialogue: 0,0:24:28.63,0:24:34.90,Default,,0000,0000,0000,,ninths and we've got five whole\Nones, so we're going to have 5 *
Dialogue: 0,0:24:34.90,0:24:37.59,Default,,0000,0000,0000,,9 lots of 9th this time.
Dialogue: 0,0:24:38.25,0:24:42.66,Default,,0000,0000,0000,,And then we need to add on the\Ntwo nights that we have here.
Dialogue: 0,0:24:42.67,0:24:50.53,Default,,0000,0000,0000,,So 5 nines of 45 plus\Nthe two and that all 9th.
Dialogue: 0,0:24:50.53,0:24:53.80,Default,,0000,0000,0000,,So we have 47 ninths.
Dialogue: 0,0:24:57.17,0:25:00.73,Default,,0000,0000,0000,,Any whole number can be written\Nas a fraction.
Dialogue: 0,0:25:01.27,0:25:04.08,Default,,0000,0000,0000,,So for example, if we take\Nthe number 2.
Dialogue: 0,0:25:05.93,0:25:10.10,Default,,0000,0000,0000,,If we write it with the\Ndenominator of one.
Dialogue: 0,0:25:11.58,0:25:13.86,Default,,0000,0000,0000,,We've written it as a fraction.
Dialogue: 0,0:25:15.05,0:25:20.14,Default,,0000,0000,0000,,And any equivalent form, so we\Ncould have 4 over 2.
Dialogue: 0,0:25:20.77,0:25:24.37,Default,,0000,0000,0000,,30 over
Dialogue: 0,0:25:24.37,0:25:31.19,Default,,0000,0000,0000,,15. And so on.\NSo any whole number can be
Dialogue: 0,0:25:31.19,0:25:35.96,Default,,0000,0000,0000,,written as a fraction with a\Nnumerator and a denominator.
Dialogue: 0,0:25:37.56,0:25:45.19,Default,,0000,0000,0000,,So fractions.\NThey can appear in a number
Dialogue: 0,0:25:45.19,0:25:50.46,Default,,0000,0000,0000,,of different forms. You might\Nsee proper fractions, improper
Dialogue: 0,0:25:50.46,0:25:52.22,Default,,0000,0000,0000,,fractions, mixed fractions.
Dialogue: 0,0:25:53.06,0:25:57.27,Default,,0000,0000,0000,,And you can see lots of\Ndifferent equivalent fractions.
Dialogue: 0,0:25:57.87,0:26:00.26,Default,,0000,0000,0000,,So that all different\Nways that we see them.