[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.62,0:00:06.31,Default,,0000,0000,0000,,In this tutorial, we're going\Nto look at the meaning of percentages
Dialogue: 0,0:00:06.31,0:00:09.71,Default,,0000,0000,0000,,and then we're going to do \Ncalculations involving percentages.
Dialogue: 0,0:00:09.71,0:00:13.55,Default,,0000,0000,0000,,And before we finish will look at
Dialogue: 0,0:00:13.55,0:00:17.38,Default,,0000,0000,0000,,how to use the percentage\Nbutton on your calculator.
Dialogue: 0,0:00:18.98,0:00:21.07,Default,,0000,0000,0000,,Now, percentages are very\Nfamiliar to us.
Dialogue: 0,0:00:21.07,0:00:24.80,Default,,0000,0000,0000,,We see them in the media an \Nawful lot,
Dialogue: 0,0:00:24.80,0:00:26.96,Default,,0000,0000,0000,,whether they're talking about the
Dialogue: 0,0:00:26.96,0:00:30.76,Default,,0000,0000,0000,,percentage of A to Cs\Ngained by youngsters in exams,
Dialogue: 0,0:00:30.76,0:00:34.56,Default,,0000,0000,0000,,or whether they're talking about the \Nsuccess of the latest
Dialogue: 0,0:00:34.56,0:00:36.74,Default,,0000,0000,0000,,medical procedures.
Dialogue: 0,0:00:36.74,0:00:41.74,Default,,0000,0000,0000,,In addition, any of those of you who work\Nyou'll pay income tax
Dialogue: 0,0:00:41.74,0:00:46.53,Default,,0000,0000,0000,,and income tax is based on a percentage\Nof your salary.
Dialogue: 0,0:00:46.53,0:00:49.03,Default,,0000,0000,0000,,The National Insurance\Ncontribution is
Dialogue: 0,0:00:49.03,0:00:51.78,Default,,0000,0000,0000,,a percentage of your salary.
Dialogue: 0,0:00:51.78,0:00:55.59,Default,,0000,0000,0000,,In addition to that, when we go\Nshopping, most of the goods that
Dialogue: 0,0:00:55.59,0:01:02.31,Default,,0000,0000,0000,,we buy have got VAT, Value Added Tax,\Nadded on at a rate of 17 1/2%
Dialogue: 0,0:01:02.31,0:01:06.91,Default,,0000,0000,0000,,So percentages are all\Naround us. They're part of our life.
Dialogue: 0,0:01:06.91,0:01:11.64,Default,,0000,0000,0000,,So what does percentage\Nactually mean?
Dialogue: 0,0:01:11.64,0:01:18.24,Default,,0000,0000,0000,,Well in mathematics our symbol that we\Nuse is the percent sign.
Dialogue: 0,0:01:18.24,0:01:24.04,Default,,0000,0000,0000,,And it means\Nout of 100.
Dialogue: 0,0:01:24.04,0:01:33.99,Default,,0000,0000,0000,,Or as a mathematical process\N'out of' means divide by 100
Dialogue: 0,0:01:33.99,0:01:36.58,Default,,0000,0000,0000,,So let's have a look at an\Nexample.
Dialogue: 0,0:01:36.58,0:01:39.68,Default,,0000,0000,0000,,Let's say you get 85 percent in a test.
Dialogue: 0,0:01:39.68,0:01:47.62,Default,,0000,0000,0000,,That means you got 85 marks out of\Na possible 100 marks
Dialogue: 0,0:01:49.73,0:01:55.17,Default,,0000,0000,0000,,Let's look at some\Nfamiliar percentages
Dialogue: 0,0:01:55.17,0:02:00.58,Default,,0000,0000,0000,,75%\Nthat means 75 out of 100.
Dialogue: 0,0:02:01.09,0:02:06.87,Default,,0000,0000,0000,,Or if we write the fraction in\Nits lowest form, it's 3/4
Dialogue: 0,0:02:08.19,0:02:13.18,Default,,0000,0000,0000,,Or if we write it\Nas a decimal 0.75
Dialogue: 0,0:02:15.26,0:02:22.54,Default,,0000,0000,0000,,50%\NThat's 50 out of 100.
Dialogue: 0,0:02:23.32,0:02:29.12,Default,,0000,0000,0000,,And its lowest form. That's\Nexactly the same as a half
Dialogue: 0,0:02:29.12,0:02:31.05,Default,,0000,0000,0000,,and as a decimal 0.5
Dialogue: 0,0:02:32.94,0:02:39.73,Default,,0000,0000,0000,,25% is 25 out of 100
Dialogue: 0,0:02:39.73,0:02:45.70,Default,,0000,0000,0000,,In its lowest form, that's a quarter.
Dialogue: 0,0:02:45.71,0:02:49.53,Default,,0000,0000,0000,,or 0.25 as a decimal
Dialogue: 0,0:02:51.50,0:02:55.08,Default,,0000,0000,0000,,Let's look at 10%. That's a very\Ncommon one.
Dialogue: 0,0:02:55.08,0:02:58.66,Default,,0000,0000,0000,,That's 10 out of 100
Dialogue: 0,0:02:58.66,0:03:02.55,Default,,0000,0000,0000,,or 1/10 as a fraction in its lowest form
Dialogue: 0,0:03:02.55,0:03:06.44,Default,,0000,0000,0000,,or 0.1 as a decimal
Dialogue: 0,0:03:10.64,0:03:14.92,Default,,0000,0000,0000,,And 5%, that's just five out of 100.
Dialogue: 0,0:03:15.67,0:03:22.07,Default,,0000,0000,0000,,And in its lowest form, that's 1/20
Dialogue: 0,0:03:22.07,0:03:25.99,Default,,0000,0000,0000,,and 0.05 as a decimal.
Dialogue: 0,0:03:26.82,0:03:29.34,Default,,0000,0000,0000,,Now it's worth noting here that
Dialogue: 0,0:03:29.34,0:03:31.85,Default,,0000,0000,0000,,to find 50% an easy way of doing it
Dialogue: 0,0:03:31.85,0:03:35.44,Default,,0000,0000,0000,,is just to find half of the number
Dialogue: 0,0:03:35.44,0:03:38.05,Default,,0000,0000,0000,,or divide by two.
Dialogue: 0,0:03:38.05,0:03:40.77,Default,,0000,0000,0000,,And to find 10% another common one
Dialogue: 0,0:03:40.77,0:03:43.32,Default,,0000,0000,0000,,You just divide by 10,
Dialogue: 0,0:03:43.32,0:03:45.88,Default,,0000,0000,0000,,finding a tenth of the number.
Dialogue: 0,0:03:46.83,0:03:53.38,Default,,0000,0000,0000,,Let's look at writing a fraction\Nas a percentage.
Dialogue: 0,0:03:53.38,0:04:01.20,Default,,0000,0000,0000,,Let's say we get 18 marks out of 20 in a test
Dialogue: 0,0:04:01.20,0:04:05.41,Default,,0000,0000,0000,,and we want to write that as a percentage.
Dialogue: 0,0:04:05.41,0:04:07.28,Default,,0000,0000,0000,,First of all, we write it as a fraction:
Dialogue: 0,0:04:07.28,0:04:09.15,Default,,0000,0000,0000,,18 out of 20
Dialogue: 0,0:04:09.15,0:04:16.78,Default,,0000,0000,0000,,Now a percentage is out of 100, \Nso we want this number at the bottom
Dialogue: 0,0:04:16.78,0:04:21.03,Default,,0000,0000,0000,,the denominator to be 100.
Dialogue: 0,0:04:21.03,0:04:25.75,Default,,0000,0000,0000,,Well 20 multiplied by 5 gives us 100
Dialogue: 0,0:04:26.65,0:04:28.11,Default,,0000,0000,0000,,So in this case
Dialogue: 0,0:04:28.11,0:04:30.90,Default,,0000,0000,0000,,we can just multiply 18 by 5.
Dialogue: 0,0:04:31.96,0:04:35.89,Default,,0000,0000,0000,,Which gives us 90 out of 100.
Dialogue: 0,0:04:35.89,0:04:39.81,Default,,0000,0000,0000,,So 18 out of 20 is the same as 90%
Dialogue: 0,0:04:42.74,0:04:47.28,Default,,0000,0000,0000,,Now that's fine when it's an\Neasy number that we've got our
Dialogue: 0,0:04:47.28,0:04:52.19,Default,,0000,0000,0000,,marks out of 20, I could easily\Nchange into 100. I know to multiply by 5
Dialogue: 0,0:04:54.70,0:04:58.35,Default,,0000,0000,0000,,But what happens if it's not quite \Nsuch a nice number
Dialogue: 0,0:04:58.35,0:04:59.53,Default,,0000,0000,0000,,Well, let's have a look.
Dialogue: 0,0:04:59.53,0:05:03.28,Default,,0000,0000,0000,,Let's take the example this time
Dialogue: 0,0:05:03.28,0:05:11.17,Default,,0000,0000,0000,,Let's say we have 53 marks.
Dialogue: 0,0:05:11.17,0:05:17.29,Default,,0000,0000,0000,,And this time let's have it out of 68.
Dialogue: 0,0:05:17.29,0:05:23.06,Default,,0000,0000,0000,,Well, we write it as a fraction.\NAgain, 53 out of 68.
Dialogue: 0,0:05:23.85,0:05:26.03,Default,,0000,0000,0000,,And what we're going to do
Dialogue: 0,0:05:26.03,0:05:28.17,Default,,0000,0000,0000,,here we multiplied by 5 and
Dialogue: 0,0:05:28.17,0:05:31.48,Default,,0000,0000,0000,,we multiplied the denominator by 5.
Dialogue: 0,0:05:31.48,0:05:35.37,Default,,0000,0000,0000,,So both numerator and denominator were \Nmultiplied by 5
Dialogue: 0,0:05:35.37,0:05:45.77,Default,,0000,0000,0000,,Well, this time we're\Ngoing to multiply both by 100
Dialogue: 0,0:05:45.77,0:05:51.17,Default,,0000,0000,0000,,Now this 100 here gives us\Nour percentage because
Dialogue: 0,0:05:51.17,0:05:54.43,Default,,0000,0000,0000,,percentage is divide by 100.
Dialogue: 0,0:05:54.95,0:06:00.44,Default,,0000,0000,0000,,So we're actually going to\Ncalculate 53 divided by 68
Dialogue: 0,0:06:01.17,0:06:03.30,Default,,0000,0000,0000,,multiply it by 100.
Dialogue: 0,0:06:03.95,0:06:08.90,Default,,0000,0000,0000,,And that will give us our percentage.
Dialogue: 0,0:06:08.90,0:06:11.48,Default,,0000,0000,0000,,And if we carry out that calculation,
Dialogue: 0,0:06:11.48,0:06:16.78,Default,,0000,0000,0000,,we find that it comes to 77.94%
Dialogue: 0,0:06:16.78,0:06:19.23,Default,,0000,0000,0000,,That's to two decimal places.
Dialogue: 0,0:06:19.23,0:06:26.30,Default,,0000,0000,0000,,Or if we put it to the nearest percent\N78%
Dialogue: 0,0:06:29.100,0:06:32.49,Default,,0000,0000,0000,,Let's look at an example now where we're
Dialogue: 0,0:06:32.49,0:06:36.79,Default,,0000,0000,0000,,finding the percentage of a quantity,
Dialogue: 0,0:06:36.79,0:06:42.76,Default,,0000,0000,0000,,Now, in many countries it's customary \Nto leave a 10% tip when you have a meal
Dialogue: 0,0:06:42.76,0:06:52.38,Default,,0000,0000,0000,,So let's say our meal costs £25.40
Dialogue: 0,0:06:52.38,0:06:57.11,Default,,0000,0000,0000,,and we want to leave a 10% tip
Dialogue: 0,0:06:57.11,0:07:07.56,Default,,0000,0000,0000,,Now we want 10% of £25.40
Dialogue: 0,0:07:07.68,0:07:10.41,Default,,0000,0000,0000,,So in mathematical language
Dialogue: 0,0:07:10.41,0:07:14.73,Default,,0000,0000,0000,,10% is 10 divided by 100
Dialogue: 0,0:07:14.73,0:07:17.83,Default,,0000,0000,0000,,'of' is multiply
Dialogue: 0,0:07:17.83,0:07:20.97,Default,,0000,0000,0000,,£25.40
Dialogue: 0,0:07:20.97,0:07:24.00,Default,,0000,0000,0000,,And that equals £2.54,
Dialogue: 0,0:07:24.00,0:07:28.77,Default,,0000,0000,0000,,so that's the tip that we would leave
Dialogue: 0,0:07:28.77,0:07:32.10,Default,,0000,0000,0000,,Now 10% I said earlier that was an easy
Dialogue: 0,0:07:32.10,0:07:34.30,Default,,0000,0000,0000,,one to calculate because you just
Dialogue: 0,0:07:34.30,0:07:36.78,Default,,0000,0000,0000,,divide by 10.
Dialogue: 0,0:07:36.78,0:07:39.15,Default,,0000,0000,0000,,But the method that I've shown here
Dialogue: 0,0:07:39.15,0:07:41.78,Default,,0000,0000,0000,,is what you would use for
Dialogue: 0,0:07:41.78,0:07:43.51,Default,,0000,0000,0000,,more complex percentages.
Dialogue: 0,0:07:43.51,0:07:49.22,Default,,0000,0000,0000,,Let's have a look at another one.
Dialogue: 0,0:07:49.22,0:07:54.96,Default,,0000,0000,0000,,Let's say we have a salesman who earns \N2% commission
Dialogue: 0,0:07:54.96,0:08:00.16,Default,,0000,0000,0000,,on orders that he gets in one month.
Dialogue: 0,0:08:00.16,0:08:07.04,Default,,0000,0000,0000,,And let's say he has orders to\Nthe value of £250,000
Dialogue: 0,0:08:07.04,0:08:09.91,Default,,0000,0000,0000,,How much is he going to earn?
Dialogue: 0,0:08:09.91,0:08:17.50,Default,,0000,0000,0000,,Well, we want 2% of £250,000
Dialogue: 0,0:08:17.50,0:08:21.12,Default,,0000,0000,0000,,Again turn to our mathematical language
Dialogue: 0,0:08:21.12,0:08:26.14,Default,,0000,0000,0000,,2% is 2 divided by 100
Dialogue: 0,0:08:26.14,0:08:32.80,Default,,0000,0000,0000,,'of' (multiply) £250,000
Dialogue: 0,0:08:32.80,0:08:37.60,Default,,0000,0000,0000,,Now in this one we can do some cancelling
Dialogue: 0,0:08:37.60,0:08:41.58,Default,,0000,0000,0000,,because 100 goes into £250,000
Dialogue: 0,0:08:41.58,0:08:44.95,Default,,0000,0000,0000,,So we've got twice 2500
Dialogue: 0,0:08:44.95,0:08:49.35,Default,,0000,0000,0000,,Giving us an answer of £5000.
Dialogue: 0,0:08:51.100,0:09:00.21,Default,,0000,0000,0000,,Now VAT, Value Added Tax, is\N17 1/2% at the moment
Dialogue: 0,0:09:00.21,0:09:02.64,Default,,0000,0000,0000,,So let's do some calculations where we
Dialogue: 0,0:09:02.64,0:09:06.35,Default,,0000,0000,0000,,need to add on VAT
Dialogue: 0,0:09:06.35,0:09:17.34,Default,,0000,0000,0000,,Let's say a computer costs
Dialogue: 0,0:09:17.34,0:09:23.29,Default,,0000,0000,0000,,£634 plus VAT
Dialogue: 0,0:09:25.48,0:09:31.87,Default,,0000,0000,0000,,Now we can look at this in\Nthe same way as we did these examples
Dialogue: 0,0:09:31.87,0:09:38.64,Default,,0000,0000,0000,,We can find 17 and a half percent of £634
Dialogue: 0,0:09:38.64,0:09:42.83,Default,,0000,0000,0000,,That's the VAT and\Nwe can add it on.
Dialogue: 0,0:09:42.83,0:09:44.75,Default,,0000,0000,0000,,Well, let's do that.
Dialogue: 0,0:09:44.75,0:09:56.12,Default,,0000,0000,0000,,So 17 1/2% of £634 is 17.5
Dialogue: 0,0:09:56.12,0:09:58.42,Default,,0000,0000,0000,,I'm going to write it as .5
Dialogue: 0,0:09:58.42,0:10:01.15,Default,,0000,0000,0000,,when I now turn it into a fraction
Dialogue: 0,0:10:01.15,0:10:09.16,Default,,0000,0000,0000,,with our percent of £634
Dialogue: 0,0:10:09.16,0:10:13.30,Default,,0000,0000,0000,,And that works out to be £110.95
Dialogue: 0,0:10:14.13,0:10:16.90,Default,,0000,0000,0000,,So if we want the total cost
Dialogue: 0,0:10:16.90,0:10:19.86,Default,,0000,0000,0000,,of the computer
Dialogue: 0,0:10:19.86,0:10:26.04,Default,,0000,0000,0000,,We would need to add that on to our £634
Dialogue: 0,0:10:26.04,0:10:29.50,Default,,0000,0000,0000,,plus our £110.95
Dialogue: 0,0:10:29.50,0:10:35.90,Default,,0000,0000,0000,,Giving us a total of £744.95.
Dialogue: 0,0:10:37.56,0:10:41.41,Default,,0000,0000,0000,,Now, if we wanted that total cost
Dialogue: 0,0:10:41.41,0:10:44.09,Default,,0000,0000,0000,,rather than perhaps what \Nthe VAT amount was
Dialogue: 0,0:10:44.09,0:10:47.30,Default,,0000,0000,0000,,we could have looked at it in\Na slightly different way.
Dialogue: 0,0:10:48.43,0:10:56.00,Default,,0000,0000,0000,,We wanted 17 1/2% and we wanted the\Noriginal 100%
Dialogue: 0,0:10:56.00,0:11:00.57,Default,,0000,0000,0000,,the computer plus the VAT
Dialogue: 0,0:11:00.57,0:11:03.47,Default,,0000,0000,0000,,So what we could have found is
Dialogue: 0,0:11:03.47,0:11:11.86,Default,,0000,0000,0000,,117 1/2% of £634
Dialogue: 0,0:11:12.40,0:11:14.20,Default,,0000,0000,0000,,So we could have done
Dialogue: 0,0:11:14.20,0:11:18.93,Default,,0000,0000,0000,,117.5 divided by 100
Dialogue: 0,0:11:18.93,0:11:23.18,Default,,0000,0000,0000,,times by 634
Dialogue: 0,0:11:23.18,0:11:27.40,Default,,0000,0000,0000,,Done that calculation directly \Nin our calculator
Dialogue: 0,0:11:27.40,0:11:31.97,Default,,0000,0000,0000,,and come out with our answer of £744.95.
Dialogue: 0,0:11:32.85,0:11:36.07,Default,,0000,0000,0000,,So it depends what information\Nyou're looking for, whether you
Dialogue: 0,0:11:36.07,0:11:41.20,Default,,0000,0000,0000,,wanted to split with the VAT or\Nwhether you just wanted the total price.
Dialogue: 0,0:11:41.20,0:11:46.07,Default,,0000,0000,0000,,All as we did here was add the \Npercentages first
Dialogue: 0,0:11:46.07,0:11:50.84,Default,,0000,0000,0000,,before finding the percentage of\Nthe £634
Dialogue: 0,0:11:50.84,0:11:56.76,Default,,0000,0000,0000,,Now there's another nice way\Nof working out VAT
Dialogue: 0,0:11:57.03,0:11:59.75,Default,,0000,0000,0000,,And we'll have a look at that\Nbecause you don't need a calculator
Dialogue: 0,0:11:59.75,0:12:02.70,Default,,0000,0000,0000,,You can work it out when you're in the \Nmiddle of the shop
Dialogue: 0,0:12:02.70,0:12:04.07,Default,,0000,0000,0000,,wherever you are. It's a good way
Dialogue: 0,0:12:04.07,0:12:10.64,Default,,0000,0000,0000,,So let's just look at our 17 1/2% and \Nlet's take the same example again, the £634
Dialogue: 0,0:12:16.81,0:12:21.62,Default,,0000,0000,0000,,Well, 10%, let's work that out first. \NThat's a nice easy one.
Dialogue: 0,0:12:21.62,0:12:26.43,Default,,0000,0000,0000,,We just divide by 10 so that\Ngives us £63.40.
Dialogue: 0,0:12:27.13,0:12:34.34,Default,,0000,0000,0000,,5% is half of our 10%, so\Nthat's half of £63.40.
Dialogue: 0,0:12:34.34,0:12:42.12,Default,,0000,0000,0000,,Well, half of 60 is 30\NHalf of 3 is £1.50
Dialogue: 0,0:12:42.12,0:12:44.89,Default,,0000,0000,0000,,So it's £31.30 plus the 20, \Nso it's £31.70.
Dialogue: 0,0:12:46.37,0:12:54.16,Default,,0000,0000,0000,,Now 2 1/2% is half of 5%,\Nso if we find half of £31.70
Dialogue: 0,0:12:54.16,0:13:01.66,Default,,0000,0000,0000,,Well, that's £15.50 + 35, so that's £15.85
Dialogue: 0,0:13:01.66,0:13:08.44,Default,,0000,0000,0000,,10% add 5% add 2 1/2% gives us our \N17 1/2%
Dialogue: 0,0:13:11.19,0:13:14.47,Default,,0000,0000,0000,,So if we aad these up, we get 5.
Dialogue: 0,0:13:15.12,0:13:22.14,Default,,0000,0000,0000,,8 Seven 1519\Ncarry the 1567
Dialogue: 0,0:13:22.14,0:13:29.16,Default,,0000,0000,0000,,gives us 310-6789\Nten 11 and
Dialogue: 0,0:13:29.16,0:13:31.50,Default,,0000,0000,0000,,there's £110.95.
Dialogue: 0,0:13:32.66,0:13:37.32,Default,,0000,0000,0000,,Now let's look at where we're\Ntaking a percentage off.
Dialogue: 0,0:13:37.32,0:13:38.87,Default,,0000,0000,0000,,So far, we've been adding percentages on
Dialogue: 0,0:13:38.87,0:13:44.56,Default,,0000,0000,0000,,Let's say we have a pair of\Ntrainers in the shop.
Dialogue: 0,0:13:47.62,0:13:51.81,Default,,0000,0000,0000,,And the cost of those trainers\Nis £75 less a 10% discount
Dialogue: 0,0:13:56.72,0:14:03.28,Default,,0000,0000,0000,,So we want 10% of £75. \NThat will be the discount
Dialogue: 0,0:14:07.74,0:14:10.88,Default,,0000,0000,0000,,So that's 10 / 100 * 75.
Dialogue: 0,0:14:10.88,0:14:14.01,Default,,0000,0000,0000,,I'm writing it the longhand way, but\Nsince it's 10% I can just divide by 10
Dialogue: 0,0:14:14.01,0:14:20.28,Default,,0000,0000,0000,,and my answer would be £7.50
Dialogue: 0,0:14:20.28,0:14:23.32,Default,,0000,0000,0000,,Of course, I then need to do the subtraction
Dialogue: 0,0:14:23.32,0:14:29.62,Default,,0000,0000,0000,,So it will be 75 take away the £7.50
Dialogue: 0,0:14:30.30,0:14:35.10,Default,,0000,0000,0000,,giving me £67.50 for the actual\Ncost of the trainers.
Dialogue: 0,0:14:35.74,0:14:38.81,Default,,0000,0000,0000,,Let's look at that the other way
Dialogue: 0,0:14:38.81,0:14:43.63,Default,,0000,0000,0000,,As we did with the adding\Non ones we looked at it two ways
Dialogue: 0,0:14:43.63,0:14:51.03,Default,,0000,0000,0000,,Of saying, well it's a 10% discount, \Nso the £75 is 100%
Dialogue: 0,0:14:51.03,0:14:58.42,Default,,0000,0000,0000,,And we actually want 100 takeaway 10%
Dialogue: 0,0:14:58.42,0:15:04.95,Default,,0000,0000,0000,,So we could work it out as being\N90% of £75
Dialogue: 0,0:15:05.73,0:15:11.55,Default,,0000,0000,0000,,Why we do 90 / 100 * 75 so that\Nwe could directly come up with
Dialogue: 0,0:15:11.55,0:15:15.56,Default,,0000,0000,0000,,our answer of £67.50 again.\NIt really depends whether
Dialogue: 0,0:15:15.56,0:15:19.20,Default,,0000,0000,0000,,you're interested in knowing\Nwhat the discount is or whether
Dialogue: 0,0:15:19.20,0:15:23.57,Default,,0000,0000,0000,,you want the final amount and\Nwhat the numbers are.
Dialogue: 0,0:15:23.57,0:15:28.66,Default,,0000,0000,0000,,This was very easy actually to do in my\Nhead to find 10% and take it away
Dialogue: 0,0:15:28.66,0:15:32.67,Default,,0000,0000,0000,,And that's easy and actually working \Nout the 90% of my head.
Dialogue: 0,0:15:32.67,0:15:36.67,Default,,0000,0000,0000,,So it depends on the context of your \Nquestion and the numbers involved
Dialogue: 0,0:15:40.59,0:15:44.27,Default,,0000,0000,0000,,Let's look at a slightly\Ndifferent situation now.
Dialogue: 0,0:15:44.91,0:15:50.81,Default,,0000,0000,0000,,Where the price includes vieti\Nand we want to work out what the
Dialogue: 0,0:15:50.81,0:15:52.63,Default,,0000,0000,0000,,price was before vieti.
Dialogue: 0,0:15:54.30,0:15:58.43,Default,,0000,0000,0000,,Let's say we've got\Nour computer again.
Dialogue: 0,0:15:59.53,0:16:07.22,Default,,0000,0000,0000,,But this time\Nit costs £699,
Dialogue: 0,0:16:07.22,0:16:09.78,Default,,0000,0000,0000,,including Vieti.
Dialogue: 0,0:16:11.63,0:16:14.39,Default,,0000,0000,0000,,Now, a common misconception.
Dialogue: 0,0:16:15.08,0:16:21.70,Default,,0000,0000,0000,,Is to find 17 1/2% of\N£699 and take it off.
Dialogue: 0,0:16:22.70,0:16:28.41,Default,,0000,0000,0000,,That's incorrect because what\Nyou're doing there is finding 17
Dialogue: 0,0:16:28.41,0:16:34.43,Default,,0000,0000,0000,,1/2% of. A number that is\Nlarger than the actual price
Dialogue: 0,0:16:34.43,0:16:39.70,Default,,0000,0000,0000,,that the 17 half percent would\Nhave been calculated on so.
Dialogue: 0,0:16:40.33,0:16:44.03,Default,,0000,0000,0000,,Don't just find 17 1/2% of\Nthat number if the 80s
Dialogue: 0,0:16:44.03,0:16:47.72,Default,,0000,0000,0000,,included, we need to look\Nat it in a different way.
Dialogue: 0,0:16:48.90,0:16:54.61,Default,,0000,0000,0000,,And what we say is, well,\Nthat's 699 pounds.
Dialogue: 0,0:16:54.61,0:17:01.18,Default,,0000,0000,0000,,Actually represents\N117 1/2%.
Dialogue: 0,0:17:03.51,0:17:09.21,Default,,0000,0000,0000,,100% of the cost of the computer\Nplus the 17 1/2% vieti.
Dialogue: 0,0:17:09.92,0:17:15.31,Default,,0000,0000,0000,,So if I want to find out what it\Ncosts without the V. 80.
Dialogue: 0,0:17:15.90,0:17:18.42,Default,,0000,0000,0000,,What I want is the 100%.
Dialogue: 0,0:17:19.59,0:17:22.46,Default,,0000,0000,0000,,So what we do?
Dialogue: 0,0:17:22.46,0:17:28.50,Default,,0000,0000,0000,,Very simply, is\Nwe divide by
Dialogue: 0,0:17:28.50,0:17:34.40,Default,,0000,0000,0000,,117 1/2. I put it\Nthis .5 because I'm using a
Dialogue: 0,0:17:34.40,0:17:40.71,Default,,0000,0000,0000,,fraction. And what we have on\Nthis side? If we divide 117 1/2
Dialogue: 0,0:17:40.71,0:17:45.62,Default,,0000,0000,0000,,by 117 1/2 is one. So we\Ncalculate what 1% is.
Dialogue: 0,0:17:46.90,0:17:49.06,Default,,0000,0000,0000,,And having got our 1%.
Dialogue: 0,0:17:49.67,0:17:55.08,Default,,0000,0000,0000,,We can then very easily\Nmultiplied by 100 to find the
Dialogue: 0,0:17:55.08,0:17:58.03,Default,,0000,0000,0000,,100%, so the cost before vieti.
Dialogue: 0,0:17:58.56,0:18:04.59,Default,,0000,0000,0000,,Or if we wanted the V. 80, we\Ncould have just multiplied by 17
Dialogue: 0,0:18:04.59,0:18:07.18,Default,,0000,0000,0000,,1/2 to find just the V-80
Dialogue: 0,0:18:07.18,0:18:14.90,Default,,0000,0000,0000,,Element. So the net cost\Nis going to be 699
Dialogue: 0,0:18:14.90,0:18:22.34,Default,,0000,0000,0000,,/. 117.5 * 100 is\Njust right. The net cost.
Dialogue: 0,0:18:24.24,0:18:31.64,Default,,0000,0000,0000,,And when we calculate that\Nwe get £594.89 and that's
Dialogue: 0,0:18:31.64,0:18:34.60,Default,,0000,0000,0000,,to the nearest penny.
Dialogue: 0,0:18:36.19,0:18:40.53,Default,,0000,0000,0000,,OK, let's look at\Nanother example.
Dialogue: 0,0:18:42.03,0:18:48.96,Default,,0000,0000,0000,,This time we've got an insurance\Ncompany charging a customer 320
Dialogue: 0,0:18:48.96,0:18:51.83,Default,,0000,0000,0000,,pounds. For his car insurance.
Dialogue: 0,0:18:52.50,0:18:59.57,Default,,0000,0000,0000,,Now this includes\Nthe government's insurance
Dialogue: 0,0:18:59.57,0:19:01.92,Default,,0000,0000,0000,,premium tax.
Dialogue: 0,0:19:02.79,0:19:09.18,Default,,0000,0000,0000,,A 5%.\NSo we want to calculate what the
Dialogue: 0,0:19:09.18,0:19:11.48,Default,,0000,0000,0000,,cost of the car insurance is.
Dialogue: 0,0:19:12.21,0:19:14.56,Default,,0000,0000,0000,,Before that, 5% been added on.
Dialogue: 0,0:19:16.37,0:19:18.98,Default,,0000,0000,0000,,Well, are 320 pounds.
Dialogue: 0,0:19:19.90,0:19:26.84,Default,,0000,0000,0000,,Represents the 100% of the cost\Nof the insurance plus the 5%.
Dialogue: 0,0:19:27.36,0:19:33.34,Default,,0000,0000,0000,,Of the premium tax. So that's\N100 and 5%.
Dialogue: 0,0:19:35.05,0:19:42.37,Default,,0000,0000,0000,,So as before, we take care\N320 pounds. We divide it by
Dialogue: 0,0:19:42.37,0:19:44.81,Default,,0000,0000,0000,,105 to get 1%.
Dialogue: 0,0:19:46.73,0:19:50.34,Default,,0000,0000,0000,,So the. Car insurance.
Dialogue: 0,0:19:51.83,0:19:54.92,Default,,0000,0000,0000,,They thought the tax has been
Dialogue: 0,0:19:54.92,0:20:02.27,Default,,0000,0000,0000,,added. Is going to\Nbe our £320 /
Dialogue: 0,0:20:02.27,0:20:04.96,Default,,0000,0000,0000,,105 * 100.
Dialogue: 0,0:20:05.99,0:20:07.68,Default,,0000,0000,0000,,And when we calculate that.
Dialogue: 0,0:20:08.70,0:20:12.51,Default,,0000,0000,0000,,We come up with 304 pounds.
Dialogue: 0,0:20:13.04,0:20:14.75,Default,,0000,0000,0000,,And 76 Pence.
Dialogue: 0,0:20:17.75,0:20:24.48,Default,,0000,0000,0000,,Let's look at another similar\Nexample, but this time a
Dialogue: 0,0:20:24.48,0:20:26.50,Default,,0000,0000,0000,,reduction in costs.
Dialogue: 0,0:20:27.63,0:20:31.11,Default,,0000,0000,0000,,Let's say a coat is reduced.
Dialogue: 0,0:20:33.07,0:20:34.09,Default,,0000,0000,0000,,In a sale.
Dialogue: 0,0:20:38.36,0:20:42.67,Default,,0000,0000,0000,,And it's reduced by\N15%.
Dialogue: 0,0:20:44.43,0:20:47.36,Default,,0000,0000,0000,,And the new cost.
Dialogue: 0,0:20:47.36,0:20:51.39,Default,,0000,0000,0000,,Is\N£127.50.
Dialogue: 0,0:20:52.51,0:20:57.34,Default,,0000,0000,0000,,And we want to calculate what\Nthe original cost was.
Dialogue: 0,0:20:59.31,0:21:05.20,Default,,0000,0000,0000,,So our £127.50? What\Ndoes that represent?
Dialogue: 0,0:21:06.47,0:21:09.16,Default,,0000,0000,0000,,Well, it's the original 100%.
Dialogue: 0,0:21:09.67,0:21:12.59,Default,,0000,0000,0000,,Minus the 15%.
Dialogue: 0,0:21:13.63,0:21:18.05,Default,,0000,0000,0000,,So it's equal to\N85%.
Dialogue: 0,0:21:21.02,0:21:27.36,Default,,0000,0000,0000,,We want to calculate what the\N100% was the original amount. So
Dialogue: 0,0:21:27.36,0:21:29.100,Default,,0000,0000,0000,,if we take the £127.50.
Dialogue: 0,0:21:30.59,0:21:34.18,Default,,0000,0000,0000,,Divided by 85.
Dialogue: 0,0:21:34.18,0:21:37.15,Default,,0000,0000,0000,,That tells us what 1% is.
Dialogue: 0,0:21:38.45,0:21:42.27,Default,,0000,0000,0000,,And then all this we have to do\Nto find the original cost.
Dialogue: 0,0:21:43.10,0:21:50.66,Default,,0000,0000,0000,,Is to multiply our 1% by\N100 so 127 pounds 50 /,
Dialogue: 0,0:21:50.66,0:21:58.22,Default,,0000,0000,0000,,85 * 100 and if you\Nwork that out, if we come
Dialogue: 0,0:21:58.22,0:22:00.74,Default,,0000,0000,0000,,up with 150 pounds.
Dialogue: 0,0:22:01.91,0:22:08.65,Default,,0000,0000,0000,,Now another percentage that\Nwe might want to
Dialogue: 0,0:22:08.65,0:22:15.40,Default,,0000,0000,0000,,calculate is a percentage\Ndecrease or a percentage
Dialogue: 0,0:22:15.40,0:22:22.14,Default,,0000,0000,0000,,increase and we've got\Na rule for this.
Dialogue: 0,0:22:22.14,0:22:25.51,Default,,0000,0000,0000,,So percentage increase or
Dialogue: 0,0:22:25.51,0:22:32.43,Default,,0000,0000,0000,,decrease. And to calculate\Nit what we do is
Dialogue: 0,0:22:32.43,0:22:35.91,Default,,0000,0000,0000,,we find the actual increase.
Dialogue: 0,0:22:37.18,0:22:38.70,Default,,0000,0000,0000,,Or decrease.
Dialogue: 0,0:22:41.67,0:22:47.76,Default,,0000,0000,0000,,And we divide it by\Nthe original amount.
Dialogue: 0,0:22:50.18,0:22:53.64,Default,,0000,0000,0000,,And then we multiply by 100%.
Dialogue: 0,0:22:54.75,0:22:59.49,Default,,0000,0000,0000,,So we find the actual increase\Nor decrease divide by the
Dialogue: 0,0:22:59.49,0:23:04.23,Default,,0000,0000,0000,,original amount and multiplied\Nby 100%. Let's have a look at
Dialogue: 0,0:23:04.23,0:23:06.82,Default,,0000,0000,0000,,some examples and put it into
Dialogue: 0,0:23:06.82,0:23:13.29,Default,,0000,0000,0000,,context. Let's say a\Ncouple paid £180,000
Dialogue: 0,0:23:13.29,0:23:16.02,Default,,0000,0000,0000,,for their house.
Dialogue: 0,0:23:17.30,0:23:20.20,Default,,0000,0000,0000,,And four years later.
Dialogue: 0,0:23:20.20,0:23:27.89,Default,,0000,0000,0000,,It was valued\Nat 350,000 pounds.
Dialogue: 0,0:23:27.93,0:23:32.24,Default,,0000,0000,0000,,What's the percentage\Nincrease?
Dialogue: 0,0:23:33.36,0:23:34.55,Default,,0000,0000,0000,,In Valley.
Dialogue: 0,0:23:35.64,0:23:37.52,Default,,0000,0000,0000,,Of that house.
Dialogue: 0,0:23:38.47,0:23:42.38,Default,,0000,0000,0000,,All right, So what\Npercentage increase?
Dialogue: 0,0:23:43.57,0:23:46.38,Default,,0000,0000,0000,,It's equal to the actual
Dialogue: 0,0:23:46.38,0:23:49.25,Default,,0000,0000,0000,,increase. So
Dialogue: 0,0:23:49.25,0:23:56.00,Default,,0000,0000,0000,,that's £350,000.\NTake away 180,000 pounds. That's
Dialogue: 0,0:23:56.00,0:24:02.46,Default,,0000,0000,0000,,the actual increase in value\Ndivided by the original amount
Dialogue: 0,0:24:02.46,0:24:05.69,Default,,0000,0000,0000,,will. Originally it costs them
Dialogue: 0,0:24:05.69,0:24:09.60,Default,,0000,0000,0000,,£180,000. We multiplied by
Dialogue: 0,0:24:09.60,0:24:15.84,Default,,0000,0000,0000,,100%. 350\Ntakeaway 180,000
Dialogue: 0,0:24:15.84,0:24:22.16,Default,,0000,0000,0000,,is £170,000\N/ 180,000
Dialogue: 0,0:24:22.16,0:24:25.32,Default,,0000,0000,0000,,pounds times
Dialogue: 0,0:24:25.32,0:24:32.48,Default,,0000,0000,0000,,100%. And when you\Ncalculate that, you find that to
Dialogue: 0,0:24:32.48,0:24:37.87,Default,,0000,0000,0000,,the nearest percentage, that's a\N94% increase in that value.
Dialogue: 0,0:24:38.41,0:24:45.50,Default,,0000,0000,0000,,Let's have a look\Nat a decrease now.
Dialogue: 0,0:24:45.63,0:24:51.64,Default,,0000,0000,0000,,Let's suppose you paid £12,000\Nfor a car.
Dialogue: 0,0:24:52.64,0:24:56.42,Default,,0000,0000,0000,,And three years later.
Dialogue: 0,0:24:57.41,0:24:59.20,Default,,0000,0000,0000,,It was only worse.
Dialogue: 0,0:25:00.08,0:25:06.01,Default,,0000,0000,0000,,8000 pounds. What\Nwas the percentage decrease?
Dialogue: 0,0:25:07.22,0:25:09.30,Default,,0000,0000,0000,,And the value of that car.
Dialogue: 0,0:25:11.14,0:25:14.12,Default,,0000,0000,0000,,Inside percentage decrease.
Dialogue: 0,0:25:15.77,0:25:23.24,Default,,0000,0000,0000,,Is equal to the actual\Ndecrease, so that's our 12,000
Dialogue: 0,0:25:23.24,0:25:26.23,Default,,0000,0000,0000,,pounds takeaway 8000 pounds.
Dialogue: 0,0:25:26.28,0:25:32.69,Default,,0000,0000,0000,,Divided by the original amounts,\Nthe original value of the car
Dialogue: 0,0:25:32.69,0:25:38.46,Default,,0000,0000,0000,,was £12,000. And we\Nmultiplied by 100%.
Dialogue: 0,0:25:38.79,0:25:46.68,Default,,0000,0000,0000,,So that's £4000 /\N12,000 pounds times 100%
Dialogue: 0,0:25:46.68,0:25:54.57,Default,,0000,0000,0000,,and that gives us\N33% to the nearest
Dialogue: 0,0:25:54.57,0:26:00.84,Default,,0000,0000,0000,,1%. Let's have a look\Nnow at using the percentage
Dialogue: 0,0:26:00.84,0:26:02.91,Default,,0000,0000,0000,,button on your Calculator.
Dialogue: 0,0:26:05.49,0:26:10.69,Default,,0000,0000,0000,,Now it very much depends when\Nyou press the percentage button
Dialogue: 0,0:26:10.69,0:26:16.37,Default,,0000,0000,0000,,in your calculation as to what\Neffect this has on your answer,
Dialogue: 0,0:26:16.37,0:26:22.99,Default,,0000,0000,0000,,and I think the easiest way is\Nif we have a look at some
Dialogue: 0,0:26:22.99,0:26:29.50,Default,,0000,0000,0000,,various calculations. So if I do\Nit in a chart with the buttons
Dialogue: 0,0:26:29.50,0:26:32.75,Default,,0000,0000,0000,,pressed. That's what we're\Nactually going to press on the
Dialogue: 0,0:26:32.75,0:26:35.78,Default,,0000,0000,0000,,Calculator. The answer
Dialogue: 0,0:26:35.78,0:26:40.98,Default,,0000,0000,0000,,that's displayed.\NThe
Dialogue: 0,0:26:40.98,0:26:46.67,Default,,0000,0000,0000,,effect. That\Nthat's actually had. So
Dialogue: 0,0:26:46.67,0:26:51.35,Default,,0000,0000,0000,,what it's done and what\Nthat actually means in
Dialogue: 0,0:26:51.35,0:26:53.43,Default,,0000,0000,0000,,terms of the calculation.
Dialogue: 0,0:26:54.66,0:26:58.59,Default,,0000,0000,0000,,So let's look at if we press
Dialogue: 0,0:26:58.59,0:27:01.47,Default,,0000,0000,0000,,48. Divided
Dialogue: 0,0:27:01.47,0:27:06.28,Default,,0000,0000,0000,,by 400. And then\Nthe percent button.
Dialogue: 0,0:27:08.20,0:27:11.73,Default,,0000,0000,0000,,Well, the answer that's\Ndisplayed is 12.
Dialogue: 0,0:27:12.35,0:27:18.43,Default,,0000,0000,0000,,So pressing that percent button\Nhas had the effect of
Dialogue: 0,0:27:18.43,0:27:20.25,Default,,0000,0000,0000,,multiplying by 100.
Dialogue: 0,0:27:21.10,0:27:27.09,Default,,0000,0000,0000,,What does that mean in terms of\Nour question? Well, what we've
Dialogue: 0,0:27:27.09,0:27:29.08,Default,,0000,0000,0000,,done is found 48.
Dialogue: 0,0:27:29.68,0:27:34.38,Default,,0000,0000,0000,,As a percentage of\N400.
Dialogue: 0,0:27:36.17,0:27:38.29,Default,,0000,0000,0000,,Let's look at another example.
Dialogue: 0,0:27:38.83,0:27:41.45,Default,,0000,0000,0000,,This time, if we do one.
Dialogue: 0,0:27:42.53,0:27:45.24,Default,,0000,0000,0000,,Divided by two.
Dialogue: 0,0:27:45.24,0:27:49.24,Default,,0000,0000,0000,,Multiplied by 300.
Dialogue: 0,0:27:49.24,0:27:50.82,Default,,0000,0000,0000,,And then press the\Npercent button.
Dialogue: 0,0:27:52.39,0:27:55.73,Default,,0000,0000,0000,,The answer that comes up is 1.5.
Dialogue: 0,0:27:57.04,0:28:03.45,Default,,0000,0000,0000,,And the effect that this is hard\Nis to divide by 100.
Dialogue: 0,0:28:05.03,0:28:07.27,Default,,0000,0000,0000,,And what we've done is, we've
Dialogue: 0,0:28:07.27,0:28:10.71,Default,,0000,0000,0000,,found. 300%.
Dialogue: 0,0:28:11.65,0:28:19.36,Default,,0000,0000,0000,,Of 1/2.\NLet's try this
Dialogue: 0,0:28:19.36,0:28:21.67,Default,,0000,0000,0000,,one 400.
Dialogue: 0,0:28:23.25,0:28:27.14,Default,,0000,0000,0000,,Multiplied by 50.
Dialogue: 0,0:28:27.15,0:28:28.93,Default,,0000,0000,0000,,And then the percent button.
Dialogue: 0,0:28:29.54,0:28:34.43,Default,,0000,0000,0000,,The answer we\Nget is 200.
Dialogue: 0,0:28:35.93,0:28:41.00,Default,,0000,0000,0000,,So this is how the effect of\Ndividing by 100.
Dialogue: 0,0:28:41.57,0:28:47.21,Default,,0000,0000,0000,,And what we've done is found\N50% of 400.
Dialogue: 0,0:28:49.74,0:28:54.32,Default,,0000,0000,0000,,Now this is a common sort of\Nquestion. 50% of 400. I know
Dialogue: 0,0:28:54.32,0:28:58.89,Default,,0000,0000,0000,,that's dead easy and you can do\Nit in your head, but let's
Dialogue: 0,0:28:58.89,0:29:02.41,Default,,0000,0000,0000,,consider what happens if we\Nactually put that into the
Dialogue: 0,0:29:02.41,0:29:05.93,Default,,0000,0000,0000,,Calculator. So if we do 50,\Npress the percent button.
Dialogue: 0,0:29:06.49,0:29:09.38,Default,,0000,0000,0000,,And multiply by 400.
Dialogue: 0,0:29:11.79,0:29:15.81,Default,,0000,0000,0000,,Well what's displayed another\Nhave written answer. It's
Dialogue: 0,0:29:15.81,0:29:20.84,Default,,0000,0000,0000,,actually what's displayed is 400\Nbecause we've not pressed any
Dialogue: 0,0:29:20.84,0:29:25.37,Default,,0000,0000,0000,,equals, so it's actually not\Ncalculating anything. It's had
Dialogue: 0,0:29:25.37,0:29:30.45,Default,,0000,0000,0000,,no effect. And there's\Nbeen no calculation.
Dialogue: 0,0:29:31.79,0:29:36.56,Default,,0000,0000,0000,,This percentage hasn't done\Nanything 50% * 400. You just got
Dialogue: 0,0:29:36.56,0:29:39.17,Default,,0000,0000,0000,,that 400 in the display still.
Dialogue: 0,0:29:40.41,0:29:44.11,Default,,0000,0000,0000,,So if we actually now press the
Dialogue: 0,0:29:44.11,0:29:47.58,Default,,0000,0000,0000,,equals Button. Afterwards, what
Dialogue: 0,0:29:47.58,0:29:52.71,Default,,0000,0000,0000,,happens? Well, the answer we get\Nthen is 20,000.
Dialogue: 0,0:29:54.16,0:29:59.18,Default,,0000,0000,0000,,Now again that pressing that\Npercent button, this had no
Dialogue: 0,0:29:59.18,0:30:04.70,Default,,0000,0000,0000,,effect is what's happened is\Nwe've just done 50 * 400.
Dialogue: 0,0:30:04.82,0:30:06.36,Default,,0000,0000,0000,,And that's the meaning that
Dialogue: 0,0:30:06.36,0:30:10.89,Default,,0000,0000,0000,,we've got there. So by all\Nmeans, use the percent
Dialogue: 0,0:30:10.89,0:30:15.17,Default,,0000,0000,0000,,button on your Calculator,\Nbut be aware of what it's
Dialogue: 0,0:30:15.17,0:30:18.16,Default,,0000,0000,0000,,actually doing to the\Ncalculation. Depending on
Dialogue: 0,0:30:18.16,0:30:22.44,Default,,0000,0000,0000,,when you press it as to what\Neffect it has.