Return to Video

www.mathcentre.ac.uk/.../Ratios.mp4

  • 0:02 - 0:05
    Today's session is on ratio.
  • 0:05 - 0:08
    I'm going to explain what a ratio is
  • 0:08 - 0:09
    and how ratios are used
  • 0:09 - 0:11
    in different situations.
  • 0:11 - 0:15
    So to start off with what is a ratio?
  • 0:15 - 0:18
    Well, a ratio is a way of comparing
  • 0:19 - 0:23
    amounts of ingredients.
  • 0:23 - 0:26
    Ratios can be used to compare
  • 0:26 - 0:30
    weights, money, length and so on.
  • 0:30 - 0:33
    So if we take this example
  • 0:33 - 0:35
    we've got a model boat
  • 0:35 - 0:38
    whose length is 1 metre
  • 0:38 - 0:41
    and the real boat
  • 0:41 - 0:43
    whose length is 25 metres.
  • 0:43 - 0:45
    Then we say the ratio of the
  • 0:45 - 0:48
    length of the model boat to the real boat
  • 0:48 - 0:52
    is 1 to 25.
  • 0:52 - 0:55
    Notice we've just used the numbers
  • 0:55 - 0:58
    without the unit (metres)
  • 0:58 - 1:00
    and we've used the colon
  • 1:00 - 1:03
    to represent the ratio.
  • 1:03 - 1:06
    Ratios are used to describe quantities
  • 1:06 - 1:09
    of ingredients in mixtures.
  • 1:09 - 1:12
    For example, in the
    pharmaceutical trade
  • 1:12 - 1:14
    when you're making medicines,
  • 1:14 - 1:17
    or in the building trade
  • 1:17 - 1:19
    when you are making cement or mortar,
  • 1:19 - 1:22
    or at home when you're making up food
  • 1:22 - 1:27
    you use different quantities
    in different proportions
  • 1:27 - 1:29
    and if you don't get them right
  • 1:29 - 1:31
    then things go wrong.
  • 1:31 - 1:34
    So it's very important to know
  • 1:34 - 1:39
    what quantities you've got and
    in what ratio.
  • 1:39 - 1:42
    So for example, if we have
  • 1:42 - 1:46
    mortar for building brick walls.
  • 1:46 - 1:48
    Mortar is made up by mixing
  • 1:48 - 1:53
    two parts of cement to
    seven parts of gravel by volume
  • 1:53 - 1:58
    and we write that ratio as 2 to 7.
  • 1:58 - 2:00
    Again notice we've used
  • 2:00 - 2:04
    the numbers without the units
  • 2:04 - 2:07
    and the colon to represent the ratio.
  • 2:07 - 2:09
    When we're making pastry at home,
  • 2:09 - 2:11
    when we're making pies and tarts,
  • 2:11 - 2:14
    we mix four ounces of flour
  • 2:14 - 2:17
    with two ounces of margarine
  • 2:17 - 2:23
    And that ratio would be 4 to 2.
  • 2:23 - 2:24
    But in this case,
  • 2:24 - 2:26
    if you look at the numbers,
  • 2:26 - 2:29
    they've got a factor of two in common
  • 2:29 - 2:31
    So we can simplify ratios just in the same
  • 2:31 - 2:34
    way as we simplify fractions.
  • 2:34 - 2:36
    We can divide by the common factor,
  • 2:36 - 2:39
    so we divide 4 by 2
  • 2:39 - 2:43
    and 2 by 2 to give 1.
  • 2:43 - 2:49
    So 2 to 1 is the simplest form
    of the ratio 4 to 2.
  • 2:49 - 2:53
    But both of the ratios are equivalent,
  • 2:53 - 3:02
    because the relationship of the numbers
    involved stays the same.
  • 3:02 - 3:06
    If we take this example
  • 3:06 - 3:10
    250 to 150
  • 3:10 - 3:13
    We can simplify this ratio.
  • 3:13 - 3:16
    We divide both by 10
  • 3:16 - 3:20
    to get 25 to 15
  • 3:20 - 3:22
    And then we can divide both by 5
  • 3:22 - 3:25
    5 into 25 will give me 5
  • 3:25 - 3:28
    5 into 15 will give me 3
  • 3:28 - 3:32
    We can't divide anymore,
  • 3:32 - 3:34
    so this is the simplest form.
  • 3:34 - 3:38
    5 to 3 the simplest form of
  • 3:38 - 3:41
    the ratio 250 to 150.
  • 3:41 - 3:44
    But all three ratios are equivalent
  • 3:44 - 3:47
    because the relationship of the numbers
  • 3:47 - 3:50
    is exactly the same.
  • 3:50 - 3:54
    In the same way, we can actually
  • 3:54 - 4:00
    simplify this ratio: 1 to 1.5
  • 4:00 - 4:04
    In ratios we like to have whole numbers
  • 4:04 - 4:06
    and in this ratio you can see
  • 4:06 - 4:08
    that we have a decimal.
  • 4:08 - 4:09
    To get rid of the decimal
  • 4:09 - 4:11
    we can multiply both sides of the
  • 4:11 - 4:13
    ratio by 10
  • 4:13 - 4:16
    and we still have an equivalent ratio.
  • 4:16 - 4:18
    Because, again, the relationship
  • 4:18 - 4:20
    between the numbers is the same.
  • 4:20 - 4:23
    So we multiply the 1 by 10
  • 4:23 - 4:24
    you get 10
  • 4:24 - 4:26
    Multiply 1.5 by 10
  • 4:26 - 4:28
    you get 15
  • 4:28 - 4:30
    10 to 15 we can simplify that.
  • 4:30 - 4:34
    Divide both sides by 5.
  • 4:34 - 4:36
    5 into 10 gives me 2
  • 4:36 - 4:40
    5 into 15 will give me 3
  • 4:40 - 4:42
    2 to 3 is the simplest form
  • 4:42 - 4:47
    of the ratio 1 to 1.5
  • 4:47 - 4:50
    Similarly, when we have fractions
  • 4:50 - 4:54
    If we had this ratio:
  • 4:54 - 4:58
    a quarter to five-eighths,
  • 4:58 - 5:00
    it just doesn't look right.
  • 5:00 - 5:02
    We want to express that ratio
  • 5:02 - 5:03
    in terms of whole numbers
  • 5:03 - 5:05
    in its simplest form.
  • 5:05 - 5:10
    So what we do first is we write
    both as fractions over 8
  • 5:10 - 5:12
    in terms of eighths.
  • 5:12 - 5:17
    A quarter is two eighths
  • 5:17 - 5:22
    and now the ratio is two eighths to five eighths.
  • 5:22 - 5:24
    And now it's dead simple
  • 5:24 - 5:28
    All we have to say is that is 2 to 5.
  • 5:28 - 5:31
    We multiply both ratios by 8
  • 5:31 - 5:33
    And 2 to 5 is the simplest ratio
  • 5:33 - 5:38
    for the ratio a quarter to five-eighths.
  • 5:38 - 5:40
    But again all three ratios are
  • 5:40 - 5:43
    equivalent because the relationship
  • 5:43 - 5:46
    between the numbers is exactly the same.
  • 5:46 - 5:48
    Moving on,
  • 5:48 - 5:51
    we must have the numbers
    in the ratios
  • 5:51 - 5:53
    having the same units.
  • 5:53 - 5:55
    So if we have this ratio
  • 5:55 - 6:03
    15 pence to 3 pounds,
  • 6:03 - 6:07
    we cannot say that the ratio is 15 to 3
  • 6:07 - 6:13
    and then simplify that to 5 to 1
  • 6:13 - 6:16
    Because we didn't start off with
  • 6:16 - 6:19
    the numbers having the same units
  • 6:19 - 6:22
    the relationship between
    the numbers is not the same,
  • 6:22 - 6:24
    because as I say,
  • 6:24 - 6:27
    we didn't start off with these numbers
  • 6:27 - 6:29
    having the same units.
  • 6:29 - 6:31
    So we must convert the numbers
  • 6:31 - 6:33
    to the same units
  • 6:33 - 6:37
    and we choose whichever unit is
    appropriate
  • 6:37 - 6:39

    In this case, it's obvious we must
  • 6:39 - 6:41
    change them to pence.
  • 6:41 - 6:49
    So we say the ratio is 15 to 300
  • 6:49 - 6:52
    as there's 300 pence for 3 pounds
  • 6:52 - 6:55
    and then we simplify as normal.
  • 6:55 - 6:57
    We divide both sides by five.
  • 6:57 - 6:59
    5 into 15 is 3
  • 6:59 - 7:02
    5 into 300 is 60
  • 7:02 - 7:06
    And then we can divide by 3
  • 7:06 - 7:07
    3 into 3 is 1
  • 7:07 - 7:10
    3 into 60 is 20
  • 7:10 - 7:15
    And notice these two ratios are
  • 7:15 - 7:17
    not the same, they're vastly different.
  • 7:17 - 7:19
    They're not equivalent because
  • 7:19 - 7:21
    the relationship between the numbers
  • 7:21 - 7:24
    is not the same.
  • 7:24 - 7:26
    So it's very important in ratios
  • 7:26 - 7:28
    that you start with numbers
  • 7:28 - 7:31
    that have the same units.
  • 7:31 - 7:32
    If they're not,
  • 7:32 - 7:34
    then you convert them to the same units
  • 7:34 - 7:42
    and then simplify if appropriate.
  • 7:42 - 7:44
    As I said before,
  • 7:44 - 7:46
    ratios are extremely useful
  • 7:46 - 7:49
    in lots of different circumstances.
  • 7:49 - 7:51
    They can be used to divide and
  • 7:51 - 7:54
    share amounts of different quantities
  • 7:54 - 7:58
    like money, weights, and so on.
  • 7:58 - 8:00
    So if I take this problem
  • 8:00 - 8:03
    just say I had an inheritance of £64,000
  • 8:03 - 8:07
    and it was to be shared between two people
  • 8:07 - 8:10
    Mrs Sharp and Mr West
  • 8:10 - 8:13
    in the ratio 5 to 3
  • 8:13 - 8:15
    What I want you to do is work out
  • 8:15 - 8:18
    what each one of those gets.
  • 8:18 - 8:21
    And that's a lot of information to take in
  • 8:21 - 8:23
    so what I do first is
  • 8:23 - 8:26
    I start off with a diagram
  • 8:26 - 8:31
    I've got the total inheritance of £64,000
  • 8:31 - 8:34
    and I divide it
  • 8:34 - 8:40
    between Mrs Sharp
  • 8:40 - 8:43
    and Mr West
  • 8:43 - 8:48
    in the ratio 5 to 3
  • 8:48 - 8:50
    And we want to work out
  • 8:50 - 8:53
    what each gets.
  • 8:53 - 8:55
    What we do first is we work out
  • 8:55 - 8:58
    the total number of parts that
  • 8:58 - 9:02
    their inheritance is split up into.
  • 9:02 - 9:05
    Well, we use the ratio for that.
  • 9:05 - 9:08
    It's five parts for Mrs Sharp
  • 9:08 - 9:10
    and three parts for Mr West
  • 9:10 - 9:12
    so altogether that is eight parts
  • 9:12 - 9:16
    Then we work out what the total value
  • 9:16 - 9:19
    of one part of the inheritance would be.
  • 9:19 - 9:23
    Now we know that the total inheritance
  • 9:23 - 9:25
    is £64,000
  • 9:25 - 9:27
    so one part
  • 9:27 - 9:36
    equals 64,000 divided by 8
  • 9:36 - 9:41
    and that is £8000
  • 9:41 - 9:43
    And then the rest is easy.
  • 9:43 - 9:48
    All we have to do now is
    take Mrs Sharp
  • 9:48 - 9:54
    and she has five parts
  • 9:54 - 10:01
    and that is 5 multiplied by £8000
  • 10:01 - 10:07
    which works out to be £40,000
  • 10:07 - 10:12
    And then Mr West
  • 10:12 - 10:16
    he has three parts
  • 10:16 - 10:22
    and that is 3 multiplied by £8000
  • 10:22 - 10:28
    which is £24,000
  • 10:28 - 10:29
    An awful lot of money!
  • 10:29 - 10:31
    But what if I made a mistake?
  • 10:31 - 10:34
    How can I check my two answers?
  • 10:34 - 10:37
    How can I check that Mrs Sharp did get
    £40,000
  • 10:37 - 10:39
    and Mr West got £24,000?
  • 10:39 - 10:42
    Well a very simple check
  • 10:42 - 10:46
    is to add up these two values
  • 10:46 - 10:47
    and if they add together
  • 10:47 - 10:49
    to make up the total inheritance
  • 10:49 - 10:53
    then we think we've done our
    calculations properly.
  • 10:53 - 10:58
    So a quick check:
  • 10:58 - 11:13
    £40,000 plus 24,000 does equal £64,000
  • 11:13 - 11:15
    For a complete check though
  • 11:15 - 11:17
    we can take the two amounts
  • 11:17 - 11:21
    and see that they will actually make an
    equivalent ratio
  • 11:21 - 11:24
    to the ratio that we started off with 5:3
  • 11:24 - 11:33
    So if we take our 40,000 that
    Mrs Sharp got
  • 11:33 - 11:37
    and then the 24,000 that Mr West got
  • 11:37 - 11:39
    and cancel them down,
  • 11:39 - 11:41
    we cancel by 1000
  • 11:41 - 11:44
    then we cancel by 4
  • 11:44 - 11:48
    so that would make 10 to 6
  • 11:48 - 11:50
    and then cancel by 2
  • 11:50 - 11:54
    so that will make 5 to 3
  • 11:54 - 11:56
    We do actually get the same ratio
  • 11:56 - 12:00
    that we started off with.
  • 12:00 - 12:03
    We're going to do another example.
  • 12:03 - 12:06
    It's an example which involves another
  • 12:06 - 12:09
    mixture: making concrete.
  • 12:09 - 12:14
    And with this, concrete is made by mixing
  • 12:14 - 12:17
    gravel, sand and cement
  • 12:17 - 12:21
    in the ratio 3 to 2 to 1
  • 12:21 - 12:25
    and in this problem we
    start with concrete.
  • 12:25 - 12:28
    The amount of concrete
    that we are going to make
  • 12:28 - 12:31
    will be 12 cubic metres.
  • 12:31 - 12:34
    And what I want to work out
  • 12:34 - 12:36
    is how much gravel will be needed
  • 12:36 - 12:40
    to make 12 cubic metres of concrete.
  • 12:40 - 12:46
    So we start with drawing a diagram
  • 12:46 - 12:50
    and that represents the concrete
  • 12:50 - 12:51
    and we know we want to make
  • 12:51 - 12:56
    12 cubic metres of concrete
  • 12:56 - 12:59
    and we know it's mixed
  • 12:59 - 13:10
    by mixing gravel, sand and cement
  • 13:10 - 13:17
    in the ratio 3 to 2 to 1
  • 13:17 - 13:19
    And we want to work out
  • 13:19 - 13:24
    the amount of concrete for 12 cubic metres
  • 13:24 - 13:25
    Well, first of all,
  • 13:25 - 13:28
    we work out the total number of parts
  • 13:28 - 13:31
    our concrete is divided up into
  • 13:31 - 13:34
    and we use our ratio for that.
  • 13:34 - 13:43
    It's 3 + 2 + 1 and that equals 6 parts
  • 13:43 - 13:45
    Now our concrete is divided up
  • 13:45 - 13:47
    into six parts
  • 13:47 - 13:50
    So one part must equal
  • 13:50 - 13:56
    our 12 cubic metres divided by 6
  • 13:56 - 14:01
    so that's 12 divided by 6 cubic metres
  • 14:01 - 14:06
    which works out to be 2 cubic metres.
  • 14:06 - 14:08
    Now we want to work out
  • 14:08 - 14:11
    how much gravel is needed.
  • 14:11 - 14:14
    Gravel is represented by 3 parts
  • 14:14 - 14:20
    so gravel, the amount that we want
  • 14:20 - 14:27
    equals 3 times 2 cubic metres
  • 14:27 - 14:31
    which is 6 cubic metres
  • 14:31 - 14:32
    and that's our answer.
  • 14:32 - 14:34
    But it's always good to check
  • 14:34 - 14:36
    and so we try and do the calculation
  • 14:36 - 14:39
    in a different way
  • 14:39 - 14:41
    and the way that I'd like to do it
  • 14:41 - 14:42
    is using fractions.
  • 14:42 - 14:45
    If we go back to the original diagram
  • 14:45 - 14:50
    we know that gravel is represented
    by 3 parts
  • 14:50 - 14:53
    and the total is 6
  • 14:53 - 14:57
    so gravel is a half of
    the total volume
  • 14:57 - 15:00
    and a half of 12 cubic metres is
  • 15:00 - 15:03
    6 cubic metres
  • 15:03 - 15:05
    so our answer is right
  • 15:05 - 15:07
    we've done a check.
  • 15:07 - 15:12
    But what if we did a similar problem
  • 15:12 - 15:13
    and we want to start off
  • 15:13 - 15:16
    with mixing our concrete
  • 15:16 - 15:18
    using gravel, sand, and cement
  • 15:18 - 15:24
    but we don't know the final volume of
    the concrete
  • 15:24 - 15:27
    but we do know that we are given
  • 15:27 - 15:30
    6 cubic metres of sand
  • 15:30 - 15:34
    and an unlimited supply of
    gravel and cement.
  • 15:34 - 15:36
    How much concrete can we make then
  • 15:36 - 15:40
    if we've got 6 cubic metres of sand?
  • 15:40 - 15:44
    Alright, we'll start the
    question or the problem
  • 15:44 - 15:47
    with a diagram.
  • 15:47 - 15:53
    We know that the mixture is
    still the same.
  • 15:53 - 15:55
    We use the same ratio
  • 15:55 - 15:58
    gravel to sand to cement
  • 15:58 - 16:04
    as 3 to 2 to 1
  • 16:04 - 16:05
    And we know that
  • 16:05 - 16:09
    we have 6 cubic metres of sand
  • 16:09 - 16:12
    but we want to work out
  • 16:12 - 16:15
    how much concrete we can make
  • 16:15 - 16:17
    with that amount of sand
  • 16:17 - 16:21
    and unlimited amounts of the other two.
  • 16:21 - 16:23
    Well, the number of parts that
  • 16:23 - 16:29
    the concrete is divided up into is still 6
  • 16:29 - 16:32
    But we know that 2 parts
  • 16:32 - 16:35
    is 6 cubic metres
  • 16:35 - 16:37
    because that's what we're given
  • 16:37 - 16:42
    so 2 parts equals 6 cubic metres.
  • 16:42 - 16:45
    So 1 part
  • 16:45 - 16:49
    equals 6 divided by 2
  • 16:49 - 16:54
    which is 3 cubic metres
  • 16:54 - 16:57
    Now the total number of parts of
  • 16:57 - 16:59
    the concrete is divided up into is 6
  • 16:59 - 17:04
    So the amount of concrete that is produced
  • 17:04 - 17:09
    is 6 times 3 cubic metres
  • 17:09 - 17:12
    and that is 18 cubic metres
  • 17:12 - 17:15
    Again, it's good to check our answer
  • 17:15 - 17:16
    and we'll do it in a different way
  • 17:16 - 17:19
    and we'll use fractions again this time.
  • 17:19 - 17:22
    We look at what we were given.
  • 17:22 - 17:24
    Sand is represented by 2 parts
  • 17:24 - 17:29
    and we know it has a volume
    of 6 cubic metres.
  • 17:29 - 17:34
    Altogether, there are 6 parts
    for our concrete.
  • 17:34 - 17:37
    So the fraction that represents sand
  • 17:37 - 17:40
    is 2 over 6, which is a third.
  • 17:40 - 17:44
    So a third of the total amount is
    6 cubic metres
  • 17:44 - 17:49
    So the whole amount of concrete must be
  • 17:49 - 17:51
    3 times 6 cubic metres
  • 17:51 - 17:54
    which is 18 cubic metres
  • 17:54 - 17:58
    Here's another ratio problem involved
    with ingredients
  • 17:58 - 18:00
    but this time the ingredients are to make
  • 18:00 - 18:03
    the Greek food houmous.
  • 18:03 - 18:08
    It's usually given as a starter
  • 18:08 - 18:11
    and there are four ingredients:
  • 18:11 - 18:16
    two cloves of garlic
  • 18:16 - 18:18
    are combined with
  • 18:18 - 18:24
    four ounces of chickpeas
  • 18:24 - 18:32
    and four tablespoonfuls
    of olive oil.
  • 18:32 - 18:35
    I sound a little bit like
    Delia Smith at this point
  • 18:35 - 18:37
    and the final secret ingredient is
  • 18:37 - 18:46
    the 5 fluid ounces of tahini paste.
  • 18:46 - 18:48
    Now when you combine these ingredients
  • 18:48 - 18:55
    together that's enough for six people
  • 18:55 - 18:57
    But what if I want to make houmous
  • 18:57 - 18:59
    for nine people?
  • 18:59 - 19:03
    What amounts do I have of these four
    ingredients
  • 19:03 - 19:06
    to make it for nine people?
  • 19:06 - 19:08
    Well, we start off with what we've got
  • 19:08 - 19:10
    and what we know
  • 19:10 - 19:13
    We've got 2 cloves of garlic
  • 19:13 - 19:16
    with 4 ounces of chickpeas
  • 19:16 - 19:19
    4 tablespoonsful of olive oil
  • 19:19 - 19:24
    and 5 fluid ounces of tahini paste
  • 19:24 - 19:29
    and that makes enough for six people
  • 19:29 - 19:33
    What I do next is that I work out
  • 19:33 - 19:35
    what each of those ingredients
  • 19:35 - 19:38
    would be for one person.
  • 19:38 - 19:39
    So I have to divide
  • 19:39 - 19:42
    each of those numbers by 6
  • 19:42 - 19:45
    So that's 2 over 6
  • 19:45 - 19:47
    4 over 6
  • 19:47 - 19:48
    4 over 6
  • 19:48 - 19:51
    and 5 over 6
  • 19:51 - 19:54
    and then we cancel down if we can
  • 19:54 - 19:55
    In this case we can
  • 19:55 - 19:58
    that's one third.
  • 19:58 - 20:03
    Cancel four sixths to two thirds.
  • 20:03 - 20:06
    And this will be the same.
  • 20:06 - 20:08
    And the last one just remains the same:
  • 20:08 - 20:09
    five sixths
  • 20:09 - 20:11
    And now it's dead easy to work out
  • 20:11 - 20:15
    what amounts we need for nine people.
  • 20:15 - 20:19
    All we have to do is multiply by 9
  • 20:19 - 20:22
    So that's 1/3 multiplied by 9
  • 20:22 - 20:25
    2/3 multiplied by 9
  • 20:25 - 20:29
    and another 2/3 multiplied by 9
  • 20:29 - 20:32
    and then 5/6 multiplied by 9
  • 20:32 - 20:36
    And we work out these
    calculations and simplify
  • 20:36 - 20:39
    3 into 9 is 3
  • 20:39 - 20:40
    3 into 9 is 3
  • 20:40 - 20:43
    and then 2 threes are 6.
  • 20:43 - 20:44
    and this works out to be the same
  • 20:44 - 20:48
    which is 6 because it's the same
    calculation
  • 20:48 - 20:50
    3 into 6 is 2
  • 20:50 - 20:52
    3 into 9 is 3
  • 20:52 - 20:56
    5 threes are 15 over 2
  • 20:56 - 21:01
    which works out to be 7 and a half
  • 21:01 - 21:03
    So our final answer
  • 21:03 - 21:05
    for the ingredients
  • 21:05 - 21:10
    is 3 cloves of garlic
  • 21:10 - 21:14
    6 ounces of chickpeas
  • 21:14 - 21:16
    combined with 6 tablespoonfuls
    of olive oil
  • 21:16 - 21:20
    and 7 and a half fluid ounces
  • 21:20 - 21:22
    of tahini paste
  • 21:22 - 21:28
    And that makes enough
    houmous for nine people.
  • 21:28 - 21:31
    In a similar way,
  • 21:31 - 21:37
    you can use this method in conversion
    problems
  • 21:37 - 21:41
    If we had the conversion that
  • 21:41 - 21:51
    1 pound is the same as 1.65 euros
  • 21:51 - 21:54
    and I wanted to work out
  • 21:54 - 22:00
    what 50 euros would be in pence
  • 22:00 - 22:02
    to the nearest pence
  • 22:02 - 22:07
    What I like doing first is to work out
  • 22:07 - 22:13
    what 1 euro is in terms of pence
  • 22:13 - 22:14
    So I start with
  • 22:14 - 22:22
    1.65 euros equals 100 pence
  • 22:22 - 22:27
    One euro would then equal
  • 22:27 - 22:33
    100 divided by the 1.65
  • 22:33 - 22:35
    And then to work out
  • 22:35 - 22:40
    what the 50 euros would be
  • 22:40 - 22:44
    I multiply this by 50
  • 22:44 - 22:49
    as 100 over 1.65 multiplied by 50
  • 22:49 - 22:53
    And that is 5000
  • 22:53 - 22:56
    divided by the 1.65
  • 22:56 - 22:58
    Now I am not going to do this by
    long division.
  • 22:58 - 23:00
    I'll use my calculator
  • 23:00 - 23:07
    and I just type in the relevant numbers
  • 23:07 - 23:13
    5000 divided by 1.65
  • 23:13 - 23:14
    equals
  • 23:14 - 23:20
    3030 point 3 0 point 3 0 repeating
  • 23:20 - 23:28
    So 50 euros equals 3030 pence
  • 23:28 - 23:29
    to the nearest pence.
  • 23:29 - 23:38
    Which is 30 pounds and 30p
  • 23:38 - 23:41
    Well, that's the session finished
    now on ratio.
  • 23:41 - 23:43
    Before I finish finally,
  • 23:43 - 23:45
    what I'd like to do is just remind you
  • 23:45 - 23:50
    of a few key points about ratio.
  • 23:50 - 23:52
    First of all, what is a ratio?
  • 23:52 - 23:54
    Well a ratio is a way of comparing
  • 23:54 - 23:57
    quantities of a similar type
  • 23:57 - 23:59
    When you write a ratio down
  • 23:59 - 24:02
    you use whole numbers
  • 24:02 - 24:05
    separated by colon.
  • 24:05 - 24:08
    The numbers should be in the
    same units.
  • 24:08 - 24:10
    If they're not, you convert them
  • 24:10 - 24:11
    to the same units
  • 24:11 - 24:14
    by using one or the other of the
    units involved
  • 24:14 - 24:17
    Just use your nous basically.
  • 24:17 - 24:21
    And then you simplify as appropriate.
  • 24:21 - 24:23
    In calculations involved in ratio
  • 24:23 - 24:30
    it is useful to work out the total
    number of parts
  • 24:30 - 24:33
    the quantity is divided up into
  • 24:33 - 24:37
    and then work out one part represents.
Title:
www.mathcentre.ac.uk/.../Ratios.mp4
Video Language:
English
Duration:
24:43

English subtitles

Revisions Compare revisions