A ratio is a numerical rela-
tionship between two similar
quantities eg: age.
    If Ann is ten years  old
and  Mary is five  years old
then the ratio of Ann's  age
to Mary's  age can be expre-
ssed as 10:5.
    This is read  10 is to 5
The ratio of  Mary's  age to
Ann's  age  is  5:10  or the
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reverse of the above.
    Simply put , for every 5
years Mary has lived Ann has
lived 10.
    A ratio may be expressed
as a  fraction in  the above
case 5/10 or 1/2 ....
    and a  fraction  may  be
expressed as a ratio eg: 1/2
= 5/10 = 1:2 = 5:10.
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Ratios  are always expressed
in  terms  of  whole numbers
so a ratio of
              1/2:1/3
would be written as
                3:2  .
    This is  done by  multi-
plying  both  sides  by  the
same number into  which they
will  both  divide ,in  this
case 6 so that the ratio can
be written as a whole number.
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A ratio is always written in
its simplest form eg:

           12:8
would be written as
            6:4
{ dividing both sides by 2 }

which in turn could be
simplified to

            3:2
{ again dividing by 2      }
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numerical
whole
similar
fractions
simplest
5:12
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Ratios are blank     relationships.

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They are always expressed as blank
numbers.

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They apply only to blank
quantities.

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Ratios may be expressed as blank    .

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They are always written in their
blank    form.

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5/12 written as a ratio would equal
blank.
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3:5
5:1
5:4
7:20
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If one ladder is 3m high and another
is 5m high the ratio of the heights
of the first ladder to the second is
blank.

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The ratio of 1 pound to 20p is blank

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If  the  ratio  of John's weight  to
James' weight is 4:5  then the ratio
of James' weight to John's weight is
blank.

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The ratio 35:100 expressed in its
simplest form is blank

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23:11
2:1
9:1
1:9
2:9
18:1
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The ratio 23:11 expressed in its
simplest form is blank

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The ratio 128:64 written in its
simplest form is blank

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if a = 27 and b = 3 then the ratio
of a to b = blank

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the ratio of b to a = blank

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the ratio of twice b to a = blank

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the ratio of twice a to b = blank

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3:1
5:1
100:1
9:1
1:6
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The ratio 36:12 expressed in its
simplest form is blank

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The ratio 15:3 written in its
simplest form is blank

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The ratio 100:1 written in its
simplest form is blank

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The ratio 81:9 written in its
simplest form is blank

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2/5:12/5 written properly as a ratio
equals blank
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7:16
47:20
2:1
3:2
2:3
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7/9:16/9 written properly as a ratio
equals blank

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235/5:100/5 written properly as a
ratio equals blank

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9:4 written properly as a ratio
equals blank

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if    x = 12 , y = 8 , z = 3

      x:y       = blank

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      y:x       = blank
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3:8
1:2
2:9
2:1
6:1
3:1
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      x = 12 , y = 8 , z = 3

      z:y       = blank

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      x/z:y     = blank

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      y/x:z     = blank

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      z x y : x = blank

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      2x : y   = blank

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      4z : y   = blank
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In order to divide any quan-
tity in  a  given  ratio eg:
( to  divide  1 kilo  in the
ratio 3:2 )
    Add  the two  components
of the  ratio  3  +  2  =  5
and divide the  quantity (1)
by that number.
( giving you 200g )
    Then  multiply this num-
ber by the components of the
ratio to get each part.
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      200g x 3 = 600g
      200g x 2 = 400g
Thus 1 kilo  divided in  the
ratio of 3:2 gives 600g:400g
    Try another  example ,if
the sum of Ann's and  John's
ages is 33 and the  ratio of
Ann's  age to John's  age is
1:2 then  applying  the same
rules as  above  you  should
find  Ann's  age  is 11  and
John's age is 22.
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add
3
11
1
2
22
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Lets go through the problem step by
step.
The sum of Ann's age and John's age
is 33.
The ratio of their ages is 1:2

We will first blank the two
components of the ratio
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which gives us blank.
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Then divide the sum of their ages 33
by 3 to give blank.
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Multiplying 11 by blank in the case
of Ann to find her age gives us 11.
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And multiplying 11 by blank in the
case of John , gives us John's age
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which is blank.
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Here's another one. A  prize
is to be divided among first
and  second  place   in  the
ratio of 3:1.
    The prize is 120 pounds.
How  much  does each  person
get ?
    After a bit of  practice
you should nearly be able to
do these sort of problems in
your head.
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Using the  method as before.
    Add  the two  components
of the ratio ,giving you  4.
    Divide  120  pounds   by
this  number  giving  you 30
pounds.
    Multiply  30  pounds  by
each component  of the ratio
to find how much each person
gets.
    90 pounds for the  first
place and 30 for the second.
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Add
5
Divide
11
Multiply
33
22
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Two  numbers add together give you 55
the ratio of the numbers is
3:2
the numbers are  . . . .

blank the two components of the ratio
^t
to give blank.

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blank   55 by this number gives us
^t
blank.

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blank    this number by each of the
coefficients of the ratio giving us
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the two numbers which are blank and
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blank.
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4
12
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Two numbers multiplied together = 48.
The ratio of the two numbers  is 1:3,
what are they ?

Adding the two components of the
ratio together we get
blank

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Dividing 48 by this number gives us
blank.

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Multiply
12
36
^t
blank    12 by each of the
coefficients to give us the two
numbers which are
^t
blank
^t
and blank.
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Add
16
Divide
15
Multiply
195
45
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Two  numbers added together give you
240 the ratio of the numbers is 13:3
the numbers are  . . . .

blank the two components of the
ratio
^t
to give blank.
^t

blank   240 by this number gives us
^t
blank.

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blank    this number by each of the
coefficients of the ratio giving us
^t
the two numbers which are blank
^t
and blank.
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What if we  wish  to  divide
something in more  than  two
lots ? eg:
    Divide 80 pounds among 3
men who have worked 7 hours,
4 hours and 9 hours respect-
ively in accordance with the
time they have worked.
    Here we have a ratio  in
the form 7:4:9.
    We can  apply  the  same
rules we have used before.
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Add  the  components  of the
ratio. ( 7 + 4 + 9 = 20 )
    Divide  the  quantity in
question by this number.
( 80  20 = 4 pounds )
    Multiply this base number
by   each  component  of  the
ratio  to  get the amount the
each of  three  men should be
payed.
( 7 x 4 , 4 x 4 , 9 x 4 )
   28  ,   16  ,   36  pounds
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add
15
Multiply
2400
900
1200
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Divide  4500  pounds  among 3 prize
winners in the ratio 8:3:4

First blank the components of the
ratio.
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Divide the prize money by blank
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blank    this base number by each of
the parts of the ratio
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The prize money is divided into
blank  pounds ,
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blank  pounds ,
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blank  pounds .
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