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

^z

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.

^z

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.

^z

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      }

^z

^q

numerical

whole

similar

fractions

simplest

5:12

^t

Ratios are blank     relationships.



^t

They are always expressed as blank

numbers.



^t

They apply only to blank

quantities.



^t

Ratios may be expressed as blank    .



^t

They are always written in their

blank    form.



^t

5/12 written as a ratio would equal

blank.

^z

^q

3:5

5:1

5:4

7:20

^t

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.



^t

The ratio of 1 pound to 20p is blank



^t

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.



^t

The ratio 35:100 expressed in its

simplest form is blank



^z

^q

23:11

2:1

9:1

1:9

2:9

18:1

^t

The ratio 23:11 expressed in its

simplest form is blank



^t

The ratio 128:64 written in its

simplest form is blank



^t

if a = 27 and b = 3 then the ratio

of a to b = blank



^t

the ratio of b to a = blank



^t

the ratio of twice b to a = blank



^t

the ratio of twice a to b = blank



^z

^q

3:1

5:1

100:1

9:1

1:6

^t

The ratio 36:12 expressed in its

simplest form is blank



^t

The ratio 15:3 written in its

simplest form is blank



^t

The ratio 100:1 written in its

simplest form is blank



^t

The ratio 81:9 written in its

simplest form is blank



^t

2/5:12/5 written properly as a ratio

equals blank

^z

^q

7:16

47:20

2:1

3:2

2:3

^t

7/9:16/9 written properly as a ratio

equals blank



^t

235/5:100/5 written properly as a

ratio equals blank



^t

9:4+ written properly as a ratio

equals blank



^t

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



      x:y       = blank



^t

      y:x       = blank

^z

^q

3:8

1:2

2:9

2:1

6:1

3:1

^t

      x = 12 ~ y = 8 ~ z = 3



      z:y       = blank



^t

      x/z:y     = blank



^t

      y/x:z     = blank



^t

      z x y : x = blank



^t

      2x : +y   = blank



^t

      4z : +y   = blank

^z

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.

^z

      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.

^z

^q

add

3

11

1

2

22

^t

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

^t

which gives us blank.

^t

Then divide the sum of their ages 33

by 3 to give blank.

^t

Multiplying 11 by blank in the case

of Ann to find her age gives us 11.

^t

And multiplying 11 by blank in the

case of John ~ gives us John's age

^t

which is blank.

^z

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.

^z

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.

^z

^q

Add

5

Divide

11

Multiply

33

22

^t

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.



^t

blank   55 by this number gives us

^t

blank.



^t

blank    this number by each of the

coefficients of the ratio giving us

^t

the two numbers which are blank and

^t

blank.

^z

^q

4

12

^t

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



^t

Dividing 48 by this number gives us

blank.



^z

^q

Multiply

12

36

^t

blank    12 by each of the

coefficients to give us the two

numbers which are

^t

blank

^t

and blank.

^z

^q

Add

16

Divide

15

Multiply

195

45

^t

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.



^t

blank    this number by each of the

coefficients of the ratio giving us

^t

the two numbers which are blank

^t

and blank.

^z

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.

^z

Add  the  components  of the

ratio. ( 7 + 4 + 9 = 20 )

    Divide  the  quantity in

question by this number.

( 80 v 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

^z

^q

add

15

Multiply

2400

900

1200

^t

Divide  4500  pounds  among 3 prize

winners in the ratio 8:3:4



First blank the components of the

ratio.

^t



Divide the prize money by blank

^t



blank    this base number by each of

the parts of the ratio

^t



The prize money is divided into

blank  pounds ~

^t

blank  pounds ~

^t

blank  pounds .

^t



