Up to now  all the maths you
have  done  involved   using
actual numbers.

     3 + 5 = 8  ... etc.

    There  is  a  branch  of
maths called  Algebra  which
is the basis for much of the
maths you  will do .It invo-
lves representing numbers by
words or  more  commonly  by
letters.
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Something + 5 = 6

What  does  something  =   ?

something = 1 of course.

     You  have  just  solved
an algebraic equation!
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In  Algebra  we  usually use
the letters  x , y  and z to
represent unknown numbers.
eg:
        x + 5 = 6
        x must = 1

    At  first  the  idea  of
adding a letter or a word to
a number may seem strange to
you , but it is no different
from     1 + 5 = ?
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Here    ?    represents  the
unknown number .
    Suppose x = 6  ,x is not
the letter x  but a name for
a number whose value we know.
    If x + 1 = y what does y
equal ? Since x = 6 , subst-
itute 6 for x
          6 + 1 = y
    Therefore     y = 7
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13
14
4
7
^t
If  x =   6     and     y = 2  then

  7 + x =  blank
^t
 12 + y =  blank
^t

If  b =   4     and   4 + a + b = 12

then  a =   blank
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if  a =   2     and     8 + ab = 22

{ where ab = a multiplied by b }

Then  b =   blank
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6.5
5
4
27.5
14
9
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If  x = 2  y = 2.5  and  z = 2  then

 7 + x = y + blank

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12.5 - y   =   z multiplied by blank.

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5x divided by y = blank.

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If    ax = 22y  then a = blank.

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x multiplied by a number = 28 what
is the number  blank.

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Double  a number plus x equals ten y
minus five , the number is blank.
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same
12
same
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Four apples plus eight oranges equals
blank
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You can't add two different things
they have to be of the same kind.

window = 7    ,    car = 5

window + car = blank

^t

Right ! Window plus car both
represent numbers , they represent
the blank thing.
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5x
.25y
5
40
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If a  certain item of clothing costs
x pounds then five items of clothing
cost blank pounds.

^t
If a spoon costs 25p how much do y
spoons cost in pounds ?
blank pounds

^t
If  x = 45  and  y = 9.
How many times does y go into x ?
blank

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a is equal to twice b , and b is
equal to three times c , c = 4.
a + b + c = blank
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x = 6            x + 1 = 7
Here  x represents a value  which we
know 6 .
    X in this case is a constant ,it
has a value of 6 which cannot change.
    Thus for example you  cannot say
x + 2 = 7.
    However x + 5 = y.
Here x  is  a variable , we  do  not
know  its  value  until  we can find
what  y  equals  and then  solve the
equation.
    eg:    y = 8
           x + 5 = y
           x + 5 = 8      x = 3
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algebra
constant
variable
2
8.5
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The  branch of maths which involves
the  substitution  of  numbers  for
letters and words is called blank
^t

x = 6 ,in this case x is a blank

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x + 5 = y ,in this case x is
a blank

^t

If y equaled 7 in the above case
x would = blank

^t
z + 14 = 22.5   z = blank
^z
In  order to be able  to use
maths in  everyday  life  we
must be able to express pro-
blems in mathematical terms.
    eg: If a computer  costs
1100 pounds to buy and incl-
udes a printer and 20MB hard
disk, and  the prices of the
computer, printer  and  hard
disk  on their  own are  850
pounds , 150 pounds and  250
pounds .
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How  much  of a saving  does
the combined price represent?
    You probably  know  that
if you simply  add  all  the
individual  prices  together
and  subtract  the  combined
price  you'll  find  out how
much you save.
    But  you  can  represent
the problem   mathematically
as follows.
  850 + 150 + 250 = 1100 + x
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Where  x  represents the  saving the
combined price  has over the sum  of
the  prices  for  each  item  bought
individually.
    This example may seem too simple
to bother using maths to  solve  yet
it  is  only  by  understanding  the
simple  problems that you can figure
out the more difficult ones.
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5 -.45
.21
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Form  the  equation  using  x  to
represent the unknown quantity in
the following problems and then
solve them.

If a shopper has 45 pence change
from five pounds and she bought four
items costing 1.60 ,1.75 , .99
how much did the fifth item cost her

The equation representing the
problem is
blank  = 1.60 + 1.75 + .99 + x
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The fourth item cost her blank
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  5 x .18  +  x
.30
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With 1 pound 20 pence a person bought
five biros  and one pen if the biros
cost .18 each. How much did the pen
cost ?

{ we will use * instead of x to
  represent multipication }

The equation of the problem is
1.2  = blank

^t
The pen costs blank

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25 - 10 = x
15
^t
For 25.00 a person bought 10  floppy
disks and received a "FREE" disk box.
    If   floppy  disks   cost   1.20
individually but only  1.00 per disk
if you  buy ten or more how much did
the disk box actually cost ?

The equation of the problem is
blank

^t
The disk box cost blank pounds
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