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.

^z

Something + 5 = 6



What  does  something  =   ?



something = 1 of course.



     You  have  just  solved

an algebraic equation!

^z

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

^z

^q

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

^t



if  a =   2     and     8 + ab = 22



{ where ab = a multiplied by b }



Then  b =   blank

^z

^q

6.5

5

4

27.5

14

9

^t

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.

^z

^q

same

12

same

^t

Four apples plus eight oranges equals

blank

^t

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.

^z

^q

5x

.25y

5

40

^t

If a  certain item of clothing costs

x pounds then five items of clothing

cost blank pounds.



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If a spoon costs 25p how much do y

spoons cost in pounds ?

blank pounds



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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

^z

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

^z

^q

algebra

constant

variable

2

8.5

^t

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

^t


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 .

^z

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

^z

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.

^z

^q

5 -.45

.21

^t

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

^t

The fourth item cost her blank

^z

^q

  5 x .18  +  x

.30

^t

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



^z

^q

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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