Computer Shopper 125/Computer Shopper CD-ROM Issue 125 (1998-07)(Dennis Publishing).iso/EuroMath/MathDemo/DataBase/learning/ID158.txt

Text File | 1997-09-04 | 10.3 KB | 564 lines

}!@seeAlso 1factors
@seeAlso 1highest common factor
@seeAlso 1prime factors
@seeAlso 1multiples





'*************************************NUMBERS***********************
'***************************************************************************
'*******************LOWEST COMMON MULTIPLE****************

@atGraphic 5,10
@Picture numbers\n0107a.bmp




@at  0,5
#<lowest common multiple#


@PlaySoundFile n010701.wav


@animate BabStand

@At 52,20

@Definition
For two or more numbers, the #Blowest#
#Bcommon multiple# is the number with
the #Blowest value# which can be
@At 10,
divided exactly by #Ball# the given numbers.

@Wait 6.5

@animate BabPointUp,BabPointWave,babPointDown




@prompt
@at 10,69
@keyPoint 9999,using lowest common multiples (part 1)
@PlaySoundFile n010702.wav

@animate BabPointUp,BabPointWave,babPointDown

To add or subtract fractions you first need to
find a common denominator.This can be done
by multiplying all the denominators together.

@Wait 0.5
@At ,+3
            #^3#ix#     #s+#     #^2#ix#    -     #^ #ix#     #s+#     #^3#ix#


#T 2#T 3#T 4#T 8
@At ,-23
#T__#T__#T__#T___


@Wait 0.5
@At 80,135
#B2# ╫ #B3# ╫ #B4# ╫ #B8# = 192
@Wait 0.5

@At 10,150
Now work out the new numerator for each
fraction like this:

@Wait 0.5
@At 25,180
192 ╫ 3#^#ix# = 288#ix#
#T2
@At 56,181
___

@Wait 0.5
@At 140,180
192 ╫ 2#^#ix# = 128#ix#
#T3
@At 171,181
___

@Wait 0.5
@At 25,205
192 ╫ #^#ix# = 48#ix#
#T4
@At 56,205
__

@Wait 0.5
@At 140,205
192 ╫ 3#^#ix# = 72#ix#
#T8
@At 171,205
___

@prompt
@keyPoint 9999,using lowest common multiples (part 2)

@animate BabPointUp,BabPointWave,babPointDown

So the calculation can be written as:
@Wait 0.5
@At 35,90
=   288#ix#   +   128#^#ix#   -   48#ix#   +   72#ix#
#T 192
@At 49,90
____________________________

@Wait 0.5

@At 100,120
=   #^440#ix#
#T192#T
@At 115,120
____

@Wait 0.5
@At 100,150
=   #^55#ix#
#T24

@At 115,150
____

@Wait 0.5
@At 10,180
However this involves a lot of calculation.


@prompt
@keyPoint 9999,using lowest common multiples (part 3)
@PlaySoundFile n010703.wav

@animate BabPointUp,BabPointWave,babPointDown


A far easier method is to find the lowest
common multiple of the denominators
@Wait 0.5
            #^3#ix#     #s+#     #^2#ix#    -     #^ #ix#     #s+#     #^3#ix#


#T 2#T 3#T 4#T 8
@At ,-23
#T__#T__#T__#T___

@Wait 0.5
@At 10,125
The lowest common multiple = #B24#


@Wait 0.5
@At 10,142
Now work out the new numerator for each
fraction like this:

@Wait 0.5
@At 25,170
24 ╫ 3#^#ix# = 36#ix#
#T2
@At 50,170
___
@Wait 0.5
@At 140,170
24 ╫ 2#^#ix# = 16#ix#
#T3
@At 164,170
___
@Wait 0.5
@At 25,195
24 ╫ #^#ix# = 6#ix#
#T4
@At 50,196
__
@Wait 0.5
@At 140,196
24 ╫ 3#^#ix# = 9#ix#
#T8
@At 164,196
___
@prompt
@keyPoint 9999,using lowest common multiples (part 4)

@animate BabPointUp,BabPointWave,babPointDown


So the calculation can be written as:
@At 35,90
=   36#ix#   +   16#^#ix#   -   6#ix#   +   9#ix#
#T 24
@At 49,90
_________________________

@Wait 0.5

@At 100,120
=   #^55#ix#
#T24#T
@At 115,120
____



@prompt
@method

@PlaySoundFile n010704.wav

@At 10,70
Find the lowest common multiple of 6, 10
and 12.

To find the lowest common multiple of a set of
numbers you need to draw up a list of the
multiples of each until you find one common
to all the lists.




'@prompt
@keyPoint 185,multiply by 2
@Wait 0.25

@PlaySoundFile n010705.wav



@animate BabStand,BabStickDown,BabGetCalculator,BabCalculate



@At ,+75
#BKey Step One#
First, #K185,*multiply by 2# to get the list going.
@At ,+10
@Wait 0.5
               #b6#                    #B10#                    #B12#
           #^                       #^                       #^
@Wait 0.25
#T╫2=12    #T╫2=20    #T╫2=24



@prompt
@method




@keyPoint 186,multiply by one more than last time
@PlaySoundFile n010706.wav

@Wait 0.25


@animate BabCalculate,BabPutCalculator,BabStickUp,BabStand

#BKey Step Two#
@Wait 0.25
Then, #K186,*multiply by one more than last time#
        #^       #^                  #^       #^                  #^       #^

@Wait 0.25
@At ,-12
               #b6#                    #B10#                    #B12#

@Wait 0.25
#T╫2#T=12    #T╫2#T= 20    #T╫2#T= 24
@At ,-1
@Wait 0.25
#T╫3#T= 18    #T╫3#T= 30    #T╫3#T= 36
@At ,-1
@Wait 0.25
#T╫4#T= 24    #T╫4#T= 40    #T╫4#T= 48
@At ,-1
@Wait 0.25
#T╫5#T= 30    #T╫5#T= 50    #T╫#B5##T= #B60#
@At ,-1
@Wait 0.25
#T╫6#T= 36    #T╫#B6##T= #B60#    #T╫6#T= 72
@At ,-1
@Wait 0.25
#T╫7#T= 42    #T╫7#T= 70    #T╫7#T= 84
@At ,-1
@Wait 0.25
#T╫8#T= 48    #T╫8#T= 80    #T╫8#T= 96
@At ,-1
@Wait 0.25
#T╫9#T= 54    #T╫9#T= 90    #T╫9#T= 108
@At ,-1
@Wait 0.25
#T╫#B10##T= #B60##T╫10#T= 100#T╫10#T= 120
@Wait 0.5
Repeat until you find the #Blowest common#
#Bmultiple#. The lowest common multiple = #B60#.


@prompt
@method


@PlaySoundFile n010707.wav

@At 10,70

The previous method involves a lot of working
out. For simple numbers you can often use trial
and improvement methods more quickly and
easily. There is another method that works
well, particularly for larger numbers:




'@prompt
@keyPoint 187,find the prime factors of each number


@Wait 0.5
@PlaySoundFile n010708.wav


@animate BabStand,BabStickDown,BabGetCalculator,BabCalculate


@At ,+65
#BKey Step One#
@Wait 0.25
#K187,*find the prime factors of each number#.
@Wait 0.25
          #^#B6#                    #^#B10#                    #^#B12#
@Wait 0.5
@At ,+5
#T =#T =#T =
@Wait 0.5
@At ,+5

                                                   2 ╫ 2 ╫ 3
@Wait 0.5
@At ,+5
        #B2# ╫ #B3#               #B2# ╫ #B5#       #B2ê# ╫ #B3#


@prompt

@method


@keyPoint 188,find the product

@PlaySoundFile n010709.wav


@animate BabCalculate,BabCalculate,BabPutCalculator,BabStickUp,BabStand

#BKey Step Two#
To find the #Blowest common multiple#, take
the highest power of each prime factor and
#K188,*find the product#.
@At ,+2
          #^#B6#                    #^#B10#                    #^#B12#
'@At ,+1
@Wait 0.5
#T =#T =#T =
'@At ,+1
@Wait 0.5
                                                   2 ╫ 2 ╫ 3
'@At ,+1
@Wait 0.5
        2 ╫ #B3#               2 ╫ #B5#       #B2ê# ╫ 3
@Wait 0.25
@At ,+1
Take each #Bprime factor# from all the lists. Do
#Bnot# take the #Bsame one twice#. If a prime
factor appears #Bmore than once#, take the one
with  the #Bhighest power#.    #B2ê#  ╫  #B3#   ╫   #B5#

@Wait 0.25
@At ,+1
The #Blowest common multiple# = #B60#

@prompt
@keyPoint 9999,summary (part 1)


#BSummary#
@Wait 0.75
@At ,+2

   *   #^#BLowest common multiples# are useful
#Tin mathematics when dealing with
#t#Bfractions#
@Wait 0.75
@At ,+2
   *   #TTo add or subtract #Bfractions#, you
#Tneed to find a #Bcommon denominator#.
#TBy finding the #Blowest common multiple#
#Tof the #Bdenominators# the amount of
#Tcalculation, simplification and the size of
#Tthe numbers are kept to a minimum.
@Wait 0.75
@At ,+2
   *   #TUsing the lowest common multiple
#Treduces the possibility of #Berrors#.
@Wait 0.75
@At 175,-2
(#Bcontinued#)



@prompt
@keyPoint 9999,summary (part 2)

#B(continued)#

@Wait 0.75
@At ,+5
To find the #Blowest common multiple# of a set
of numbers you need to draw up a list of the
multiples of each until you find one common
to all the lists.
@Wait 0.75
@At ,+5
   *   #TFirst, #K185,*multiply by 2# to get the list going
@Wait 0.75
@At ,+5
   *   #TThen #K186,multiply by one more than last#
#t#K186,time#
@Wait 0.75
@At ,+5
   *   #TRepeat until you find the #Blowest common#
#T#Bmultiple#.
@Wait 0.75
@At ,+5
@At 175,
(#Bcontinued#)



@prompt
@keyPoint 9999,summary (part 3)

#B(continued)#

@Wait 0.75
@At ,+4

The previous method involves a lot of
working out. For simple numbers you can
often use #Btrial and improvement# methods
more quickly and easily.
@Wait 0.75
@At ,+4
The method that works well for larger
numbers is:
@Wait 0.75
@At ,+4
   *   #TFirst, #K187,find the prime factors of each#
#T#K187, number#
@Wait 0.75
@At ,+4
   *   #TTo find the #Blowest common multiple#,
#Ttake the highest power of each prime
#Tfactor and #K188,*find the product#.
 highest power of each prime
#Tfactor and #K188,*find the product#.
he #Bhighest power#.    #B2ê#  ╫  #B3#   ╫   #B5#

@Wait 0.25
@At ,+1
The #Blowest common multiple# = #B60#

@prompt
@keyPoint 9999,summary (part 1)


#BSummary#
@Wait 0.75
@At ,+2

   *   #^#BLowest common multiples# are useful
#Tin mathematics when dealing with
#t#Bfractions#
@Wait 0.75
@At ,+2
   *   #TTo add or subtract #Bfractions#, you
#Tneed to find a #Bcommon denominator#.
#TBy finding the #Blowest common multiple#
#Tof the #Bdenominators# the amount of
#Tcalculation, simplification and the size of
#Tthe numbers are kept to a minimum.
@Wait 0.75
@At ,+2
   *   #TUsing the lowest common multiple
#Treduces the possibility of #Berrors#.
@Wait 0.75
@At 175,-2
(#Bcontinued#)



@prompt
@keyPoint 9999,summary (part 2)

#B(continued)#

@Wait 0.75
@At ,+5
To find the #Blowest common multiple# of a set
of numbers you need to draw up a list of the
multiples of each until you find one common
to all the lists.
@Wait 0.75
@At ,+5
   *   #TFirst, #K185,*multiply by 2# to get the list going
@Wait 0.75
@At ,+5
   *   #TThen #K186,multiply by one more than last#
#t#K186,time#
@Wait 0.75
@At ,+5
   *   #TRepeat until you find the #Blowest common#
#T#Bmultiple#.
@Wait 0.75
@At ,+5
@At 175,
(#Bcontinued#)



@prompt
@keyPoint 9999,summary (part 3)

#B(continued)#

@Wait 0.75
@At ,+4

The previous method involves a lot of
working out. For simple numbers you can
often use #Btrial and improvement# methods
more quickly and easily.
@Wait 0.75
@At ,+4
The method that works well for larger
numbers is:
@Wait 0.75
@At ,+4
   *   #TFirst, #K187,find the prime factors of each#
#T#K187, number#
@Wait 0.75
@At ,+4
   *   #TTo find the #Blowest common multiple#,
#Ttake the highest power of each prime
#Tfactor and #K188,*find the product#.