Lesson 3
Negative Numbers
Real values of less than nothing
Page 95
We have seen that we would arrive at the result
b − 1 by applying our division rule o the problem
( b 2 )/( b 3 ) , so we can write
b − 1 = ( b 2 )/( b 3 )
and then we can write out
b 2 and
b 3 fully to see what
b − 1 should mean:
b − 1 = ( b 2 )/( b 3 ) ( b × b )/( b × b × b ) ( b b )/( b b b )
Now, when we cancel factors in the last step shown at the right, we don’t leave zeros. Remember your basic arithmetic:
( 2 )/( 2 ) (
1
2
)/(
2
1
) ( 1 )/( 1 ) and ( 3 )/( 3 ) (
1
3
)/(
3
1
) ( 1 )/( 1 )
Or, in algebraic form:
( a × b )/( a × b × c ) (
1
1
a
×
b
)/(
a
×
b
×
c
1
1
) ( 1 )/( c )
Well, similarly,
b − 1 = (
1
1
b
×
b
)/(
b
×
b
×
b
1
1
) ( 1 )/( b )
Now return to Page 101 and try again.
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