Problem 1
Write
as an addition of a series of fractional powers of
and then as a series of simplified fractions.
Problem 2
Find the sum of
Problem 3
Try to find the product of
without performing the actual multiplication.
Problem 4
Solve the equation
Problem 5
Solve the equation
Problem 6
Find a Rational number in between a.
and
b.
and
c.
and
Problem 7
Divide
into
's and give each fractional value in both improper and mixed fractional form.
Problem 8
Divide
into
's and give each fractional value in both improper and mixed fractional form.
Problem 9
Divide the number line interval of
to
into 4 equal spaces and give the values of the endpoints of each space.
Problem 10
Divide the number line interval of
to
into 10 equal spaces and give the values of the endpoints of each space.
Problem 11
Name at least 4 Rational numbers that are between a.
and
b.
and
c.
and
Problem 12
Solve:
Problem 13
How many
's are in a.
b.
c.
d.
Problem 14
What is the fractional distance between these sets of points
on the number line? Interval 1:
and
Interval 2:
and
Interval 3:
and
Interval 4:
and
Problem 15
What is the midpoint of each of these intervals on the number line? a.
and
b.
and
c.
and
Problem 16
How many Rational numbers are there between
?
Problem 17
What happens to the denominator and overall value of the Rational number
when a.
is less than
but greater than
and
is approaching
is greater than
but less than
and it is approaching
(approaching
from the negative side)
is less than
and approaches
as an addition of a series of fractional powers of
and then again as a series of simplified fractions.
Powers of : 
Simplified Fractions: 
Problem 2 Solution
Find the sum of
Problem 3 Solution
Try to find the product of
without performing the actual multiplication.
The denominator of each fraction cancels with the numerator of the fraction following it.
The denominator in cancels the numerator in etc.
The only 2 numbers that don't cancel are the numerator
in
and the denominator
in
leaving
We can also rearrange the numerators to make 4 of the fractions equivalent to
Problem 4 Solution
Solve the equation
Problem 5 Solution
Solve the equation
Problem 6 Solution
Find a Rational number in between a.
and
and 
There is no fraction with a denominator of 
between 
and 
.
Converting denominators gives 
and 
There is a fraction in between 
and 
,
namely 
and .
b.
and
and 
and 
There is a fraction between 
and 
,
namely 
.
c.
and
and 
into
's and give each fractional value in improper and mixed fraction form.
Interval 
into 
1. 
 2. 
 3. 
 4. 
                                                  5. 
Problem 8 Solution
Divide
into
and give each fractional value in both improper and mixed form.
Interval 
into
1. 
 2. 
3. 
 4. 
                                            5. 
   6. 
   7. 
  8. 
   9. 
                                          10. 
Problem 9 Solution
Divide the number line interval of
to
into
and give each value.
Number Line Distance: 
Spaces: 
Interval 1: 
Interval 2: 
Interval 3: 
                               Interval 4: 
Problem 10 Solution
Divide the number line interval of
to
into
and give each value.
Number Line Distance: 
Spaces: 
Number Line Start and Finish: 
and 
Interval 1: 
                            Interval 2: 
                            Interval 3: 
                            Interval 4: 
 Interval 5: 
                            Interval 6:
Interval 7:
Interval 8:
Interval 9:
Interval 10:
Problem 11 Solution
and
Here are quite a few Rational numbers between and
b.
and
and
Problem 13 Solution
How many
's are in a.
b.
c.
d.
Problem 14 Solution
What is the fractional distance
between these sets of points
on the number line? Interval 1:
and
Interval 2:
and
and 
Interval 3:
and
Interval 4:
and
and 
Problem 15 Solution
What is the midpoint
of each of these intervals on the number line? a.
b.
and 
c.
and 
Problem 16 Solution
How many Rational numbers
are there between
?
There are an infinite amount of Rational numbers in between any 2 other Rational numbers.
Problem 17 Solution
What happens to the denominator and overall value of the Rational number
when a.
is less than
but greater than
and
is approaching
gets bigger and bigger as 
.
and 
and and and
is greater than
but less than
and
is approaching
(approaches
from the negative side)
gets bigger and bigger negatively as .
and 
and and and
is less than
and approaches
gets smaller and smaller negatively as 
.
and 
and 
and 
and 
(-100<-1)[/latex] gives [latex]\dfrac{1}{x}=\frac{1}{-100}=-\frac{1}{100}[/latex]
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