Chapters
- Problem 1
- Problem 2
- Problem 3
- Problem 4
- Problem 5
- Problem 6
- Problem 7
- Problem 8
- Problem 9
- Problem 10
- Problem 11
- Problem 12
- Problem 13
- Problem 14
- Problem 15
- Problem 16
- Problem 17
- Problem 1 Solution
- Problem 2 Solution
- Problem 3 Solution
- Problem 4 Solution
- Problem 5 Solution
- Problem 6 Solution
- Problem 7 Solution
- Problem 8 Solution
- Problem 9 Solution
- Problem 10 Solution
- Problem 11 Solution
- Problem 12 Solution
- Problem 13 Solution
- Problem 14 Solution
- Problem 15 Solution
- Problem 16 Solution
- Problem 17 Solution
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
b. is greater than 
but less than and it is approaching (approaching from the negative side)
c. is less than and approaches 
and 
Problem 1 Solution
Write 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 
This is just one of infinitely many fractions between and .
b. and
and 
and 
There is a fraction between 
and 
,
namely 
.
c. and
and 
Problem 7 Solution
Divide 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
Name at least 4 Rational numbers that are between
a. and
Here are quite a few Rational numbers between and
b. and
c. and
Problem 12 Solution
Solve:
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
with 
or 
The Rational number gets bigger and bigger as .
and 
gives 
and 
gives 
and 
gives 
and 
gives 
b. is greater than but less than and is approaching (approaches from the negative side)
with or 
The Rational number gets bigger and bigger negatively as .
and 
gives 
and 
gives 
and 
gives 
and 
gives 
c. is less than and approaches
and 
The Rational number gets smaller and smaller negatively as 
.
and 
gives 
and 
gives 
and 
gives 
and 
gives 
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