Chapters

## Problem 1

Write as an addition of a series of fractional powers of and then as a series of simplified fractions.

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Matthew
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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

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:

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

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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