Download Unit 3.1 What is a Rational Number Handout

Mathematics Grade 9
File Name: Unit 3.1 Lesson
Unit: Rational Number
Lesson 3.1: What is a Rational Number?
Objectives:
Students will compare and order rational numbers. (9N3)
Procedure:
This unit will introduce the concept of rational numbers. This is not really a new thing, as it
is a defining of a number class so for future learning. Lets review number classes quickly:
Natural Numbers
_______________________________________
Whole Numbers
_______________________________________
Integers
_______________________________________
Rational Numbers are numbers which
Fractions as Rational Numbers
Look at the following Fractions, which ones are equal?
1 −1 1
1
,
,
, −
4 4 −4
4
It may help to change each on into its decimal form.
1
= _______ = ______
4
−1
= _______ = _______
4
1
= __________ = ______
−4
−
1
= ________ = _______
4
Unit 3.1 What is a Rational Number Handout.doc
1
Mathematics Grade 9
File Name: Unit 3.1 Lesson
List the fractions which are equal:
______________________
How can they be the same?
If you think of multiplying
−1
−1
by 1, when 1 is in the form of
, it makes sense.
4
−1
−1 −1
× =
4 −1
=
You can use the same way to convert
How is
1
−1
to
.
−4
4
1
and the rest of them different?
4
1
1
and − are called
4
4
__________________.
In decimal form they are called _____________________. So 0.25 and –0.25 are called
_____________________
List 3 opposite pairs of fractions:
List 3 opposite pairs of decimals:
Unit 3.1 What is a Rational Number Handout.doc
2
Mathematics Grade 9
File Name: Unit 3.1 Lesson
Mixed numbers as Rational Numbers.
Are mixed numbers Rational numbers? What was the definition of a rational number that
related to fractions?
Rational Numbers are ________________________________________________
So any number that is a mixed number can be written as a _____________, for example:
2
3
=
4
=
Are all mixed fractions rational numbers?
Why?
Lets look at mixed decimals
What is 1.2 in fraction form?
1.2 = 1
=1
=
=
Is this a rational number?
Do you think all mixed decimals can be written as fractions?
Unit 3.1 What is a Rational Number Handout.doc
3
Mathematics Grade 9
File Name: Unit 3.1 Lesson
Which of the following are rational numbers?
4
5
− , 1.333..., 4 , − 4, 7, − 5.6
5
7
Number Lines:
Number lines are an excellent way to show rational numbers, on both sides of the zero.
On the number line below place the following numbers.
−1.1, 1.1, 1.3, 0.4, − 0.5, 0.45
-1
0
1
Why is –1.1 less than –0.5?
A classmate tells you that –1.1 is greater than 0.4 because 1.1 is larger than 0.4, how
would you correct your classmate’s thinking?
Unit 3.1 What is a Rational Number Handout.doc
4
Mathematics Grade 9
File Name: Unit 3.1 Lesson
Name three rational numbers between:
a)
0 and 1
_______________________________________
b)
0 and –0.5
_______________________________________
c)
1.1 and 1.3
_______________________________________
d)
-1 and –1.1
_______________________________________
Lets try the same exercise with fractions.
Place the following fractions on the number line below:
1
1
3
2 , −1 , − ,
4
2
4
-3
-2
-1
Unit 3.1 What is a Rational Number Handout.doc
0
−5
1
, 2
8
3
3
3
, −1 ,
4
4
1
2
3
5
Mathematics Grade 9
File Name: Unit 3.1 Lesson
Name three rational numbers in fraction form between:
a)
−3
3
and −1
4
4
_______________________________________
b)
3
and 2
4
_______________________________________
c)
2 and 2
d)
−3
1
and −1
4
2
1
4
_______________________________________
_______________________________________
Ordering Rational Numbers in Decimal or Fraction Form
Decimals:
Place the following in order:
0.25,
− 0.2,
0.25, 1.7,
− 1.6
It may be easier to use equivalent decimals to write them all in thousandths.
Now place them in order.
Unit 3.1 What is a Rational Number Handout.doc
6
Mathematics Grade 9
File Name: Unit 3.1 Lesson
Try these.
0.69,
− 2.3,
2.2, 2.27,
− 2.33
Again make them all have the same amount of decimals.
Now order them:
Now lets try some fractions:
In grade 7 we did this by converting all the fractions to decimals and then ordering the
decimals, then using the decimals to rewrite the original fractions down.
For example:
Order the following fractions in order from least to greatest.
4
− ,
5
5
,
7
−12
,
3
1
−4 ,
5
3
,
4
7
3
First change the fractions into decimal form:
Now place these in order:
You may need to rewrite with same number of decimals places.
Now rewrite them in their fraction forms:
Unit 3.1 What is a Rational Number Handout.doc
7
Mathematics Grade 9
File Name: Unit 3.1 Lesson
Example:
Order the following fractions from least to greatest.
Another way of doing this is to convert all the fractions to having the same denominator;
this is a lot of work.
−2
,
3
1
,
4
3
,
8
5
,
6
1
− ,
2
−
5
12
The lowest common denominator is 24, so convert each fraction to having a denominator
of 24:
Now they can be ordered using their equivalent fractions.
Now change them back into their original fractions.
Unit 3.1 What is a Rational Number Handout.doc
8
Mathematics Grade 9
File Name: Unit 3.1 Lesson
The last part is to order fractions and decimals when they are together.
Here is an example from the textbook.
Order the following and place them on a number line.
1.13,
−10
, − 3.4, 2.7,
3
3
2
, −2
7
5
First convert the fractions to decimal form.
Now place them in order.
Since it is easier to find locations of decimals on a number line, find the locations first, then
place the original number down.
-6
-5
-4
-3
-2
Unit 3.1 What is a Rational Number Handout.doc
-1
0
1
2
3
4
5
6
9
Mathematics Grade 9
File Name: Unit 3.1 Lesson
Example:
What rational number does the letter on the number line below represent?
B
A
C
-2
-3
A-
_______________
B
_______________
C-
_______________
How did you decide what the decimal portion of the number was going to be?
Example:
What rational number does the letter on the number line below represent?
C
B
A
-3
-4
A-
_______________
B-
_______________
C-
_______________
-2
How did you decide what the decimal portion of the number was going to be?
Unit 3.1 What is a Rational Number Handout.doc
10
Mathematics Grade 9
File Name: Unit 3.1 Lesson
Example:
What rational number does the letter on the number line below represent?
B
C
-2
-1
A-
_______________
B-
_______________
C-
_______________
A
0
1
How did you decide what the fractions portion of the number was going to be?
Complete the following
Page 100-103#1-13,
#14 without number line,
#15-21,
#23,24,25 order them showing how you did it; do not draw the number line.
Unit 3.1 What is a Rational Number Handout.doc
11