38 ­ Comparing Rational Numbers.notebook
11/1
10/31
Monday
Tuesday
November 02, 2016
11/2
11/3
11/4
Wednesday
Thursday
Friday
No School
Comparing Test Spooktacular Rational Revisions
WS
Numbers
You need your INB
and Table of Contents
Page
4­5
6­7
Focus
3
Classifying Rational/Irrational
Comparing Rational Numbers
1
38 ­ Comparing Rational Numbers.notebook
Warm UP
November 02, 2016
Page 6
Copy and complete the statement.
Warm Up
6
I know I have a Rational
Number when...
... it is a decimal that stops or repeats
... it's a fraction
... it's a whole number
... it can be negative
... 0
... it is a perfect square root
Today's target:
• I can compare rational numbers.
Today's EQ:
• What could I convert the numbers
to when comparing them?
(Identify)
2
38 ­ Comparing Rational Numbers.notebook
November 02, 2016
There are many ways to compare rational and irrational numbers.
Today we are going to focus on changing them to decimals first, then comparing the decimals.
Let's start with changing fractions and mixed numbers to a decimal.
http://www.youtube.com/watch?v=keB7r3rLRGs&feature=channel&list=UL
(watch start of video to 5:07)
Practice
What will you do first?
Compare each of the following numbers using >, <, or =.
2) 1) 3) 16
25
6
­5
27
5) 5
4) ­4
5.3
­3
­2
­1
6) 27
9
4
0
20
1
2
3
4
5
4 3
10
3
38 ­ Comparing Rational Numbers.notebook
November 02, 2016
Sometimes we will have to compare more than 2 numbers.
What will you do first?
7) Put the numbers below in order from least to greatest.
7
2
3.1, , , , 3 10 10
10
3
8) Put the numbers below in order from least to greatest.
­12
2
­5.5, , 25 ,
­10
4
1
­5
, 5
You're not always going to have a calculator...
Our second strategy is to compare numbers using estimation.
Example:
Start by separating the numbers into 2 groups (positive & negative)
Next compare. Consider using some benchmarks like 1/2, 1 or even 1/4.
4
38 ­ Comparing Rational Numbers.notebook
November 02, 2016
9) Place the following rational numbers in order from least to greatest.
7
3
­1.5, , 4 ,
­12
6
4
2
, 8
Irratio
9) Place the following rational numbers in order from least to greatest.
7
­3.4, 24
9
6 , 9 , 0 ,
What if I am comparing two decimals that are very close?
11
3.3166247...
14
6
3.3
5
38 ­ Comparing Rational Numbers.notebook
November 02, 2016
page 7
Target: • I can compare rational numbers.
EQ: • What could I convert the numbers to when
comparing them? (Identify)
Examples
Compare using >, <, or =.
1) ­3.4 ___ ­7
2
3
2) 36 ___ 6 12
3) 2.4 ___ 2.333...
How do I change
a mixed number
into a fraction?
Summary:
6
38 ­ Comparing Rational Numbers.notebook
November 02, 2016
7
38 ­ Comparing Rational Numbers.notebook
November 02, 2016
Table of Contents
2
4 Rational/Irrational &
Decimals Fractions
6 Comparing Rational #s
8
10
12
14
16
3
1 Cover
T.o.C.
3 Rational/Irrational &
5 Decimals Fractions
7 Comparing Rational #s
9
11
13
15
17
8
38 ­ Comparing Rational Numbers.notebook
Homework Check
7) rational 1/3
11) rational & terminating
16) d
17)c
22) <
28
25
November 02, 2016
4
9) rational 3 or 34/10
10
13) rational & terminating 15) irrational & neither 18) c
20) ­8/3
23) >
27
26
Warm Up
Classify each of the numbers as either rational or irrational.
1) ­13
3) 12
2)
4) 0.121212...
Compare using >, <, or =.
5) 4 ___ 16
6) ­3 ___ ­5
6) |­7| ___ 5
6
9
38 ­ Comparing Rational Numbers.notebook
November 02, 2016
Warm Up
Convert the mixed numbers into improper fractions.
1) 3
2
5
2) 4
2
3
3) 5
1
2
Convert the decimals to fractions in lowest terms.
(Hint: write it like you say it!)
4) 0.25
5) 0.22
6) 0.6
4
page 5
Target:
• I can classify a number as rational or irrational.
• I know that every rational number can be written as a fraction.
Def. Rational A rational number is any number that can be
Number written as a fraction.
Rational Numbers include:
integers
fractions & mixed numbers
repeating decimals
terminating decimals
square roots of perfect squares
Def. Irrational An irrational number is any number that
Number
cannot be written as a fraction.
Irrational Numbers include:
non­terminating decimals
non­repeating decimals
any square root that is not a perfect root
How do I prove that
a number is a
rational number? We can prove a number is rational by changing it into a fraction.
Examples
How do I change
an integer into a
fraction?
Classify each number as either rational or irrational.
­4
3
4
How do I change
a decimal into a
fraction?
20
How do I change
a mixed number
into a fraction?
35
2
0.7777777...
36
0
0.24562571...
0.25
Summary:
10